Package 'statpsych'

Description

Computes adjusted standard errors in a general linear model after one or more predictor variables with nonsignificant slopes have been dropped from the model. The adjusted standard errors are then used to compute adjusted t-values, p-values, and confidence intervals. The mean square error and error degrees of freedom from the full model are used to compute the adjusted standard errors. These adjusted results are less susceptible to the negative effects of an exploratory model selection.

For more details, see Section 2.25 of Bonett (2021, Volume 2)

Usage

adj.se(alpha, mse1, mse2, dfe1, se, b)

Arguments

Value

Returns adjusted standard error, t-statistic, p-value, and confidence interval for each slope coefficient

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

se <- c(1.57, 3.15, 0.982)
b <- c(3.78, 8.21, 2.99)
adj.se(.05, 10.26, 8.37, 114, se, b)

# Should return:
#      Estimate   adj SE        t  df       p        LL        UL
# [1,]     3.78 1.738243 2.174609 114 0.03173 0.3365531  7.223447
# [2,]     8.21 3.487559 2.354082 114 0.02028 1.3011734 15.118827
# [3,]     2.99 1.087233 2.750102 114 0.00693 0.8362007  5.143799

Description

Computes confidence intervals and tests for the AB interaction effect, main effect of A, main effect of B, simple main effects of A, and simple main effects of B in a 2x2 between-subjects factorial design with a quantitative response variable. A Satterthwaite adjustment to the degrees of freedom is used and equality of population variances is not assumed.

For more details, see Sections 3.8 and 3.9 of Bonett (2021, Volume 1)

Usage

ci.2x2.mean.bs(alpha, y11, y12, y21, y22)

Arguments

Value

Returns a 7-row matrix (one row per effect). The columns are:

• Estimate - estimate of effect

• SE - standard error

• t - t test statistic

• df - degrees of freedom

• p - two-sided p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

y11 <- c(14, 15, 11, 7, 16, 12, 15, 16, 10, 9)
y12 <- c(18, 24, 14, 18, 22, 21, 16, 17, 14, 13)
y21 <- c(16, 11, 10, 17, 13, 18, 12, 16, 6, 15)
y22 <- c(18, 17, 11, 9, 9, 13, 18, 15, 14, 11)
ci.2x2.mean.bs(.05, y11, y12, y21, y22)

# Should return:
#          Estimate       SE       t    df       p         LL         UL
# AB:         -5.10 2.224860 -2.2923 35.48 0.02793 -9.6145264 -0.5854736
# A:           1.65 1.112430  1.4832 35.48 0.14684 -0.6072632  3.9072632
# B:          -2.65 1.112430 -2.3822 35.48 0.02270 -4.9072632 -0.3927368
# A at b1:    -0.90 1.545244 -0.5824 17.56 0.56768 -4.1522367  2.3522367
# A at b2:     4.20 1.600694  2.6239 17.94 0.01725  0.8362274  7.5637726
# B at a1:    -5.20 1.536952 -3.3833 17.61 0.00339 -8.4341379 -1.9658621
# B at a2:    -0.10 1.608657 -0.0622 17.92 0.95112 -3.4807927  3.2807927

Description

Computes confidence intervals and tests for the AB interaction effect, main effect of A, main effect of B, simple main effects of A, and simple main effects of B in a 2x2 mixed factorial design with a quantitative response variable where Factor A is a within-subjects factor and Factor B is a between-subjects factor. A Satterthwaite adjustment to the degrees of freedom is used and equality of population variances is not assumed.

For more details, see Section 4.16 of Bonett (2021, Volume 1)

Usage

ci.2x2.mean.mixed(alpha, y11, y12, y21, y22)

Arguments

Value

Returns a 7-row matrix (one row per effect). The columns are:

• Estimate - estimate of effect

• SE - standard error

• t - t test statistic

• df - degrees of freedom

• p - two-sided p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

y11 <- c(18, 19, 20, 17, 20, 16)
y12 <- c(19, 16, 16, 14, 16, 18)
y21 <- c(19, 18, 19, 20, 17, 16)
y22 <- c(16, 10, 12,  9, 13, 15)
ci.2x2.mean.mixed(.05, y11, y12, y21, y22)

# Should return:
#            Estimate        SE       t   df       p         LL        UL
# AB:      -3.8333333 0.9803627 -3.9101 8.35 0.00412 -6.0778198 -1.588847
# A:        2.0833333 0.4901814  4.2501 8.35 0.00254  0.9610901  3.205577
# B:        3.7500000 1.0226599  3.6669 7.60 0.00693  1.3700362  6.129964
# A at b1:  0.1666667 0.8333333  0.2000 5.00 0.84936 -1.9754849  2.308818
# A at b2:  4.0000000 0.5163978  7.7460 5.00 0.00057  2.6725572  5.327443
# B at a1:  1.8333333 0.9803627  1.8701 9.94 0.09117 -0.3527241  4.019391
# B at a2:  5.6666667 1.2692955  4.4644 7.67 0.00233  2.7173445  8.615989

Description

Computes confidence intervals and tests for the AB interaction effect, main effect of A, main effect of B, simple main effects of A, and simple main effects of B in a 2x2 within-subjects factorial design with a quantitative response variable.

For more details, see Section 4.14 of Bonett (2021, Volume 1)

Usage

ci.2x2.mean.ws(alpha, y11, y12, y21, y22)

Arguments

Value

Returns a 7-row matrix (one row per effect). The columns are:

• Estimate - estimate of effect

• SE - standard error

• t - t test statistic

• df - degrees of freedom

• p - two-sided p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

y11 <- c(1,2,3,4,5,7,7)
y12 <- c(1,0,2,4,3,8,7)
y21 <- c(4,5,6,7,8,9,8)
y22 <- c(5,6,8,7,8,9,9)
ci.2x2.mean.ws(.05, y11, y12, y21, y22)

# Should return:
#             Estimate        SE       t df       p          LL          UL
# AB:       1.28571429 0.5654449  2.2738  6 0.06334 -0.09787945  2.66930802
# A:       -3.21428571 0.4862042 -6.6110  6 0.00058 -4.40398462 -2.02458681
# B:       -0.07142857 0.2296107 -0.3111  6 0.76626 -0.63326579  0.49040865
# A at b1: -2.57142857 0.2973809 -8.6469  6 0.00013 -3.29909331 -1.84376383
# A at b2: -3.85714286 0.7377111 -5.2285  6 0.00196 -5.66225692 -2.05202879
# B at a1:  0.57142857 0.4285714  1.3333  6 0.23081 -0.47724794  1.62010508
# B at a2: -0.71428571 0.2857143 -2.5000  6 0.04653 -1.41340339 -0.01516804

Description

Computes distribution-free confidence intervals for the AB interaction effect, main effect of A, main effect of B, simple main effects of A, and simple main effects of B in a 2x2 between-subjects factorial design with a quantitative response variable. The effects are defined in terms of medians rather than means. Tied scores within each group are assumed to be rare.

For more details, see Section 3.21 of Bonett (2021, Volume 1)

Usage

ci.2x2.median.bs(alpha, y11, y12, y21, y22)

Arguments

Value

Returns a 7-row matrix (one row per effect). The columns are:

• Estimate - estimate of effect

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG, Price RM (2002). “Statistical inference for a linear function of medians: Confidence intervals, hypothesis testing, and sample size requirements.” Psychological Methods, 7(3), 370–383. ISSN 1939-1463. doi:10.1037/1082-989X.7.3.370.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

y11 <- c(19.2, 21.1, 14.4, 13.3, 19.8, 15.9, 18.0, 19.1, 16.2, 14.6)
y12 <- c(21.3, 27.0, 19.1, 21.5, 25.2, 24.1, 19.8, 19.7, 17.5, 16.0)
y21 <- c(16.5, 11.3, 10.3, 17.7, 13.8, 18.2, 12.8, 16.2, 6.1, 15.2)
y22 <- c(18.7, 17.3, 11.4, 12.4, 13.6, 13.8, 18.3, 15.0, 14.4, 11.9)
ci.2x2.median.bs(.05, y11, y12, y21, y22)

# Should return:
#          Estimate       SE        LL         UL
# AB:        -3.850 2.951019 -9.633891  1.9338914
# A:          4.525 1.475510  1.633054  7.4169457
# B:         -1.525 1.475510 -4.416946  1.3669457
# A at b1:    2.600 1.992028 -1.304302  6.5043022
# A at b2:    6.450 2.177232  2.182703 10.7172971
# B at a1:   -3.450 2.045086 -7.458294  0.5582944
# B at a2:    0.400 2.127472 -3.769769  4.5697694

Description

Computes distribution-free confidence intervals for the AB interaction effect, main effect of A, main effect of B, simple main effects of A, and simple main effects of B in a 2x2 mixed factorial design where Factor A is the within-subjects factor and Factor B is the between subjects factor. Tied scores within each group and within each within-subjects level are assumed to be rare.

Usage

ci.2x2.median.mixed(alpha, y11, y12, y21, y22)

Arguments

Value

Returns a 7-row matrix (one row per effect). The columns are:

• Estimate - estimate of effect

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG, Price RM (2020). “Interval estimation for linear functions of medians in within-subjects and mixed designs.” British Journal of Mathematical and Statistical Psychology, 73(2), 333–346. ISSN 0007-1102. doi:10.1111/bmsp.12171.

Examples

y11 <- c(18.3, 19.5, 20.1, 17.4, 20.5, 16.1)
y12 <- c(19.2, 16.4, 16.5, 14.0, 16.9, 18.3)
y21 <- c(19.1, 18.4, 19.8, 20.0, 17.2, 16.8)
y22 <- c(16.5, 10.2, 12.7,  9.9, 13.5, 15.0)
ci.2x2.median.mixed(.05, y11, y12, y21, y22)

# Should return:
#          Estimate        SE         LL         UL
# AB:        -3.450 1.6317863 -6.6482423 -0.2517577
# A:          1.875 0.8158931  0.2758788  3.4741212
# B:          3.925 1.4262367  1.1296274  6.7203726
# A at b1:    0.150 1.4243192 -2.6416144  2.9416144
# A at b2:    3.600 0.7962670  2.0393454  5.1606546
# B at a1:    2.200 1.5812792 -0.8992503  5.2992503
# B at a2:    5.650 1.7027101  2.3127496  8.9872504

Description

Computes distribution-free confidence intervals for the AB interaction effect, main effect of A, main effect of B, simple main effects of A, and simple main effects of B in a 2x2 within-subjects factorial design. The effects are defined in terms of medians rather than means. Tied scores within each level combination are assumed to be rare.

Usage

ci.2x2.median.ws(alpha, y11, y12, y21, y22)

Arguments

Value

Returns a 7-row matrix (one row per effect). The columns are:

• Estimate - estimate of effect

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG, Price RM (2020). “Interval estimation for linear functions of medians in within-subjects and mixed designs.” British Journal of Mathematical and Statistical Psychology, 73(2), 333–346. ISSN 0007-1102. doi:10.1111/bmsp.12171.

Examples

y11 <- c(222, 402, 333, 301, 284, 182, 281, 230, 290, 182, 133, 278)
y12 <- c(221, 371, 340, 288, 293, 150, 317, 211, 286, 161, 126, 234)
y21 <- c(219, 371, 314, 279, 284, 155, 278, 185, 296, 169, 118, 229)
y22 <- c(170, 332, 280, 273, 272, 160, 260, 204, 252, 153, 137, 223)
ci.2x2.median.ws(.05, y11, y12, y21, y22)

# Should return:
#          Estimate        SE           LL       UL
# AB:          3.50 21.050122 -37.75748155 44.75748
# A:          24.25  9.603490   5.42750463 43.07250
# B:          17.75  9.101881  -0.08935904 35.58936
# A at b1:    26.00 11.813742   2.84549058 49.15451
# A at b2:    22.50 16.323093  -9.49267494 54.49267
# B at a1:    19.50 15.710347 -11.29171468 50.29171
# B at a2:    16.00 11.850202  -7.22596953 39.22597

Description

Computes adjusted Wald confidence intervals and tests for the AB interaction effect, main effect of A, main effect of B, simple main effects of A, and simple main effects of B in a 2x2 between-subjects factorial design with a dichotomous response variable. The input vector of frequency counts is f = [ f11, f12, f21, f22 ], and the input vector of sample sizes is n = [ n11, n12, n21, n22 ] where the first subscript represents the levels of Factor A and the second subscript represents the levels of Factor B.

For more details, see Section 2.14 of Bonett (2021, Volume 3)

Usage

ci.2x2.prop.bs(alpha, f, n)

Arguments

Value

Returns a 7-row matrix (one row per effect). The columns are:

• Estimate - adjusted estimate of effect

• SE - standard error

• z - z test statistic

• p - two-sided p-value

• LL - lower limit of the adjusted Wald confidence interval

• UL - upper limit of the adjusted Wald confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Price RM, Bonett DG (2004). “An improved confidence interval for a linear function of binomial proportions.” Computational Statistics & Data Analysis, 45(3), 449–456. ISSN 01679473. doi:10.1016/S0167-9473(03)00007-0.

Examples

f <- c(15, 24, 28, 23)
n <- c(50, 50, 50, 50)
ci.2x2.prop.bs(.05, f, n)

# Should return:
#             Estimate         SE       z       p          LL          UL
# AB:      -0.27450980 0.13692496 -2.0048 0.04498 -0.54287780 -0.00614181
# A:       -0.11764706 0.06846248 -1.7184 0.08572 -0.25183106  0.01653694
# B:       -0.03921569 0.06846248 -0.5728 0.56678 -0.17339968  0.09496831
# A at b1: -0.25000000 0.09402223 -2.6589 0.00784 -0.43428019 -0.06571981
# A at b2:  0.01923077 0.09787658  0.1965 0.84423 -0.17260380  0.21106534
# B at a1: -0.17307692 0.09432431 -1.8349 0.06652 -0.35794917  0.01179533
# B at a2:  0.09615385 0.09758550  0.9853 0.32446 -0.09511021  0.28741790

Description

Computes adjusted Wald confidence intervals and tests for the AB interaction effect, main effect of A, main effect of B, simple main effects of A, and simple main effects of B in a 2x2 mixed factorial design with a dichotomous response variable where Factor A is a within-subjects factor and Factor B is a between-subjects factor. The 4x1 vector of frequency counts for Factor A within each group is f00, f01, f10, f11 where fij is the number of participants with a response of i = 0 or 1 at level 1 of Factor A and a response of j = 0 or 1 at level 2 of Factor A.

For more details, see Section 2.2 of Bonett (2021, Volume 3)

Usage

ci.2x2.prop.mixed(alpha, group1, group2)

Arguments

Value

Returns a 7-row matrix (one row per effect). The columns are:

• Estimate - adjusted estimate of effect

• SE - standard error of estimate

• z - z test statistic

• p - two-sided p-value

• LL - lower limit of the adjusted Wald confidence interval

• UL - upper limit of the adjusted Wald confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

group1 <- c(125, 14, 10, 254)
group2 <- c(100, 16, 9, 275)
ci.2x2.prop.mixed (.05, group1, group2)

# Should return:
#              Estimate          SE       z       p          LL           UL
# AB:       0.007555369 0.017716073  0.4265 0.66976 -0.02716750  0.042278234
# A:       -0.013678675 0.008858036 -1.5442 0.12254 -0.03104011  0.003682758
# B:       -0.058393219 0.023032656 -2.5352 0.01124 -0.10353640 -0.013250043
# A at b1: -0.009876543 0.012580603 -0.7851 0.43242 -0.03453407  0.014780985
# A at b2: -0.017412935 0.012896543 -1.3502 0.17695 -0.04268969  0.007863824
# B at a1: -0.054634236 0.032737738 -1.6688 0.09515 -0.11879902  0.009530550
# B at a2: -0.062170628 0.032328556 -1.9231 0.05447 -0.12553343  0.001192177

Description

Computes confidence intervals for standardized AB interaction effect, main effect of A, main effect of B, simple main effects of A, and simple main effects of B in a 2x2 between-subjects factorial design with a quantitative response variable. Equality of population variances is not assumed. A square root unweighted average variance standardizer is used, which is the recommended standardizer when both factors are treatment factors.

Usage

ci.2x2.stdmean.bs(alpha, y11, y12, y21, y22)

Arguments

Value

Returns a 7-row matrix (one row per effect). The columns are:

• Estimate - estimate of standardized effect

• adj Estimate - bias adjusted estimate of standardized effect

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2008). “Confidence intervals for standardized linear contrasts of means.” Psychological Methods, 13(2), 99–109. ISSN 1939-1463. doi:10.1037/1082-989X.13.2.99.

Examples

y11 <- c(14, 15, 11, 7, 16, 12, 15, 16, 10, 9)
y12 <- c(18, 24, 14, 18, 22, 21, 16, 17, 14, 13)
y21 <- c(16, 11, 10, 17, 13, 18, 12, 16, 6, 15)
y22 <- c(18, 17, 11, 9, 9, 13, 18, 15, 14, 11)
ci.2x2.stdmean.bs(.05, y11, y12, y21, y22)

# Should return:
#          Estimate adj Estimate      SE      LL      UL
# AB:       -1.4498      -1.4194 0.68852 -2.7992 -0.1003
# A:         0.4690       0.4592 0.33795 -0.1933  1.1314
# B:        -0.7533      -0.7375 0.34512 -1.4297 -0.0769
# A at b1:  -0.2558      -0.2505 0.46402 -1.1653  0.6536
# A at b2:   1.1939       1.1689 0.50014  0.2137  2.1742
# B at a1:  -1.4782      -1.4472 0.49284 -2.4441 -0.5122
# B at a2:  -0.0284      -0.0278 0.48204 -0.9732  0.9163

Description

Computes confidence intervals for the standardized AB interaction effect, main effect of A, main effect of B, simple main effects of A, and simple main effects of B in a 2x2 mixed factorial design where Factor A is a within-subjects factor, and Factor B is a between-subjects factor. Equality of population variances is not assumed. A square root unweighted average variance standardizer is used.

Usage

ci.2x2.stdmean.mixed(alpha, y11, y12, y21, y22)

Arguments

Value

Returns a 7-row matrix (one row per effect). The columns are:

• Estimate - estimated standardized effect

• adj Estimate - bias adjusted standardized effect estimate

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2008). “Confidence intervals for standardized linear contrasts of means.” Psychological Methods, 13(2), 99–109. ISSN 1939-1463. doi:10.1037/1082-989X.13.2.99.

Examples

y11 <- c(18, 19, 20, 17, 20, 16)
y12 <- c(19, 16, 16, 14, 16, 18)
y21 <- c(19, 18, 19, 20, 17, 16)
y22 <- c(16, 10, 12,  9, 13, 15)
ci.2x2.stdmean.mixed(.05, y11, y12, y21, y22)

# Should return:
#          Estimate adj Estimate      SE      LL      UL
# AB:       -1.9515      -1.8014 0.54074 -3.0114 -0.8917
# A:         1.0606       1.0113 0.27977  0.5123  1.6090
# B:         1.9091       1.7623 0.57589  0.7804  3.0378
# A at b1:   0.0848       0.0759 0.46504 -0.8266  0.9963
# A at b2:   2.0364       1.8214 0.29956  1.4493  2.6235
# B at a1:   0.9333       0.8615 0.50364 -0.0538  1.9205
# B at a2:   2.8849       2.6630 0.74772  1.4194  4.3504

Description

Computes confidence intervals for standardized AB interaction effect, main effect of A, main effect of B, simple main effects of A, and simple main effects of B in a 2x2 within-subjects factorial design. Equality of population variances is not assumed. A square root unweighted average variance standardizer is used.

Usage

ci.2x2.stdmean.ws(alpha, y11, y12, y21, y22)

Arguments

Value

Returns a 7-row matrix (one row per effect). The columns are:

• Estimate - estimated standardized effect

• adj Estimate - bias adjusted standardized effect estimate

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2008). “Confidence intervals for standardized linear contrasts of means.” Psychological Methods, 13(2), 99–109. ISSN 1939-1463. doi:10.1037/1082-989X.13.2.99.

Examples

y11 <- c(21, 39, 32, 29, 27, 17, 27, 21, 28, 17, 12, 27)
y12 <- c(20, 36, 33, 27, 28, 14, 30, 20, 27, 15, 11, 22)
y21 <- c(21, 36, 30, 27, 28, 15, 27, 18, 29, 16, 11, 22)
y22 <- c(18, 34, 29, 28, 28, 17, 27, 21, 26, 16, 14, 23)
ci.2x2.stdmean.ws(.05, y11, y12, y21, y22)

# Should return:
#          Estimate adj Estimate      SE      LL     UL
# AB:        0.1725       0.1645 0.13655 -0.0951 0.4401
# A:         0.1092       0.1042 0.05753 -0.0035 0.2220
# B:         0.0747       0.0713 0.05921 -0.0413 0.1908
# A at b1:   0.1955       0.1864 0.08461  0.0297 0.3613
# A at b2:   0.0230       0.0219 0.09372 -0.1607 0.2067
# B at a1:   0.1610       0.1535 0.09457 -0.0244 0.3463
# B at a2:  -0.0115      -0.0110 0.08596 -0.1800 0.1570

Description

Computes an adjusted Wald confidence interval for a G-index of agreement between two polychotomous ratings. This function requires the number of objects that were given the same rating by both raters. The G-index corrects for chance agreement. The G-index is a better measure of agreement than Cohen's kappa, and the confidence interval for the G-index used here has better small-sample properties than the confidence interval for Cohen's kappa.

For more details, see Section 3.5 of Bonett (2021, Volume 3)

Usage

ci.agree(alpha, n, f, k)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - maximum likelihood estimate of G-index

• SE - standard error

• LL - lower limit of the adjusted Wald confidence interval

• UL - upper limit of the adjusted Wald confidence interval

References

Bonett DG (2022). “Statistical inference for G-indices of agreement.” Journal of Educational and Behavioral Statistics, 47(4), 438–458. doi:10.3102/10769986221088561.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.agree(.05, 250, 214, 3)

# Should return:
#  Estimate      SE     LL     UL
#     0.784 0.03331 0.7098 0.8414

Description

Computes adjusted Wald confidence intervals for a G-index of agreement for all pairs of raters in a 3-rater design with a dichotomous rating, and computes adjusted Wald confidence intervals for differences of all pairs of G agreement. An adjusted Wald confidence interval for unanimous G agreement among the three raters is also computed. In the three-rater design, unanimous G agreement is equal to the average of all pairs of G agreement. The G-index corrects for chance agreement.

Usage

ci.agree.3rater(alpha, f)

Arguments

Value

Returns a 7-row matrix. The rows are:

• G(1,2): G-index for raters 1 and 2

• G(1,3): G-index for raters 1 and 3

• G(2,3): G-index for raters 2 and 3

• G(1,2)-G(1,3): difference in G(1,2) and G(1,3)

• G(1,2)-G(2,3): difference in G(1,2) and G(2,3)

• G(2,3)-G(1,3): difference in G(2,3) and G(1,3)

• G(3): G-index of unanimous agreement for all three raters

The columns are:

• Estimate - estimate of G-index (two-rater, difference, or unanimous)

• LL - lower limit of adjusted Wald confidence interval

• UL - upper limit of adjusted Wald confidence interval

References

Bonett DG (2022). “Statistical inference for G-indices of agreement.” Journal of Educational and Behavioral Statistics, 47(4), 438–458. doi:10.3102/10769986221088561.

Examples

f <- c(100, 6, 4, 40, 20, 1, 9, 120)
ci.agree.3rater(.05, f)

# Should return:
#               Estimate      LL      UL
# G(1,2)          0.5667  0.4660  0.6524 
# G(1,3)          0.5000  0.3956  0.5912
# G(2,3)          0.8667  0.7970  0.9135
# G(1,2)-G(1,3)   0.0667  0.0058  0.1266
# G(1,2)-G(2,3)  -0.3000 -0.4068 -0.1892
# G(2,3)-G(1,3)  -0.3667 -0.4622 -0.2663
# G(3)            0.6444  0.5738  0.7069

Description

Computes adjusted Wald confidence intervals for the G-index of agreement within each group and the difference of G-indices.

For more details, see Section 3.5 of Bonett (2021, Volume 3)

Usage

ci.agree2(alpha, n1, f1, n2, f2, k)

Arguments

Value

Returns a 3-row matrix. The rows are:

• Row 1: G-index for group 1

• Row 2: G-index for group 2

• Row 3: G-index difference

The columns are:

• Estimate - maximum likelihood estimate of G-index and difference

• SE - standard error

• LL - lower limit of adjusted Wald confidence interval

• UL - upper limit of adjusted Wald confidence interval

References

Bonett DG (2022). “Statistical inference for G-indices of agreement.” Journal of Educational and Behavioral Statistics, 47(4), 438–458. doi:10.3102/10769986221088561.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.agree2(.05, 75, 70, 60, 45, 2)

# Should return:
#         Estimate      SE     LL     UL
# G1        0.8667 0.02880 0.6975 0.9481
# G2        0.5000 0.05590 0.2523 0.6852
# G1 - G2   0.3667 0.06289 0.1117 0.6089

Description

Computes an approximate Bayesian credible interval for a Pearson or partial correlation with a skeptical prior. The skeptical prior distribution is Normal with a mean of 0 and a small standard deviation. A skeptical prior assumes that the population correlation is within a range of small values (-r to r). If the skeptic is 95% confident that the population correlation is between -r and r, then the prior standard deviation can be set to r/1.96. A correlation that is less than .2 in absolute value is typically considered to be "small", and the prior standard deviation could then be set to .2/1.96. A correlation value that is considered to be small will depend on the application. Set s = 0 for a Pearson correlation.

For more details, see Section 1.33 of Bonett (2021, Volume 2)

Usage

ci.bayes.cor(alpha, prior_sd, cor, s, n)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Posterior mean - posterior mean (Bayesian estimate of correlation)

• LL - lower limit of the credible interval

• UL - upper limit of the credible interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.bayes.cor(.05, .1, .536, 0, 50)

# Should return:
# Posterior mean     LL     UL
#         0.1874  0.028 0.3375

ci.bayes.cor(.05, .1, .536, 0, 300)

# Should return:
# Posterior mean     LL     UL
#         0.4195 0.3352 0.4971

Description

Computes an approximate Bayesian credible interval for a normal prior distribution. This function can be used with any parameter estimator (e.g., mean, mean difference, linear contrast of means, slope coefficient, standardized mean difference, standardized linear contrast of means, median, median difference, linear contrast of medians, etc.) that has an approximate normal sampling distribution. The mean and standard deviation of the posterior normal distribution are also reported.

For more details, see Section 1.32 of Bonett (2021, Volume 1)

Usage

ci.bayes.normal(alpha, prior_mean, prior_sd, est, se)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Posterior mean - posterior mean of Normal distribution

• Posterior SD - posterior standard deviation of Normal distribution

• LL - lower limit of the credible interval

• UL - upper limit of the credible interval

References

Gelman A, Carlin JB, Stern HS, Rubin DB (2004). Bayesian Data Analysis, 2nd edition. Chapman & Hall.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.bayes.normal(.05, 50, 5, 38.3, 2.57)

# Should return:
# Posterior mean Posterior SD       LL       UL
#       40.74511     2.285735 36.26515 45.22506

Description

Computes a Bayesian credible interval for a population proportion using the mean and standard deviation of a prior Beta distribution along with sample information. The mean and standard deviation of the posterior Beta distribution are also reported. For a noninformative prior, set the prior mean to .5 and the prior standard deviation to 1/sqrt(12) (which corresponds to a Beta(1,1) distribution). The prior variance must be less than m(1 - m) where m is the prior mean.

For more details, see Section 1.18 of Bonett (2021, Volume 3)

Usage

ci.bayes.prop(alpha, prior_mean, prior_sd, f, n)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Posterior mean - posterior mean of Beta distribution

• Posterior SD - posterior standard deviation of Beta distribution

• LL - lower limit of the credible interval

• UL - upper limit of the credible interval

References

Gelman A, Carlin JB, Stern HS, Rubin DB (2004). Bayesian Data Analysis, 2nd edition. Chapman & Hall.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.bayes.prop(.05, .25, .1, 120, 300)

# Should return:
# Posterior mean Posterior SD        LL        UL
#      0.3916208   0.02742595 0.3387206 0.4458133

Description

Computes an approximate Bayesian credible interval for a semipartial correlation with a skeptical prior. The skeptical prior distribution is Normal with a mean of 0 and a small standard deviation. A skeptical prior assumes that the population semipartial correlation is within a range of small values (-r to r). If the skeptic is 95% confident that the population correlation is between -r and r, then the prior standard deviation can be set to r/1.96. A semipartial correlation that is less than .2 in absolute value is typically considered to be "small", and the prior standard deviation could then be set to .2/1.96. A semipartial correlation value that is considered to be small will depend on the application. This function requires the standard error of the estimated semipartial correlation which can be obtained from the ci.spcor function.

For more details, see Section 2.36 of Bonett (2021, Volume 2)

Usage

ci.bayes.spcor(alpha, prior_sd, cor, se)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Posterior mean - posterior mean (Bayesian estimate of correlation)

• LL - lower limit of the credible interval

• UL - upper limit of the credible interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.bayes.spcor(.05, .1, .582, .137)

# Should return:
# Posterior mean     LL    UL
#         0.2273 0.0729 0.371

Description

Computes a confidence interval for a population biserial-phi correlation using a transformation of a confidence interval for an odds ratio with .5 added to each cell frequency. This measure of association assumes the group variable is naturally dichotomous and the response variable is artificially dichotomous.

For more details, see Section 3.4 of Bonett (2021, Volume 3)

Usage

ci.biphi(alpha, f1, f2, n1, n2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimate of biserial-phi correlation

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Ulrich R, Wirtz M (2004). “On the correlation of a naturally and an artificially dichotomized variable.” British Journal of Mathematical and Statistical Psychology, 57(2), 235–251. ISSN 00071102. doi:10.1348/0007110042307203.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.biphi(.05, 34, 22, 50, 50)

# Should return:
#  Estimate     SE    LL    UL
#     0.275 0.1075 0.049 0.464

Description

Computes a confidence interval for a population biserial correlation. A biserial correlation can be used when one variable is quantitative and the other variable has been artificially dichotomized to create two groups. The biserial correlation estimates the correlation between the observed quantitative variable and the unobserved quantitative variable that has been measured on a dichotomous scale.

Usage

ci.bscor(alpha, m1, m2, sd1, sd2, n1, n2)

Arguments

Details

This function computes a point-biserial correlation and its standard error as a function of a standardized mean difference with a weighted variance standardizer. Then the point-biserial estimate is transformed into a biserial correlation using the traditional adjustment. The adjustment is also applied to the point-biserial standard error to obtain the standard error for the biserial correlation.

The biserial correlation assumes that the observed quantitative variable and the unobserved quantitative variable have a bivariate normal distribution. Bivariate normality is a crucial assumption underlying the transformation of a point-biserial correlation to a biserial correlation. Bivariate normality also implies equal variances of the observed quantitative variable at each level of the dichotomized variable, and this assumption is made in the computation of the standard error.

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated biserial correlation

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2020). “Point-biserial correlation: Interval estimation, hypothesis testing, meta-analysis, and sample size determination.” British Journal of Mathematical and Statistical Psychology, 73(S1), 113–144. ISSN 0007-1102. doi:10.1111/bmsp.12189.

Examples

ci.bscor(.05, 28.32, 21.48, 3.81, 3.09, 40, 40)

# Should return:
# Estimate     SE      LL     UL
#   0.8856 0.0613  0.7376 0.9844

Description

Computes a confidence interval for a population coefficient of dispersion (COD). The COD is a mean absolute deviation from the median divided by the median. The coefficient of dispersion assumes ratio-scale scores and is a robust alternative to the coefficient of variation (see ci.cv). An approximate standard error is recovered from the confidence interval.

For more details, see Section 1.27 of Bonett (2021, Volume 1)

Usage

ci.cod(alpha, y)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated coefficient of dispersion

• SE - recovered standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG, Seier E (2006). “Confidence interval for a coefficient of dispersion in nonnormal distributions.” Biometrical Journal, 48(1), 144–148. ISSN 0323-3847. doi:10.1002/bimj.200410148.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

y <- c(30, 20, 15, 10, 10, 60, 20, 25, 20, 30, 10, 5, 50, 40,
       20, 10, 0, 20, 50)
ci.cod(.05, y)

# Should return:
#  Estimate        SE        LL       UL
# 0.5921053 0.1814708 0.3813259 1.092679

Description

Computes confidence intervals and test statistics for population conditional slopes (simple slopes) in a general linear model that includes a predictor variable (x1), a moderator variable (x2), and a product predictor variable (x1*x2). Conditional slopes are computed at specified low and high values of the moderator variable.

For more details, see Section 2.13 of Bonett (2021, Volume 2)

Usage

ci.condslope(alpha, b1, b2, se1, se2, cov, lo, hi, dfe)

Arguments

Value

Returns a 2-row matrix. The columns are:

• Estimate - estimated conditional slope

• t - t test statistic

• p - two-sided p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.condslope(.05, .132, .154, .031, .021, .015, 5.2, 10.6, 122)

# Should return:
#                   Estimate        SE        t  df           p 
# At low moderator    0.9328 0.4109570 2.269824 122 0.024973618 
# At high moderator   1.7644 0.6070517 2.906507 122 0.004342076 
#                           LL       UL
# At low moderator   0.1192696 1.746330
# At high moderator  0.5626805 2.966119

Description

Computes confidence intervals and test statistics for population conditional slopes (simple slopes) in a logistic model that includes a predictor variable (x1), a moderator variable (x2), and a product predictor variable (x1*x2). Conditional slopes are computed at low and high values of the moderator variable.

For more details, see Section 4.9 of Bonett (2021, Volume 3)

Usage

ci.condslope.log(alpha, b1, b2, se1, se2, cov, lo, hi)

Arguments

Value

Returns a 2-row matrix. The columns are:

• Estimate - estimated conditional slope

• exp(Estimate) - estimated exponentiated conditional slope

• z - z test statistic

• p - two-sided p-value

• LL - lower limit of the exponentiated confidence interval

• UL - upper limit of the exponentiated confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.condslope.log(.05, .132, .154, .031, .021, .015, 5.2, 10.6)

# Should return:
#                   Estimate exp(Estimate)      z       p 
# At low moderator    0.9328      2.541616 2.2698 0.02322 
# At high moderator   1.7644      5.838068 2.9065 0.00365 
#                          LL        UL
# At low moderator   1.135802  5.687444
# At high moderator  1.776421 19.186357

Description

Computes a Fisher confidence interval for a population Pearson correlation or partial correlation with s control variables. Set s = 0 for a Pearson correlation. A bias adjustment is used to reduce the bias of the Fisher transformed correlation. This function uses an estimated correlation as input. Use the cor.test function for raw data input.

For more details, see Section 1.14 of Bonett (2021, Volume 2)

Usage

ci.cor(alpha, cor, s, n)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated correlation (from input)

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Snedecor GW, Cochran WG (1989). Statistical Methods, 8th edition. ISU University Pres, Ames, Iowa.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.cor(.05, .60, 0, 150)

# Should return:
# Estimate      SE    LL     UL
#      0.6 0.05243 0.485 0.6925

ci.cor(.05, .70, 1, 135)

# Should return:
# Estimate      SE     LL     UL
#      0.7 0.04406 0.6002 0.7763

Description

Computes a confidence interval for a difference in population Pearson correlations that are estimated from the same sample and have one variable in common. A bias adjustment is used to reduce the bias of each Fisher transformed correlation. An approximate standard error is recovered from the confidence interval.

For more details, see Section 2.17 of Bonett (2021, Volume 2)

Usage

ci.cor.dep(alpha, cor1, cor2, cor12, n)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated correlation difference

• SE - recovered standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Zou GY (2007). “Toward using confidence intervals to compare correlations.” Psychological Methods, 12(4), 399–413. ISSN 1939-1463. doi:10.1037/1082-989X.12.4.399.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.cor.dep(.05, .396, .179, .088, 166)

# Should return:
# Estimate     SE     LL     UL
#    0.217 0.1027 0.0132 0.4158

Description

Computes a confidence interval for a difference in population Pearson correlations in a 2-group design. A bias adjustment is used to reduce the bias of each Fisher transformed correlation.

For more details, see Section 2.17 of Bonett (2021, Volume 2)

Usage

ci.cor2(alpha, cor1, cor2, n1, n2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated correlation difference

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Zou GY (2007). “Toward using confidence intervals to compare correlations.” Psychological Methods, 12(4), 399–413. ISSN 1939-1463. doi:10.1037/1082-989X.12.4.399.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.cor2(.05, .64, .31, 200, 200)

# Should return:
# Estimate      SE      LL     UL
#     0.33 0.07692  0.1797 0.4814

Description

Computes a 100(1 - alpha)% confidence interval for a difference in population correlations in a 2-group design. The correlations can be Pearson, Spearman, partial, semipartial, or point-biserial correlations. The correlations could also be correlations between two latent factors. The function requires a point estimate and a 100(1 - alpha)% confidence interval for each correlation as input. The confidence intervals for each correlation can be obtained using ci.fisher.

For more details, see Section 2.17 of Bonett (2021, Volume 2)

Usage

ci.cor2.gen(cor1, ll1, ul1, cor2, ll2, ul2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated correlation difference

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Zou GY (2007). “Toward using confidence intervals to compare correlations.” Psychological Methods, 12(4), 399–413. ISSN 1939-1463. doi:10.1037/1082-989X.12.4.399.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.cor2.gen(.64, .55, .71, .31, .18, .43)

# Should return:
# Estimate    LL     UL
#      0.33 0.18 0.4776

Description

Computes a distribution-free confidence interval for a population coefficient of quartile variation which is defined as (Q3 - Q1)/(Q3 + Q1) where Q1 is the 25th percentile and Q3 is the 75th percentile. The coefficient of quartile variation assumes ratio-scale scores and is a robust alternative to the coefficient of variation (see ci.cv). The 25th and 75th percentiles are computed using the type = 2 method (SAS default).

For more details, see Section 1.27 of Bonett (2021, Volume 1)

Usage

ci.cqv(alpha, y)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated coefficient of quartile variation

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2006). “Confidence interval for a coefficient of quartile variation.” Computational Statistics and Data Analysis, 50(11), 2953–2957. doi:10.1016/j.csda.2005.05.007.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

y <- c(30, 20, 15, 10, 10, 60, 20, 25, 20, 30, 10, 5, 50, 40,
       20, 10, 0, 20, 50)
ci.cqv(.05, y)

# Should return:
# Estimate        SE        LL       UL
#      0.5 0.1552485 0.2617885 0.8841821

Description

Computes a confidence interval for a population Cramer's V coefficient of nominal association for an r x s contingency table. The confidence interval is based on a noncentral chi-square distribution, and an approximate standard error is recovered from the confidence interval.

For more details, see Section 3.10 of Bonett (2021, Volume 3)

Usage

ci.cramer(alpha, chisqr, r, c, n)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimate of Cramer's V

• SE - recovered standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Smithson M (2003). Confidence Intervals. Sage.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.cramer(.05, 19.21, 2, 3, 200)

# Should return:
# Estimate     SE   LL    UL
#     0.31 0.0718 0.16 0.442

Description

Computes a confidence interval for a population Cronbach reliability. The point estimate of Cronbach reliability assumes essentially tau-equivalent measurements and the confidence interval assumes parallel measurements.

For more details, see Section 4.19 of Bonett (2021, Volume 1)

Usage

ci.cronbach(alpha, rel, r, n)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated Cronbach reliability (from input)

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Feldt LS (1965). “The approximate sampling distribution of Kuder-Richardson reliability coefficient twenty.” Psychometrika, 30(3), 357–370. ISSN 0033-3123. doi:10.1007/BF02289499.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.cronbach(.05, .85, 7, 89)

# Should return:
# Estimate       SE     LL     UL
#     0.85  0.02457 0.7971 0.8932

Description

Computes a confidence interval for a difference in population Cronbach reliability coefficients in a 2-group design. The number of measurements (items, raters, forms) used in each group need not be equal.

For more details, see Section 2.15 of Bonett (2021, Volume 4)

Usage

ci.cronbach2(alpha, rel1, rel2, r1, r2, n1, n2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated reliability difference

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Bonett DG, Wright TA (2015). “Cronbach's alpha reliability: Interval estimation, hypothesis testing, and sample size planning.” Journal of Organizational Behavior, 36(1), 3–15. ISSN 08943796. doi:10.1002/job.1960.

Examples

ci.cronbach2(.05, .88, .76, 8, 8, 200, 250)

# Should return:
# Estimate     LL     UL
#     0.12 0.0697 0.1733

Description

Computes a confidence interval for a population coefficient of variation (standard deviation divided by mean). This confidence interval is the reciprocal of a confidence interval for a standardized mean (see ci.stdmean). An approximate standard error is recovered from the confidence interval. The coefficient of variation assumes ratio-scale scores.

For more details, see Section 1.27 of Bonett (2021, Volume 1)

Usage

ci.cv(alpha, m, sd, n)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated coefficient of variation

• SE - recovered standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.cv(.05, 24.5, 3.65, 40)

# Should return:
#  Estimate        SE        LL       UL
# 0.1489796 0.01817373 0.1214381 0.1926778

Description

Computes estimates, standard errors, and approximate confidence intervals for the Berger-Parker, Simpson, and Shannon diversity indices. For the Shannon index, the value 1/r is added to each frequency count where r is the number of categories. These indices have a range of 0 to 1 where 0 indicates no diversity and 1 indicates maximum diversity.

For more details, see Section 1.13 of Bonett (2021, Volume 3)

Usage

ci.diversity(alpha, f)

Arguments

Value

Returns a 3-row matrix. The columns are:

• Estimate - estimate of diversity index

• SE - standard error of estimate

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

f = c(847, 320, 57, 274, 36)
ci.diversity(.05, f)

# Should return:
#         Estimate      SE     LL     UL
# Berger    0.5598 0.01587 0.5287 0.5909
# Simpson   0.7722 0.01229 0.7481 0.7963
# Shannon   0.7292 0.01224 0.7052 0.7532

Description

Computes a confidence interval for a population eta-squared, partial eta-squared, or generalized eta-squared in a fixed-factor between-subjects design. An approximate bias adjusted estimate is computed, and an approximate standard error is recovered from the confidence interval.

For more details, see Section 3.7 of Bonett (2021, Volume 1)

Usage

ci.etasqr(alpha, etasqr, df1, df2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Eta-squared - eta-squared (from input)

• adj Eta-squared - bias adjusted eta-squared estimate

• SE - recovered standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.etasqr(.05, .15, 2, 57)

# Should return:
# Eta-squared  adj Eta-squared       SE      LL      UL
#        0.15           0.1202  0.07414  0.0102  0.3008

Description

Computes a Fisher confidence interval for any type of correlation (e.g., Pearson, Spearman, Kendall-tau, tetrachoric, phi, partial, semipartial, etc.) or ordinal association such as gamma, Somers' d, or tau-b. The correlation could also be between two latent factors obtained from a SEM analysis (the Fisher CI will be more accurate than the large-sample CI from a SEM analysis). The standard error can be a traditional standard error, a bootstrap standard error, or a robust standard error from a SEM analysis.

Usage

ci.fisher(alpha, cor, se)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - correlation (from input)

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

Examples

ci.fisher(.05, .692, .049)

# Should return:
# Estimate     LL     UL
#    0.692 0.5833 0.7763

Description

Computes a confidence interval for a population intraclass reliability coefficient using mean squared estimates from a two-way ANOVA. This function will compute point and interval estimates of the ICC(C, 1) and ICC(C, r) reliability coefficients where ICC(C, 1) is the reliability of a single measurements (e.g., a single rater or a single form of a test) and ICC(C, r) is the reliability of a sum or average of r measurements. ICC(C, r) is the same as Cronbach's reliability coefficient. The ci.cronbach function uses a point estimate of Cronbach's reliability as input. The confidence intervals used in this function assume parallel measurements which implies a compound symmetric covariance matrix of the r measurements.

Usage

ci.icc(alpha, MSr, MSe, r, n)

Arguments

Value

Returns a 2-row matrix. The first row results are for ICC(C, 1) and the second row results are for ICC(C, r). The columns are:

• Estimate - estimated reliability

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

McGraw KO, Wong SP (1996). “Forming inferences about some intraclass correlation coefficients.” Psychological Methods, 1(1), 30–46. doi:10.1037/1082-989X.1.1.30.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.icc(.05, 48.2, 11.3, 5, 30)

# Should return:
#           Estimate      SE     LL     UL
# ICC(C, 1)   0.3951 0.09166 0.2311 0.5853
# ICC(C, r)   0.7656 0.07005 0.6005 0.8759

Description

Computes a Monte Carlo confidence interval (500,000 trials) for a population unstandardized or standardized indirect effect in a path model and a Sobel standard error. This function is not recommended for a standardized indirect if the standardized slopes are greater than .4 The Monte Carlo method is general in that the slope estimates and standard errors do not need to be OLS estimates with homoscedastic standard errors. For example, LAD slope estimates and their standard errors, OLS slope estimates and heteroscedastic-consistent standard errors also could be used. In models with no direct effects, distribution-free Theil-Sen slope estimates with recovered standard errors (see ci.theil) also could be used.

For more details, see Section 1.18 of Bonett (2021, Volume 4)

Usage

ci.indirect(alpha, b1, b2, se1, se2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated indirect effect

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.indirect (.05, 2.48, 1.92, .586, .379)

# Should return (within sampling error):
# Estimate       SE       LL       UL
#   4.7616 1.625282 2.178812 7.972262

Description

Computes confidence intervals for the intraclass kappa coefficient and Cohen's kappa coefficient with two dichotomous ratings. The G-index of agreement (see ci.agree) is arguably a better measure of agreement.

For more details, see Section 3.5 of Bonett (2021, Volume 3)

Usage

ci.kappa(alpha, f00, f01, f10, f11)

Arguments

Value

Returns a 2-row matrix. The results in row 1 are for the intraclass kappa. The results in row 2 are for Cohen's kappa. The columns are:

• Estimate - estimate of interrater reliability

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Fleiss JL, Paik MC (2003). Statistical Methods for Rates and Proportions, 3rd edition. Wiley.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.kappa(.05, 31, 12, 4, 58)

# Should return:
#              Estimate     SE    LL    UL
# IC kappa:       0.674 0.0748 0.527 0.821
# Cohen kappa:    0.676 0.0734 0.532 0.820

Description

Computes the estimate, standard error, and approximate confidence interval for a linear contrast of any type of parameter where each parameter value has been estimated from a different sample. The parameter values are assumed to be of the same type and their sampling distributions are assumed to be approximately normal.

Usage

ci.lc.gen.bs(alpha, est, se, v)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimate of linear contrast

• SE - standard error of linear contrast

• LL - lower limit of confidence interval

• UL - upper limit of confidence interval

Examples

est <- c(3.86, 4.57, 2.29, 2.88)
se <- c(0.185, 0.365, 0.275, 0.148)
v <- c(.5, .5, -.5, -.5)
ci.lc.gen.bs(.05, est, se, v)

# Should return:
# Estimate        SE       LL       UL
#     1.63 0.2573806 1.125543 2.134457

Description

Computes the estimate, standard error, and confidence interval for a linear contrast of parameters in a general linear model using coef(object) and vcov(object) where "object" is a fitted model object from the lm function.

For more details, see Section 2.28 of Bonett (2021, Volume 2)

Usage

ci.lc.glm(alpha, n, b, V, q)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimate of linear function

• SE - standard error

• t - t test statistic

• df - degrees of freedom

• p - two-sided p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

y <- c(43, 62, 49, 60, 36, 79, 55, 42, 67, 50)
x1 <- c(3, 6, 4, 6, 2, 7, 4, 2, 7, 5)
x2 <- c(4, 6, 3, 7, 1, 9, 3, 3, 8, 4)
out <- lm(y ~ x1 + x2)
b <- coef(out)
V <- vcov(out)
n <- length(y)
q <- c(0, .5, .5)
b
ci.lc.glm(.05, n, b, V, q)

#  Should return:
# (Intercept)          x1          x2 
#   26.891111    3.648889    2.213333 
#
# Estimate        SE      t df       p       LL       UL
# 2.931111 0.4462518 6.5683  7 0.00031 1.875893 3.986329

Description

Computes a test statistic and confidence interval for a linear contrast of means in a between-subjects design. This function computes both unequal variance and equal variance confidence intervals and test statistics. A Satterthwaite adjustment to the degrees of freedom is used with the unequal variance method.

For more details, see Section 3.3 of Bonett (2021, Volume 1)

Usage

ci.lc.mean.bs(alpha, m, sd, n, v)

Arguments

Value

Returns a 2-row matrix. The columns are:

• Estimate - estimated linear contrast

• SE - standard error

• t - t test statistic

• df - degrees of freedom

• p - two-sided p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Snedecor GW, Cochran WG (1989). Statistical Methods, 8th edition. ISU University Pres, Ames, Iowa.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

m <- c(24.9, 23.1, 16.4)
sd <- c(5.21, 4.67, 4.98)
n <- c(30, 30, 30)
v <- c(.5, .5, -1)
ci.lc.mean.bs(.05, m, sd, n, v)

# Should return:
#                              Estimate       SE      t    df p       LL       UL
# Equal Variances Assumed:          7.6 1.108703 6.8549 87.00 0 5.396332 9.803668
# Equal Variances Not Assumed:      7.6 1.111135 6.8399 57.59 0 5.375484 9.824516

m <- c(33.5, 37.9, 38.0, 44.1)
sd <- c(3.84, 3.84, 3.65, 4.98)
n <- c(10, 10, 10, 10)
v <- c(.5, .5, -.5, -.5)
ci.lc.mean.bs(.05, m, sd, n, v)

# Should return:
#                              Estimate       SE      t    df       p 
# Equal Variances Assumed:        -5.35 1.300136 -4.115 36.00 0.00022 
# Equal Variances Not Assumed:    -5.35 1.300136 -4.115 33.52 0.00024 
#                                     LL        UL
# Equal Variances Assumed:     -7.986797 -2.713203
# Equal Variances Not Assumed: -7.993583 -2.706417

Description

Computes a Scheffe confidence interval for a linear contrast of population means in a between-subjects design. A Scheffe p-value is computed for the test statistic. The Scheffe method assumes equal population variances. This function is useful in exploratory studies where the linear contrast of means was not planned but was suggested by the pattern of sample means. Use the ci.lc.mean.bs function with a Bonferroni adjusted alpha value to compute simultaneous confidence intervals for two or more planned linear contrasts of means.

Usage

ci.lc.mean.scheffe(alpha, m, sd, n, v)

Arguments

Value

Returns a 2-row matrix. The columns are:

• Estimate - estimated linear contrast

• SE - standard error

• t - t test statistic

• df - degrees of freedom

• p - two-sided Scheffe p-value

• LL - lower limit of the Scheffe confidence interval

• UL - upper limit of the Scheffe confidence interval

References

Snedecor GW, Cochran WG (1989). Statistical Methods, 8th edition. ISU University Pres, Ames, Iowa.

Examples

m <- c(33.5, 37.9, 38.0, 44.1)
sd <- c(3.49, 3.84, 3.65, 4.98)
n <- c(10, 10, 10, 10)
v <- c(.5, .5, -.5, -.5)
ci.lc.mean.scheffe(.05, m, sd, n, v)

# Should return:
#  Estimate       SE       t       p        LL        UL
#     -5.35 1.275231 -4.1953 0.00228 -9.089451 -1.610549

Description

Computes a distribution-free confidence interval for a linear contrast of medians in a between-subjects design using estimated medians and their standard errors. The sample median and standard error for each group can be computed using the ci.median function.

For more details, see Section 3.21 of Bonett (2021, Volume 1)

Usage

ci.lc.median.bs(alpha, m, se, v)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated linear contrast of medians

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG, Price RM (2002). “Statistical inference for a linear function of medians: Confidence intervals, hypothesis testing, and sample size requirements.” Psychological Methods, 7(3), 370–383. ISSN 1939-1463. doi:10.1037/1082-989X.7.3.370.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

m <- c(46.13, 29.19, 30.32, 49.15)
se <- c(6.361, 5.892, 4.887, 6.103)
v <- c(1, -1, -1, 1)
ci.lc.median.bs(.05, m, se, v)

# Should return:
# Estimate       SE       LL       UL
#    35.77 11.67507 12.88727 58.65273

Description

Computes an adjusted Wald confidence interval for a linear contrast of population proportions in a between-subjects design.

For more details, see Section 2.8 of Bonett (2021, Volume 3)

Usage

ci.lc.prop.bs(alpha, f, n, v)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - adjusted estimate of proportion linear contrast

• SE - adjusted standard error

• z - z test statistic

• p - two-sided p-value

• LL - lower limit of the adjusted Wald confidence interval

• UL - upper limit of the adjusted Wald confidence interval

References

Price RM, Bonett DG (2004). “An improved confidence interval for a linear function of binomial proportions.” Computational Statistics & Data Analysis, 45(3), 449–456. ISSN 01679473. doi:10.1016/S0167-9473(03)00007-0.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

f <- c(26, 24, 38)
n <- c(60, 60, 60)
v1 <- c(-.5, -.5, 1)
ci.lc.prop.bs(.05/2, f, n, v1)

# Should return:
#  Estimate         SE      z       p        LL        UL
# 0.2119565 0.07602892 2.7878 0.00531 0.0415451 0.3823679

v2 <- c(1, -1, 0)
ci.lc.prop.bs(.05/2, f, n, v2)

# Should return:
#   Estimate         SE       z       p         LL        UL
# 0.03225806 0.08857951 0.36417 0.71573 -0.1662843 0.2308004

Description

Computes an adjusted Wald confidence interval for a linear contrast of population proportions in a between-subjects design using a Scheffe critical value. A Scheffe p-value is computed for the test statistic. This function is useful in exploratory studies where the linear contrast of proportions was not planned but was suggested by the pattern of sample proportions. Use the ci.lc.prop.bs function with a Bonferroni adjusted alpha value to compute simultaneous confidence intervals for two or more planned linear contrasts of proportions.

For more details, see Section 2.9 of Bonett (2021, Volume 3)

Usage

ci.lc.prop.scheffe(alpha, f, n, v)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - adjusted estimate of proportion linear contrast

• SE - adjusted standard error

• z - z test statistic

• p - two-sided Scheffe p-value

• LL - lower limit of the Scheffe confidence interval

• UL - upper limit of the Scheffe confidence interval

References

Price RM, Bonett DG (2004). “An improved confidence interval for a linear function of binomial proportions.” Computational Statistics & Data Analysis, 45(3), 449–456. ISSN 01679473. doi:10.1016/S0167-9473(03)00007-0.

Marascuilo LA, McSweeney M (1977). Nonparametric and Distribution-Free Methods for the Social Sciences. Brooks/Cole.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

f <- c(26, 24, 38)
n <- c(60, 60, 60)
v <- c(-.5, -.5, 1)
ci.lc.prop.scheffe(.05, f, n, v)

# Should return:
#  Estimate         SE      z       p         LL        UL
# 0.2119565 0.07602892 2.7878 0.02053 0.02585698 0.3980561

Description

Computes a confidence interval and test statistic for a linear contrast of population regression coefficients (e.g., a y-intercept or a slope coefficient) across groups in a multiple group regression model. Equality of error variances across groups is not assumed. A Satterthwaite adjustment to the degrees of freedom is used to improve the accuracy of the confidence interval.

For more details, see Section 2.20 of Bonett (2021, Volume 2)

Usage

ci.lc.reg(alpha, est, se, n, s, v)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated linear contrast

• SE - standard error

• t - t test statistic

• df - degrees of freedom

• p - two-sided p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

est <- c(1.74, 1.83, 0.482)
se <- c(.483, .421, .395)
n <- c(40, 40, 40)
v <- c(.5, .5, -1)
ci.lc.reg(.05, est, se, n, 4, v)

# Should return:
# Estimate        SE      t      df       p        LL       UL
#    1.303 0.5085838 2.5620 78.8197 0.01231 0.2906532 2.315347

Description

Computes confidence intervals for a population standardized linear contrast of means in a between-subjects design. The unweighted standardizer is recommended in experimental designs. The weighted standardizer is recommended in nonexperimental designs with simple random sampling. The group 1 standardizer is useful in both experimental and nonexperimental designs. Equality of variances is not assumed.

For more details, see Section 3.4 of Bonett (2021, Volume 1)

Usage

ci.lc.stdmean.bs(alpha, m, sd, n, v)

Arguments

Value

Returns a 3-row matrix. The columns are:

• Estimate - estimated standardized linear contrast

• adj Estimate - bias adjusted standardized linear contrast estimate

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2008). “Confidence intervals for standardized linear contrasts of means.” Psychological Methods, 13(2), 99–109. ISSN 1939-1463. doi:10.1037/1082-989X.13.2.99.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

m <- c(6.94, 7.15, 4.60, 3.68)
sd <- c(2.21, 2.83, 2.29, 1.90)
n <- c(40, 40, 40, 40)
v <- c(.5, .5, -.5, -.5)
ci.lc.stdmean.bs(.05, m, sd, n, v)

# Should return:
#                          Estimate adj Estimate      SE     LL     UL
# Unweighted standardizer:   1.2459       1.2399 0.17621 0.9005 1.5912 
# Weighted standardizer:     1.2459       1.2399 0.17313 0.9065 1.5852
# Group 1 standardizer:      1.3145       1.2890 0.22515 0.8732 1.7558

Description

Computes confidence intervals for two types of population standardized linear contrast of means (unweighted standardizer and level 1 standardizer) in a within-subjects design. Equality of variances is not assumed, but the correlations among the repeated measures are assumed to be approximately equal.

For more details, see Section 4.7 of Bonett (2021, Volume 1)

Usage

ci.lc.stdmean.ws(alpha, m, sd, cor, n, q)

Arguments

Value

Returns a 2-row matrix. The columns are:

• Estimate - estimated standardized linear contrast

• adj Estimate - bias adjusted standardized linear contrast estimate

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2008). “Confidence intervals for standardized linear contrasts of means.” Psychological Methods, 13(2), 99–109. ISSN 1939-1463. doi:10.1037/1082-989X.13.2.99.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

m <- c(33.5, 37.9, 38.0, 44.1)
sd <- c(3.84, 3.84, 3.65, 4.98)
q <- c(.5, .5, -.5, -.5)
ci.lc.stdmean.ws(.05, m, sd, .672, 20, q)

# Should return:
#                          Estimate adj Estimate      SE      LL      UL
# Unweighted standardizer:  -1.3013      -1.2666 0.31479 -1.9182 -0.6843
# Level 1 standardizer:     -1.3932      -1.3375 0.36618 -2.1109 -0.6755

Description

Computes a confidence interval for a population mean absolute deviation from the median (MAD). The MAD is a robust alternative to the standard deviation.

For more details, see Section 1.26 of Bonett (2021, Volume 1)

Usage

ci.mad(alpha, y)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated mean absolute deviation

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG, Seier E (2003). “Confidence intervals for mean absolute deviations.” The American Statistician, 57(4), 233–236. ISSN 0003-1305. doi:10.1198/0003130032323.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

y <- c(30, 20, 15, 10, 10, 60, 20, 25, 20, 30, 10, 5, 50, 40, 
       20, 10, 0, 20, 50)
ci.mad(.05, y)

# Should return:
# Estimate       SE       LL       UL
#     12.5 2.876103 7.962667 19.62282

Description

Computes a distribution-free confidence interval for the Mann-Whitney parameter (a "common language effect size"). In a 2-group experiment, this parameter is the proportion of members in the population with scores that would be higher under treatment 1 than treatment 2. In a 2-group nonexperiment where participants are sampled from two subpopulations of sizes N1 and N2, the parameter is the proportion of all N1 x N2 pairs in which a member from subpopulation 1 has a larger score than a member from subpopulation 2.

For more details, see Section 2.12 of Bonett (2021, Volume 1)

Usage

ci.mann(alpha, y1, y2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated proportion

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Sen PK (1967). “A note on asymptotically distribution-free confidence bounds for P(X < Y), based on two independent samples.” The Indian Journal of Statistics, Series A, 29(1), 95–102.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

y1 <- c(9.4, 10.3, 58.3, 106.0, 31.0, 46.2, 12.0, 19.0, 135.0, 159.0)
y2 <- c(14.6, 5.1, 8.1, 22.7, 6.4, 4.4, 19.0, 3.2)
ci.mann(.05, y1, y2)

# Should return:
# Estimate        SE        LL UL
#  0.86875 0.1222202 0.6292028  1

Description

Computes a confidence interval for a population mean absolute prediction error (MAPE) in a general linear model. The MAPE is a more robust alternative to the residual standard deviation. This function requires a vector of estimated residuals from a general linear model. This confidence interval does not assume zero excess kurtosis but does assume symmetry of the population prediction errors.

For more details, see Section 1.16 of Bonett (2021, Volume 2)

Usage

ci.mape(alpha, res, s)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated mean absolute prediction error

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

res <- c(-2.70, -2.69, -1.32, 1.02, 1.23, -1.46, 2.21, -2.10, 2.56,
      -3.02, -1.55, 1.46, 4.02, 2.34)
ci.mape(.05, res, 1)

# Should return:
# Estimate        SE       LL       UL
#   2.3744 0.3314752 1.751678 3.218499

Description

Computes a confidence interval for a population mean using the estimated mean, estimated standard deviation, and sample size. Use the t.test function for raw data input.

For more details, see Section 1.7 of Bonett (2021, Volume 1)

Usage

ci.mean(alpha, m, sd, n)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated mean

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Snedecor GW, Cochran WG (1989). Statistical Methods, 8th edition. ISU University Pres, Ames, Iowa.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.mean(.05, 38.3, 8.14, 10)

# Should return:
# Estimate        SE       LL       UL
#     38.3  2.574094 32.47699 44.12301

Description

Computes a confidence interval for a population mean with a finite population correction (fpc) using the estimated mean, estimated standard deviation, sample size, and population size. This function is useful when the sample size is not a small fraction of the population size.

For more details, see Section 1.33 of Bonett (2021, Volume 1)

Usage

ci.mean.fpc(alpha, m, sd, n, N)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated mean

• SE - standard error with fpc

• LL - lower limit of the confidence interval with fpc

• UL - upper limit of the confidence interval with fpc

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.mean.fpc(.05, 24.5, 3.65, 40, 300)

# Should return:
# Estimate        SE       LL       UL
#     24.5 0.5381631 23.41146 25.58854

Description

Computes confidence intervals for three population generalized means (square-root, geometric, and harmonic) using a vector of response scores as input. The square-root mean requires non-negative scores. The geometric and harmonic means require positive scores. The standard errors are recovered from the confidence intervals.

Usage

ci.mean.gen(alpha, y)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated mean

• SE - recovered standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

Examples

y <- c(32, 47, 28, 15, 20, 41, 87)
ci.mean.gen(.05, y)

# Should return:
#             Estimate       SE       LL       UL
# Square-root 35.79395 8.141122 18.64498 58.48619
# Geometric   33.26410 7.633328 19.47124 56.82741
# Harmonic    29.07073 7.978149 19.35236 58.39602

Description

Computes a confidence interval for a population paired-samples mean difference using the estimated means, estimated standard deviations, estimated correlation, and sample size. Also computes a paired-samples t-test. Use the t.test function for raw data input.

For more details, see Section 4.2 of Bonett (2021, Volume 1)

Usage

ci.mean.ps(alpha, m1, m2, sd1, sd2, cor, n)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated mean difference

• SE - standard error

• t - t test statistic

• df - degrees of freedom

• p - two-sided p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Snedecor GW, Cochran WG (1989). Statistical Methods, 8th edition. ISU University Pres, Ames, Iowa.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.mean.ps(.05, 58.2, 51.4, 7.43, 8.92, .537, 30)

# Should return:
# Estimate       SE      t df      p       LL       UL
#      6.8 1.455922 4.6706 29  6e-05 3.822304 9.777696

Description

Computes equal variance and unequal variance confidence intervals for a population 2-group mean difference using the estimated means, estimated standard deviations, and sample sizes. Also computes equal variance and unequal variance independent-samples t-tests. Use the t.test function for raw data input.

For more details, see Section 2.3 of Bonett (2021, Volume 1)

Usage

ci.mean2(alpha, m1, m2, sd1, sd2, n1, n2)

Arguments

Value

Returns a 2-row matrix. The columns are:

• Estimate - estimated mean difference

• SE - standard error

• t - t test statistic

• df - degrees of freedom

• p - two-sided p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Snedecor GW, Cochran WG (1989). Statistical Methods, 8th edition. ISU University Pres, Ames, Iowa.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.mean2(.05, 19.4, 11.3, 2.70, 2.10, 40, 40)
# Should return:
#                              Estimate        SE       t    df p
# Equal Variances Assumed:          8.1 0.5408327 14.9769 78.00 0
# Equal Variances Not Assumed:      8.1 0.5408327 14.9769 73.54 0
#                                    LL       UL
# Equal Variances Assumed:     7.023285 9.176715
# Equal Variances Not Assumed: 7.022256 9.177744

Description

Computes a distribution-free confidence interval for a population median. Tied scores are assumed to be rare.

For more details, see Section 1.25 of Bonett (2021, Volume 1)

Usage

ci.median(alpha, y)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated median

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Snedecor GW, Cochran WG (1989). Statistical Methods, 8th edition. ISU University Pres, Ames, Iowa.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

y <- c(25, 29, 35, 36, 36, 40, 41, 43, 44, 54)
ci.median(.05, y)

# Should return:
#  Estimate       SE  LL  UL
#        38 3.261774  29  44

Description

Computes a distribution-free confidence interval for a difference of population medians in a paired-samples design. This function also computes the standard error of each median and the covariance between the two estimated medians. Tied scores within each measurement are assumed to be rare.

For more details, see Section 4.23 of Bonett (2021, Volume 1)

Usage

ci.median.ps(alpha, y1, y2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Median1 - estimated median for measurement 1

• Median2 - estimated median for measurement 2

• Median1-Median2 - estimated difference of medians

• SE1 - standard error of median 1

• SE2 - standard error of median 2

• COV - covariance of the two estimated medians

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG, Price RM (2020). “Interval estimation for linear functions of medians in within-subjects and mixed designs.” British Journal of Mathematical and Statistical Psychology, 73(2), 333–346. ISSN 0007-1102. doi:10.1111/bmsp.12171.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

y1 <- c(21.1, 4.9, 9.2, 12.4, 35.8, 18.1, 10.7, 22.9, 24.0, 1.2, 6.1, 8.3, 13.1, 16.2)
y2 <- c(67.0, 28.1, 30.9, 28.6, 52.0, 40.8, 25.8, 37.4, 44.9, 10.3, 14.9, 20.2, 28.8, 40.6)
ci.median.ps(.05, y1, y2)

# Should return:
#  Median1 Median2 Median1-Median2       SE        LL        UL
#    12.75   29.85           -17.1 3.704248 -24.36019 -9.839807
#       SE1      SE2     COV
#  3.379695 4.968956 11.1957

Description

Computes a distribution-free confidence interval for a difference of population medians in a 2-group design. Tied scores within each group are assumed to be rare.

For more details, see Section 2.12 of Bonett (2021, Volume 1)

Usage

ci.median2(alpha, y1, y2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Median1 - estimated median for group 1

• Median2 - estimated median for group 2

• Median1-Median2 - estimated difference of medians

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG, Price RM (2002). “Statistical inference for a linear function of medians: Confidence intervals, hypothesis testing, and sample size requirements.” Psychological Methods, 7(3), 370–383. ISSN 1939-1463. doi:10.1037/1082-989X.7.3.370.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

y1 = c(70, 394, 43, 95, 62, 128, 2, 203, 81, 436, 85, 35, 
        156, 1, 3, 27, 63, 181, 184, 18)
y2 = c(102, 120, 78, 78, 417, 124, 86, 171, 176, 129, 230, 
       194, 100, 157, 306, 411, 164, 103, 193, 312)
ci.median2(.05, y1, y2)

# Should return:
#  Median1 Median2 Median1-Median2       SE        LL        UL
#     75.5   160.5             -85 37.11502 -157.7441 -12.25589

Description

Computes a confidence interval for an odds ratio with .5 added to each cell frequency. This function requires the frequency counts from a 2 x 2 contingency table for two dichotomous variables.

For more details, see Section 3.4 of Bonett (2021, Volume 3)

Usage

ci.oddsratio(alpha, f00, f01, f10, f11)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimate of odds ratio

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Fleiss JL, Paik MC (2003). Statistical Methods for Rates and Proportions, 3rd edition. Wiley.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.oddsratio(.05, 229, 28, 96, 24)

# Should return:
#  Estimate        SE       LL       UL
#  2.044451 0.6154578 1.133267 3.688254

Description

Computes adjusted Wald confidence intervals for pairwise proportion differences of a multinomial variable in a single sample. These adjusted Wald confidence intervals use the same method that is used to compare the two proportions in a paired-samples design.

For more details, see Section 1.12 of Bonett (2021, Volume 3)

Usage

ci.pairs.mult(alpha, f)

Arguments

Value

Returns a matrix with the number of rows equal to the number of pairwise comparisons. The columns are:

• Estimate - adjusted estimate of proportion difference

• SE - adjusted standard error

• LL - lower limit of the adjusted Wald confidence interval

• UL - upper limit of the adjusted Wald confidence interval

References

Bonett DG, Price RM (2012). “Adjusted wald confidence interval for a difference of binomial proportions based on paired data.” Journal of Educational and Behavioral Statistics, 37(4), 479–488. ISSN 1076-9986. doi:10.3102/1076998611411915.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

f <- c(87, 49, 31, 133)
ci.pairs.mult(.05, f)

# Should return:
#         Estimate         SE           LL          UL
#  1 2  0.12582781 0.03821865  0.050920628  0.20073500
#  1 3  0.18543046 0.03466808  0.117482270  0.25337866
#  1 4 -0.15231788 0.04855183 -0.247477718 -0.05715804
#  2 3  0.05960265 0.02978792  0.001219398  0.11798590
#  2 4 -0.27814570 0.04196760 -0.360400688 -0.19589070
#  3 4 -0.33774834 0.03797851 -0.412184859 -0.26331183

Description

Computes adjusted Wald confidence intervals for all pairwise differences of population proportions in a between-subjects design using a Bonferroni adjusted alpha level.

For more details, see Section 2.7 of Bonett (2021, Volume 3)

Usage

ci.pairs.prop.bs(alpha, f, n)

Arguments

Value

Returns a matrix with the number of rows equal to the number of pairwise comparisons. The columns are:

• Estimate - adjusted estimate of proportion difference

• SE - adjusted standard error

• z - z test statistic

• p - two-sided p-value

• LL - lower limit of the adjusted Wald confidence interval

• UL - upper limit of the adjusted Wald confidence interval

References

Agresti A, Caffo B (2000). “Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures.” The American Statistician, 54(4), 280-288. ISSN 00031305. doi:10.2307/2685779.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

f <- c(111, 161, 132)
n <- c(200, 200, 200)
ci.pairs.prop.bs(.05, f, n)

# Should return:
#        Estimate         SE       z       p          LL          UL
# 1 2  -0.2475248 0.04482323 -5.5222 0.00000 -0.35483065 -0.14021885
# 1 3  -0.1039604 0.04833562 -2.1508 0.03149 -0.21967489  0.01175409
# 2 3   0.1435644 0.04358401  3.2940 0.00099  0.03922511  0.24790360

Description

Computes confidence intervals for two types of population point-biserial correlations. One type uses a weighted average of the group variances and is appropriate for nonexperimental designs with simple random sampling (but not stratified random sampling). The other type uses an unweighted average of the group variances and is appropriate for experimental designs. Equality of variances is not assumed for either type.

For more details, see Section 1.18 of Bonett (2021, Volume 2)

Usage

ci.pbcor(alpha, m1, m2, sd1, sd2, n1, n2)

Arguments

Value

Returns a 2-row matrix. The columns are:

• Estimate - estimated point-biserial correlation

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2020). “Point-biserial correlation: Interval estimation, hypothesis testing, meta-analysis, and sample size determination.” British Journal of Mathematical and Statistical Psychology, 73(S1), 113–144. ISSN 0007-1102. doi:10.1111/bmsp.12189.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.pbcor(.05, 28.32, 21.48, 3.81, 3.09, 40, 40)

# Should return:
#             Estimate      SE     LL     UL
# Weighted:     0.7066 0.04891 0.5885 0.7854
# Unweighted:   0.7021 0.05019 0.5808 0.7829

Description

Computes a Fisher confidence interval for a population phi correlation. This function requires the frequency counts from a 2 x 2 contingency table for two dichotomous variables. This measure of association is usually most appropriate when both dichotomous variables are naturally dichotomous.

For more details, see Section 3.4 of Bonett (2021, Volume 3)

Usage

ci.phi(alpha, f00, f01, f10, f11)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimate of phi correlation

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bishop YMM, Fienberg SE, Holland PW (1975). Discrete Multivariate Analysis. MIT Press.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.phi(.05, 229, 28, 96, 24)

# Should return:
#  Estimate     SE    LL    UL
#     0.123 0.0548 0.015 0.229

Description

Computes a confidence interval for a population Poisson rate. This function requires the number of occurrences (f) of a specific event that were observed over a specific period of time (t).

Usage

ci.poisson(alpha, f, t)

Arguments

Details

The time period (t) does not need to be an integer and can be expressed in any unit of time such as seconds, hours, or months. The occurances are assumed to be independent of one another and the unknown occurance rate is assumed to be constant over time.

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated Poisson rate

• SE - recovered standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Hahn GJ, Meeker WQ (1991). Statistical Intervals: A Guide for Practitioners. Wiley. ISBN 9780470316771. doi:10.1002/9780470316771.

Examples

ci.poisson(.05, 23, 5.25)

# Should return:
# Estimate        SE       LL      UL
# 4.380952 0.9684952 2.777148 6.57358

Description

Computes a Wald confidence interval for an unknown population size using mark-recapture sampling. This method assumes independence of the two samples. This function requires the frequency counts from an incomplete 2 x 2 contingency table for the two samples (f11 is the unknown number of people who were not observed in either sample). This method sets the estimated odds ratio (with .5 added to each cell) to 1 and solves for unobserved cell frequency. An approximate standard error is recovered from the confidence interval.

For more details, see Section 3.7 of Bonett (2021, Volume 3)

Usage

ci.popsize(alpha, f00, f01, f10)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimate of the unknown population size

• SE - recovered standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.popsize(.05, 85, 196, 184)

# Should return:
# Estimate    SE  LL   UL
#      889 67.35 777 1041

Description

Computes adjusted Wald (Agresi-Coull), Wilson, and exact confidence intervals for a population proportion. The Wilson confidence interval uses a continuity correction.

For more details, see Section 1.5 of Bonett (2021, Volume 3)

Usage

ci.prop(alpha, f, n)

Arguments

Value

Returns a 2-row matrix. The columns of row 1 are:

• Estimate - adjusted estimate of proportion

• SE - standard error of adjusted estimate

• LL - lower limit of the adjusted Wald confidence interval

• UL - upper limit of the adjusted Wald confidence interval

The columns of row 2 are:

• Estimate - ML estimate of proportion

• SE - standard error of ML estimate

• LL - lower limit of the Wilson confidence interval

• UL - upper limit of the Wilson confidence interval

The columns of row 3 are:

• Estimate - ML estimate of proportion

• SE - standard error of ML estimate

• LL - lower limit of the exact confidence interval

• UL - upper limit of the exact confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Agresti A, Coull BA (1998). “Approximate is better than 'exact' for interval estimation of binomial proportions.” The American Statistician, 52(2), 119–126. ISSN 0003-1305. doi:10.1080/00031305.1998.10480550.

Examples

ci.prop(.05, 120, 300)

# Should return:
#                 Estimate         SE        LL        UL
# Adjusted Wald  0.4013158 0.02811287 0.3462156 0.4564160
# Wilson with cc 0.4000000 0.02828427 0.3445577 0.4580464
# Exact          0.4000000 0.02828427 0.3441290 0.4578664

Description

Computes an adjusted Wald interval for a population proportion with a finite population correction (fpc). This confidence interval is useful when the sample size is not a small fraction of the population size.

For more details, see Section 1.20 of Bonett (2021, Volume 3)

Usage

ci.prop.fpc(alpha, f, n, N)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - adjusted estimate of proportion

• SE - adjusted standard error with fpc

• LL - lower limit of the confidence interval with fpc

• UL - upper limit of the confidence interval with fpc

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.prop.fpc(.05, 61, 75, 415)

# Should return:
#   Estimate         SE       LL        UL
#  0.7974684 0.04097594 0.717157 0.8777797

Description

Computes an exact confidence interval for a population proportion when inverse sampling has been used. An approximate standard error is recovered from the confidence interval. With inverse sampling, the number of participants who have the attribute (f) is predetermined and sampling continues until f attains its prespecified value. With inverse sampling, the sample size (n) will not be known in advance.

For more details, see Section 1.19 of Bonett (2021, Volume 3)

Usage

ci.prop.inv(alpha, f, n)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimate of proportion

• SE - recovered standard error

• LL - lower limit of confidence interval

• UL - upper limit of confidence interval

References

Zou GY (2010). “Confidence interval estimation under inverse sampling.” Computational Statistics & Data Analysis, 54(1), 55–64. ISSN 0167-9473. doi:10.1016/j.csda.2005.05.007.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.prop.inv(.05, 10, 87)

# Should return:
#  Estimate         SE         LL        UL
# 0.1149425 0.03389574 0.05651668 0.1893855

Description

Computes an adjusted Wald confidence interval for a difference of population proportions in a paired-samples design. This function requires the frequency counts from a 2 x 2 contingency table for two repeated dichotomous measurements.

For more details, see Section 3.2 of Bonett (2021, Volume 3)

Usage

ci.prop.ps(alpha, f00, f01, f10, f11)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - adjusted estimate of proportion difference

• SE - adjusted standard error

• LL - lower limit of the adjusted Wald confidence interval

• UL - upper limit of the adjusted Wald confidence interval

References

Bonett DG, Price RM (2012). “Adjusted wald confidence interval for a difference of binomial proportions based on paired data.” Journal of Educational and Behavioral Statistics, 37(4), 479–488. ISSN 1076-9986. doi:10.3102/1076998611411915.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.prop.ps(.05, 12, 4, 26, 6)

# Should return:
# Estimate         SE        LL        UL
#     0.44 0.09448809 0.2548067 0.6251933

Description

Computes an adjusted Wald confidence interval for a population proportion difference in a 2-group design.

For more details, see Section 2.2 of Bonett (2021, Volume 3)

Usage

ci.prop2(alpha, f1, f2, n1, n2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - adjusted estimate of proportion difference

• SE - adjusted standard error

• LL - lower limit of the adjusted Wald confidence interval

• UL - upper limit of the adjusted Wald confidence interval

References

Agresti A, Caffo B (2000). “Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures.” The American Statistician, 54(4), 280-288. ISSN 00031305. doi:10.2307/2685779.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.prop2(.05, 57, 15, 100, 100)

# Should return:
#   Estimate         SE        LL        UL
#  0.4117647 0.06083948 0.2925215 0.5310079

Description

Computes an approximate confidence interval for a population proportion difference when inverse sampling has been used. An approximate standard error is recovered from the confidence interval. With inverse sampling, the number of participants who have the attribute within group 1 (f1) and group 2 (f2) are predetermined, and sampling continues within each group until f1 and f2 attain their prespecified values. With inverse sampling, the sample sizes (n1 and n2) will not be known in advance.

Usage

ci.prop2.inv(alpha, f1, f2, n1, n2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimate of proportion difference

• SE - recovered standard error

• LL - lower limit of confidence interval

• UL - upper limit of confidence interval

References

Zou GY (2010). “Confidence interval estimation under inverse sampling.” Computational Statistics & Data Analysis, 54(1), 55–64. ISSN 0167-9473. doi:10.1016/j.csda.2005.05.007.

Examples

ci.prop2.inv(.05, 10, 10, 48, 213)

# Should return:
#  Estimate         SE         LL        UL
#  0.161385 0.05997618 0.05288277 0.2879851

Description

Computes adjusted Wald confidence intervals for positive and negative predictive values (PPV and NPV) of a diagnostic test with retrospective sampling where the population prevalence rate is assumed to be known. With retrospective sampling, one random sample is obtained from a subpopulation that is known to have a "positive" outcome, a second random sample is obtained from a subpopulation that is known to have a "negative" outcome, and then the diagnostic test (scored "pass" or "fail") is given in each sample. PPV and NPV can be expressed as a function of proportion ratios and the known population prevalence rate (the population proportion who would "pass"). The confidence intervals for PPV and NPV are based on the Price-Bonett adjusted Wald confidence interval for a proportion ratio.

For more details, see Section 3.6 of Bonett (2021, Volume 3)

Usage

ci.pv(alpha, f1, f2, n1, n2, prev)

Arguments

Value

Returns a 2-row matrix. The columns are:

• Estimate - adjusted estimate of the predictive value

• LL - lower limit of the adjusted Wald confidence interval

• UL - upper limit of the adjusted Wald confidence interval

References

Price RM, Bonett DG (2008). “Confidence intervals for a ratio of two independent binomial proportions.” Statistics in Medicine, 27(26), 5497–5508. ISSN 02776715. doi:10.1002/sim.3376.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.pv(.05, 89, 5, 100, 100, .16)

# Should return:
#        Estimate        LL        UL
# PPV:  0.7640449 0.5838940 0.8819671
# NPV:  0.9779978 0.9623406 0.9872318