Package 'statpsych'

Description

Computes an adjusted standard error 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.

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

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 0.031725582 0.3365531  7.223447
# [2,]     8.21 3.487559 2.354082 114 0.020279958 1.3011734 15.118827
# [3,]     2.99 1.087233 2.750102 114 0.006930554 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 design with a quantitative response variable. A Satterthwaite adjustment to the degrees of freedom is used and equality of population variances is not assumed.

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

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 -2.29227953 35.47894 0.027931810 -9.6145264 -0.5854736
# A:           1.65 1.112430  1.48323970 35.47894 0.146840430 -0.6072632  3.9072632
# B:          -2.65 1.112430 -2.38217285 35.47894 0.022698654 -4.9072632 -0.3927368
# A at b1:    -0.90 1.545244 -0.58243244 17.56296 0.567678242 -4.1522367  2.3522367
# A at b2:     4.20 1.600694  2.62386142 17.93761 0.017246053  0.8362274  7.5637726
# B at a1:    -5.20 1.536952 -3.38331916 17.61093 0.003393857 -8.4341379 -1.9658621
# B at a2:    -0.10 1.608657 -0.06216365 17.91650 0.951120753 -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.

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

Examples

y11 <- c(18, 19, 20, 17, 20, 16)
y12 <- c(19, 18, 19, 20, 17, 16)
y21 <- c(19, 16, 16, 14, 16, 18)
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 -3.910117 8.346534 0.0041247610 -6.0778198 -1.588847
# A:        2.0833333 0.4901814  4.250128 8.346534 0.0025414549  0.9610901  3.205577
# B:        3.7500000 1.0226599  3.666908 7.601289 0.0069250119  1.3700362  6.129964
# A at b1:  0.1666667 0.8333333  0.200000 5.000000 0.8493605140 -1.9754849  2.308818
# A at b2:  4.0000000 0.5163978  7.745967 5.000000 0.0005732451  2.6725572  5.327443
# B at a1:  1.8333333 0.9803627  1.870056 9.943850 0.0911668588 -0.3527241  4.019391
# B at a2:  5.6666667 1.2692955  4.464419 7.666363 0.0023323966  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 design with a quantitative response variable.

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

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  2.2738102  6 0.0633355395 -0.09787945  2.66930802
# A:       -3.21428571 0.4862042 -6.6109784  6 0.0005765210 -4.40398462 -2.02458681
# B:       -0.07142857 0.2296107 -0.3110855  6 0.7662600658 -0.63326579  0.49040865
# A at b1: -2.57142857 0.2973809 -8.6469203  6 0.0001318413 -3.29909331 -1.84376383
# A at b2: -3.85714286 0.7377111 -5.2285275  6 0.0019599725 -5.66225692 -2.05202879
# B at a1:  0.57142857 0.4285714  1.3333333  6 0.2308094088 -0.47724794  1.62010508
# B at a2: -0.71428571 0.2857143 -2.5000000  6 0.0465282323 -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 design with a quantitative response variable. The effects are defined in terms of medians rather than means. Tied scores are assumed to be rare.

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.

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 design where Factor A is the within-subjects factor and Factor B is the between-subjects factor. Effects are defined in terms of medians rather than means. Tied scores 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(19.1, 18.4, 19.8, 20.0, 17.2, 16.8)
y21 <- c(19.2, 16.4, 16.5, 14.0, 16.9, 18.3)
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 design. The effects are defined in terms of medians rather than means. Tied scores 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(221, 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, 221)
ci.2x2.median.ws(.05, y11, y12, y21, y22)

# Should return:
#          Estimate       SE         LL        UL
# AB:          2.50 21.050122 -38.757482 43.75748
# A:          24.75  9.603490   5.927505 43.57250
# B:          18.25  9.101881   0.410641 36.08936
# A at b1:    26.00 11.813742   2.845491 49.15451
# A at b2:    23.50 16.323093  -8.492675 55.49267
# B at a1:    19.50 15.710347 -11.291715 50.29171
# B at a2:    17.00 11.850202  -6.225970 40.22597

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.

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 for test of null hypothesis

• 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.

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 -2.0048193 0.044982370 -0.54287780 -0.00614181
# A:       -0.11764706 0.06846248 -1.7184165 0.085720668 -0.25183106  0.01653694
# B:       -0.03921569 0.06846248 -0.5728055 0.566776388 -0.17339968  0.09496831
# A at b1: -0.25000000 0.09402223 -2.6589456 0.007838561 -0.43428019 -0.06571981
# A at b2:  0.01923077 0.09787658  0.1964798 0.844234654 -0.17260380  0.21106534
# B at a1: -0.17307692 0.09432431 -1.8349132 0.066518551 -0.35794917  0.01179533
# B at a2:  0.09615385 0.09758550  0.9853293 0.324462356 -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.

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

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  0.4264697 0.66976559 -0.02716750  0.042278234
# A:       -0.013678675 0.008858036 -1.5442107 0.12253730 -0.03104011  0.003682758
# B:       -0.058393219 0.023032656 -2.5352360 0.01123716 -0.10353640 -0.013250043
# A at b1: -0.009876543 0.012580603 -0.7850612 0.43241768 -0.03453407  0.014780985
# A at b2: -0.017412935 0.012896543 -1.3502018 0.17695126 -0.04268969  0.007863824
# B at a1: -0.054634236 0.032737738 -1.6688458 0.09514794 -0.11879902  0.009530550
# B at a2: -0.062170628 0.032328556 -1.9230871 0.05446912 -0.12553343  0.001192177

Description

Computes confidence intervals for standardized linear contrasts of means (AB interaction, main effect of A, main effect of B, simple main effects of A, and simple main effects of B) in a 2x2 between-subjects design with a quantitative response variable. Equality of population variances is not assumed. An unweighted 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:      -1.44976487    -1.4193502 0.6885238 -2.7992468 -0.1002829
# A:        0.46904158     0.4592015 0.3379520 -0.1933321  1.1314153
# B:       -0.75330920    -0.7375055 0.3451209 -1.4297338 -0.0768846
# A at b1: -0.25584086    -0.2504736 0.4640186 -1.1653006  0.6536189
# A at b2:  1.19392401     1.1688767 0.5001423  0.2136630  2.1741850
# B at a1: -1.47819163    -1.4471806 0.4928386 -2.4441376 -0.5122457
# B at a2: -0.02842676    -0.0278304 0.4820369 -0.9732017  0.9163482

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.

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, 18, 19, 20, 17, 16)
y21 <- c(19, 16, 16, 14, 16, 18)
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:      -1.95153666   -1.80141845 0.5424100 -3.0146407 -0.8884326
# A:        1.06061775    1.01125934 0.2780119  0.5157244  1.6055111
# B:        1.90911195    1.76225718 0.5743510  0.7834047  3.0348192
# A at b1:  0.08484942    0.07589163 0.4649598 -0.8264549  0.9961538
# A at b2:  2.03638608    1.82139908 0.2964013  1.4554502  2.6173219
# B at a1:  0.93334362    0.86154796 0.5487927 -0.1422703  2.0089575
# B at a2:  2.88488027    2.66296641 0.7127726  1.4878717  4.2818889

Description

Computes confidence intervals for standardized linear contrasts of means (AB interaction, main effect of A, main effect of B, simple main effects of A, and simple main effects of B) in a 2x2 within-subjects design. Equality of population variances is not assumed. An unweighted 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:       0.17248839    0.16446123 0.13654635 -0.095137544 0.4401143
# A:        0.10924265    0.10415878 0.05752822 -0.003510596 0.2219959
# B:        0.07474497    0.07126653 0.05920554 -0.041295751 0.1907857
# A at b1:  0.19548684    0.18638939 0.08460680  0.029660560 0.3613131
# A at b2:  0.02299845    0.02192816 0.09371838 -0.160686202 0.2066831
# B at a1:  0.16098916    0.15349715 0.09457347 -0.024371434 0.3463498
# B at a2: -0.01149923   -0.01096408 0.08595873 -0.179975237 0.1569768

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.

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.

Examples

ci.agree(.05, 100, 80, 4)

# Should return:
#  Estimate         SE        LL        UL
# 0.7333333 0.05333333 0.6132949 0.8226025

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)         0.56666667  0.46601839  0.6524027
# G(1,3)         0.50000000  0.39564646  0.5911956
# G(2,3)         0.86666667  0.79701213  0.9135142
# G(1,2)-G(1,3)  0.06666667  0.00580397  0.1266464
# G(1,2)-G(2,3) -0.30000000 -0.40683919 -0.1891873
# G(2,3)-G(1,3) -0.36666667 -0.46222023 -0.2662566
# G(3)           0.64444444  0.57382971  0.7068720

Description

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

Usage

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

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.

Examples

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

# Should return:
#          Estimate         SE        LL        UL
# G1      0.8666667 0.02880329 0.6974555 0.9481141
# G2      0.5000000 0.05590170 0.2523379 0.6851621
# G1 - G2 0.3666667 0.06288585 0.1117076 0.6088621

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.

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, B. CJ, Stern HS, Rubin DB (2004). Bayesian Data Analysis, 2nd edition. Chapman & Hall.

Examples

ci.bayes.normal(.05, 30, 2, 24.5, 0.577)

# Should return:
# Posterior mean Posterior SD       LL       UL
#        24.9226    0.5543895 23.83602 26.00919

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.

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, B. CJ, Stern HS, Rubin DB (2004). Bayesian Data Analysis, 2nd edition. Chapman & Hall.

Examples

ci.bayes.prop(.05, .4, .1, 12, 100)

# Should return:
# Posterior mean Posterior SD       LL        UL
#           0.15   0.03273268  0.09218 0.2188484

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.

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.

Examples

ci.biphi(.05, 46, 15, 100, 100)

# Should return:
#  Estimate         SE        LL       UL
# 0.4145733 0.07551281 0.2508866 0.546141

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
#  0.8855666 0.06129908  0.7376327 0.984412

Description

Computes a confidence interval for a population coefficient of dispersion which is defined as a mean absolute deviation from the median divided by a median. The coefficient of dispersion assumes ratio-scale scores and is a robust alternative to the coefficient of variation. An approximate standard error is recovered from the confidence interval.

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.

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.

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 - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

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.

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

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 2.269824 0.023218266 
# At high moderator   1.7644      5.838068 2.906507 0.003654887 
#                          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.

Usage

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

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated correlation

• 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.

Examples

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

# Should return:
# Estimate        SE        LL        UL
#    0.536 0.1018149 0.2978573 0.7058914

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.

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.

Examples

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

# Should return:
# Estimate        SE         LL       UL
#    0.217 0.1026986 0.01323072 0.415802

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.

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.

Examples

ci.cor2(.05, .886, .802, 200, 200)

# Should return:
# Estimate         SE         LL        UL
#    0.084 0.02967934 0.02803246 0.1463609

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 can be obtained using the ci.fisher function.

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.

Examples

ci.cor2.gen(.4, .35, .47, .2, .1, .32)

# Should return:
# Estimate   LL        UL
#      0.2 0.07 0.3220656

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. The 25th and 75th percentiles are computed using the type = 2 method (SAS default).

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.

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 and its approximate standard error. The confidence interval is based on a noncentral chi-square distribution, and an approximate standard error is recovered from the confidence interval.

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.

Examples

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

# Should return:
# Estimate     SE     LL     UL
#   0.3099 0.0718 0.1601 0.4417

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.

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.

Examples

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

# Should return:
# Estimate          SE        LL        UL
#     0.85  0.02456518 0.7971254 0.8931436

Description

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

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, 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 0.06973411 0.173236

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.

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

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 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.

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

Examples

ci.etasqr(.05, .241, 3, 116)

# Should return:
# Eta-squared  adj Eta-squared         SE        LL        UL
#       0.241        0.2213707 0.06258283 0.1040229 0.3493431

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, .641, .052)

# Should return:
# Estimate        LL        UL
#    0.641 0.5276396 0.7319293

Description

Computes a Monte Carlo confidence interval (500,000 trials) for a population unstandardized indirect effect in a path model and a Sobel standard error. This function is not recommended for a standardized indirect effect. 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, and (in models with no direct effects) distribution-free Theil-Sen slope estimates with recovered standard errors also could be used.

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

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.

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.

Examples

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

# Should return:
#               Estimate         SE        LL        UL
# IC kappa:    0.6736597 0.07479965 0.5270551 0.8202643
# Cohen kappa: 0.6756757 0.07344761 0.5317210 0.8196303

Description

Computes the estimate, standard error, and approximate confidence interval for a linear contrast of any type of parameter (e.g., quartile, logistic regression slope, path coefficient) where each parameter value has been estimated from a different sample. The parameter values are assumed to be of the same type (e.g., all unstandardized path coefficients) 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.

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 - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

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 6.56829  7 0.000313428 1.875893 3.986329

Description

Computes a test statistic and confidence interval for a linear contrast of means. 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.

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.

Examples

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 
# Equal Variances Assumed:        -5.35 1.300136 -4.114955 36.00000 
# Equal Variances Not Assumed:    -5.35 1.300136 -4.114955 33.52169 
#                                         p         LL        UL
# Equal Variances Assumed:     0.0002152581  -7.986797 -2.713203
# Equal Variances Not Assumed: 0.0002372436  -7.993583 -2.706417

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.

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.

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.

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.

Examples

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

# Should return:
#  Estimate         SE        z           p         LL        UL
# 0.2119565 0.07602892 2.787841 0.005306059 0.06294259 0.3609705

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.

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 - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

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 2.562016 78.8197 0.01231256 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.

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.

Examples

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.stdmean.bs(.05, m, sd, n, v)

# Should return:
#                           Estimate  adj Estimate        SE        LL         UL
# Unweighted standardizer: -1.301263     -1.273964 0.3692800 -2.025039 -0.5774878
# Weighted standardizer:   -1.301263     -1.273964 0.3514511 -1.990095 -0.6124317
# Group 1 standardizer:    -1.393229     -1.273810 0.4849842 -2.343781 -0.4426775

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.

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.

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: -1.301263     -1.266557 0.3147937 -1.918248 -0.6842788
# Level 1 standardizer:    -1.393229     -1.337500 0.3661824 -2.110934 -0.6755248

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.

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.

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.

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.

Examples

y2 <- c(36, 44, 47, 42, 49, 39, 46, 31, 33, 48)
y1 <- c(32, 39, 26, 35, 43, 27, 40, 37, 34, 29)
ci.mann(.05, y1, y2)

# Should return:
# Estimate        SE        LL UL
#    0.795 0.1401834 0.5202456  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.

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

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.

ci.mean1 is deprecated and will soon be removed from statpsych; please switch to ci.mean

Usage

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

ci.mean1(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.

Examples

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

# Should return:
# Estimate        SE       LL       UL
#     24.5 0.5771157 23.33267 25.66733

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.

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

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 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.

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

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 4.670578 29  6.33208e-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.

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.

Examples

ci.mean2(.05, 15.4, 10.3, 2.67, 2.15, 30, 20)

# Should return:
#                              Estimate       SE        t      df      
# Equal Variances Assumed:          5.1 1.602248 3.183029 48.0000 
# Equal Variances Not Assumed:      5.1 1.406801 3.625247 44.1137 
#                                          p       LL       UL
# Equal Variances Assumed:      0.0025578586 1.878465 8.321535
# Equal Variances Not Assumed:  0.0007438065 2.264986 7.935014

Description

Computes a distribution-free confidence interval for a population median.

ci.median1 is deprecated and will soon be removed from statpsych; please switch to ci.median

Usage

ci.median(alpha, y)

ci.median1(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.

Examples

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

# Should return:
# Estimate       SE LL UL
#       20 4.270922 10 30

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.

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.

Examples

y1 <- c(21, 4, 9, 12, 35, 18, 10, 22, 24, 1, 6, 8, 13, 16, 19)
y2 <- c(67, 28, 30, 28, 52, 40, 25, 37, 44, 10, 14, 20, 28, 40, 51)
ci.median.ps(.05, y1, y2)

# Should return:
# Median1 Median2 Median1-Median2       SE        LL        UL  
#      13      30             -17 3.362289 -23.58996 -10.41004 
#      SE1      SE2      COV
# 3.085608 4.509735 9.276849

Description

Computes a distribution-free confidence interval for a difference of population medians in a 2-group design.

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.

Examples

y1 <- c(32, 39, 26, 35, 43, 27, 40, 37, 34, 29)
y2 <- c(36, 44, 47, 42, 49, 39, 46, 31, 33, 48)
ci.median2(.05, y1, y2)

# Should return:
# Median1 Median2 Median1-Median2       SE        LL          UL
#    34.5      43            -8.5 4.316291 -16.95977 -0.04022524

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.

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.

Examples

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

# Should return:
#      Estimate        SE       LL       UL
# [1,] 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.

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.

Examples

f <- c(125, 82, 92)
ci.pairs.mult(.05, f)

# Should return:
#        Estimate         SE          LL         UL
# 1 2  0.14285714 0.04731825  0.05011508 0.23559920
# 1 3  0.10963455 0.04875715  0.01407230 0.20519680
# 2 3 -0.03322259 0.04403313 -0.11952594 0.05308076

Description

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

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.

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 -5.522243 3.346989e-08 -0.35483065 -0.14021885
# 1 3  -0.1039604 0.04833562 -2.150803 3.149174e-02 -0.21967489  0.01175409
# 2 3   0.1435644 0.04358401  3.293968 9.878366e-04  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.

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.

Examples

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

# Should return:
#              Estimate         SE        LL        UL
# Weighted:   0.7065799 0.04890959 0.5885458 0.7854471
# Unweighted: 0.7020871 0.05018596 0.5808366 0.7828948

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.

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.

Examples

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

# Should return:
#  Estimate         SE         LL        UL
#  0.1229976 0.05477117 0.01462398 0.2285149

Description

Computes a confidence interval for a population Poisson rate. This function requires the number of occurences (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, http://dx.doi.org/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.

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

Examples

ci.popsize(.05, 794, 710, 741)

# Should return:
# Estimate       SE   LL   UL
#     2908 49.49071 2818 3012

Description

Computes adjusted Wald and Wilson confidence intervals for a population proportion. The Wilson confidence interval uses a continuity correction.

ci.prop1 is deprecated and will soon be removed from statpsych; please switch to ci.prop

Usage

ci.prop(alpha, f, n)

ci.prop1(alpha, f, n)

Arguments

Value

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

• Estimate - adjusted estimate of proportion

• SE - adjusted standard error

• 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

• LL - lower limit of the Wilson confidence interval

• UL - upper limit of the Wilson confidence interval

References

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, 12, 100)

# Should return:
#                  Estimate         SE         LL        UL
# Adjusted Wald   0.1346154 0.03346842 0.06901848 0.2002123
# Wilson with cc  0.1200000 0.03249615 0.06625153 0.2039772

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.

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

Examples

ci.prop.fpc(.05, 12, 100, 400)

# Should return:
#   Estimate         SE         LL        UL
#  0.1346154  0.0290208 0.07773565 0.1914951

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.

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.

Examples

ci.prop.inv(.05, 5, 67)

# Should return:
#   Estimate         SE         LL        UL
# 0.07462687 0.03145284 0.02467471 0.1479676

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.

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.

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.

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.

Examples

ci.prop2(.05, 35, 21, 150, 150)

# Should return:
#   Estimate         SE          LL        UL
# 0.09210526 0.04476077 0.004375769 0.1798348

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.

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.

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

Description

Computes estimates and confidence intervals for four parameters of the one-way random effects ANOVA: 1) the superpopulation grand mean, 2) the square-root within-group variance component, 3) the square-root between-group variance component, and 4) the omega-squared coefficient. This function assumes equal sample sizes.

Usage

ci.random.anova(alpha, m, sd, n)

Arguments

Value

Returns a 4-row matrix. The rows are:

• Grand mean - the mean of the superpopulation of means

• Within SD - the square-root within-group variance component

• Between SD - the square-root between-group variance component

• Omega-squared - the omega-squared coefficient

The columns are:

• Estimate - estimate of parameter

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

Examples

m <- c(56.1, 51.2, 60.3, 68.2, 48.9, 70.5)
sd <- c(9.45, 8.79, 9.71, 8.90, 8.31, 9.75)
ci.random.anova(.05, m, sd, 20)

# Should return:
#                 Estimate         LL         UL
# Grand mean     59.200000 49.9363896 68.4636104
# Within SD:      9.166782  8.0509046 10.4373219
# Between SD:     8.585948  8.3239359  8.8562078
# Omega-squared:  0.467317  0.2284142  0.8480383

Description

Computes a confidence interval for a ratio of population dispersion coefficients (mean absolute deviation from median divided by median) in a 2-group design. Ratio-scale scores are assumed.

Usage

ci.ratio.cod2(alpha, y1, y2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• COD1 - estimated coefficient of dispersion in group 1

• COD2 - estimated coefficient of dispersion in group 2

• COD1/COD2 - estimated ratio of dispersion coefficients

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

Examples

y1 <- c(32, 39, 26, 35, 43, 27, 40, 37, 34, 29)
y2 <- c(36, 44, 47, 42, 49, 39, 46, 31, 33, 48)
ci.ratio.cod2(.05, y1, y2)

# Should return:
#      COD1      COD2 COD1/COD2       LL       UL
# 0.1333333 0.1232558  1.081761 0.494964 2.282254

Description

Computes a confidence interval for a ratio of population coefficients of variation (CV) in a 2-group design. This confidence interval uses the confidence interval for each CV and then uses the MOVER-DL method (see Newcombe, page 138) to obtain a confidence interval for CV1/CV2. The CV assumes ratio-scale scores.

Usage

ci.ratio.cv2(alpha, m1, m2, sd1, sd2, n1, n2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimated ratio of coefficients of variation

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Newcombe RG (2013). Confidence Interval for Proportions and Related Measures of Effect Size. CRC Press.

Examples

ci.ratio.cv2(.05, 34.5, 26.1, 4.15, 2.26, 50, 50)

# Should return:
# Estimate       LL       UL
# 1.389188 1.041478 1.854101

Description

Computes a confidence interval for a ratio of population MADs (mean absolute deviation from median) in a paired-samples design.

Usage

ci.ratio.mad.ps(alpha, y1, y2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• MAD1 - estimated MAD for measurement 1

• MAD2 - estimated MAD for measurement 2

• MAD1/MAD2 - estimate of MAD ratio

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG, Seier E (2003). “Statistical inference for a ratio of dispersions using paired samples.” Journal of Educational and Behavioral Statistics, 28(1), 21–30. ISSN 1076-9986, doi:10.3102/10769986028001021.

Examples

y2 <- c(21, 4, 9, 12, 35, 18, 10, 22, 24, 1, 6, 8, 13, 16, 19)
y1 <- c(67, 28, 30, 28, 52, 40, 25, 37, 44, 10, 14, 20, 28, 40, 51)
ci.ratio.mad.ps(.05, y1, y2)

# Should return:
#     MAD1  MAD2  MAD1/MAD2       LL       UL
# 12.71429   7.5   1.695238 1.109176 2.590961

Description

Computes a confidence interval for a ratio of population MADs (mean absolute deviation from median) in a 2-group design.

Usage

ci.ratio.mad2(alpha, y1, y2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• MAD1 - estimated MAD for group 1

• MAD2 - estimated MAD for group 2

• MAD1/MAD2 - estimate of MAD ratio

• 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.

Examples

y1 <- c(32, 39, 26, 35, 43, 27, 40, 37, 34, 29)
y2 <- c(36, 44, 47, 42, 49, 39, 46, 31, 33, 48)
ci.ratio.mad2(.05, y1, y2)

# Should return:
#     MAD1     MAD2  MAD1/MAD2        LL       UL
# 5.111111 5.888889  0.8679245 0.4520879 1.666253

Description

Computes a confidence interval for a ratio of population mean absolute prediction errors from a general linear model in two independent groups. The number of predictor variables can differ across groups and the two models can be non-nested. This function requires a vector of estimated residuals from each group. This function does not assume zero excess kurtosis but does assume symmetry in the population prediction errors for the two models.

Usage

ci.ratio.mape2(alpha, res1, res2, s1, s2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• MAPE1 - bias adjusted mean absolute prediction error for group 1

• MAPE2 - bias adjusted mean absolute prediction error for group 2

• MAPE1/MAPE2 - ratio of bias adjusted mean absolute prediction errors

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

Examples

res1 <- 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)
res2 <- c(-0.71, -0.89, 0.72, -0.35, 0.33 -0.92, 2.37, 0.51, 0.68, -0.85,
        -0.15, 0.77, -1.52, 0.89, -0.29, -0.23, -0.94, 0.93, -0.31 -0.04)
ci.ratio.mape2(.05, res1, res2, 1, 1)

# Should return:
#   MAPE1     MAPE2 MAPE1/MAPE2       LL       UL
# 2.58087 0.8327273    3.099298 1.917003 5.010761

Description

Compute a confidence interval for a ratio of population means of ratio-scale measurements in a paired-samples design. Equality of variances is not assumed.

Usage

ci.ratio.mean.ps(alpha, y1, y2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Mean1 - estimated measurement 1 mean

• Mean2 - estimated measurement 2 mean

• Mean1/Mean2 - estimate of mean ratio

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG, Price RM (2020). “Confidence intervals for ratios of means and medians.” Journal of Educational and Behavioral Statistics, 45(6), 750–770. doi:10.3102/1076998620934125.

Examples

y1 <- c(3.3, 3.6, 3.0, 3.1, 3.9, 4.2, 3.5, 3.3)
y2 <- c(3.0, 3.1, 2.7, 2.6, 3.2, 3.8, 3.2, 3.0)
ci.ratio.mean.ps(.05, y1, y2)

# Should return:
#  Mean1 Mean2 Mean1/Mean2      LL       UL
# 3.4875 3.075    1.134146 1.09417 1.175583

Description

Computes a confidence interval for a ratio of population means of ratio-scale measurements in a 2-group design. Equality of variances is not assumed.

Usage

ci.ratio.mean2(alpha, y1, y2)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Mean1 - estimated mean for group 1

• Mean2 - estimated mean for group 2

• Mean1/Mean2- estimated mean ratio

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG, Price RM (2020). “Confidence intervals for ratios of means and medians.” Journal of Educational and Behavioral Statistics, 45(6), 750–770. doi:10.3102/1076998620934125.

Examples

y2 <- c(32, 39, 26, 35, 43, 27, 40, 37, 34, 29, 49, 42, 40)
y1 <- c(36, 44, 47, 42, 49, 39, 46, 31, 33, 48)
ci.ratio.mean2(.05, y1, y2)

# Should return:
#
# Mean1    Mean2 Mean1/Mean2        LL       UL
#  41.5 36.38462    1.140592 0.9897482 1.314425

Description

Computes a distribution-free confidence interval for a ratio of population medians in a paired-samples design. Ratio-scale measurements are assumed.

Usage

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

Arguments