Cohensdp {CohensdpLibrary}

Cohen's standardized mean difference.

Description

Cohensdp() computes the Cohen's d (noted $d_p$) and its confidence interval in either within-subject, between-subject design and single-group design. For the between-subject design, MBESS already has an implementation based on the "pivotal" method but the present method is faster, using the method based on the Lambda prime distribution (Lecoutre 2007). See Hedges (1981); Cousineau (2022, submitted); Goulet-Pelletier and Cousineau (2018).

Usage

Cohensdp(statistics, design, gamma, method )

Arguments

statistics

a list of pre-computed statistics. The statistics to provide depend on the design: - for "between": m1, m2 the means of the two groups, s1, s2 the standard deviation of the two groups, and n1, n2, the sample sizes of the two groups; - for "within": m1, m2, s1, s2, n, and r or rho the correlation between the measure; - for "single": m, s, n and m0 the reference mean from which m is standardized).

design

the design of the measures ("within", "between", or "single");

gamma

the confidence level of the confidence interval (default 0.95)

method

In "within"-subject design only, choose among methods "piCI", or "adjustedlambdaprime" (default), "alginakeselman2003", "morris2000", and "regressionapproximation".

Details

This function uses the exact method in "single"-group and "between"-subject designs. In "within"-subject design, the default is the adjusted Lambda prime confidence interval ("adjustedlambdaprime") which is based on an approximate method. This method is described in Cousineau (submitted). Other methods are available, described in Morris (2000); Algina and Keselman (2003); Cousineau and Goulet-Pelletier (2021); Fitts (2022)

Value

The Cohen's $d_p$ statistic and its confidence interval. The return value is internally a dpObject which can be displayed with print, explain or summary/summarize.

References

Algina J, Keselman HJ (2003). “Approximate confidence intervals for effect sizes.” Educational and Psychological Measurement, 63, 537 – 553. doi:10.1177/0013164403256358.

Cousineau D (2022). “The exact distribution of the Cohen's d_p in repeated-measure designs.” doi:10.31234/osf.io/akcnd, https://psyarxiv.com/akcnd/.

Cousineau D, Goulet-Pelletier J (2021). “A study of confidence intervals for Cohen's dp in within-subject designs with new proposals.” The Quantitative Methods for Psychology, 17, 51 – 75. doi:10.20982/tqmp.17.1.p051.

Cousineau D (submitted). “The exact confidence interval of the Cohen's d_p in repeated-measure designs.” The Quantitative Methods for Psychology.

Fitts DA (2022). “Point and interval estimates for a standardized mean difference in paired-samples designs using a pooled standard deviation.” The Quantitative Methods for Psychology, 18(2), 207-223. doi:10.20982/tqmp.18.2.p207.

Goulet-Pelletier J, Cousineau D (2018). “A review of effect sizes and their confidence intervals, Part I: The Cohen's d family.” The Quantitative Methods for Psychology, 14(4), 242-265. doi:10.20982/tqmp.14.4.p242.

Hedges LV (1981). “Distribution theory for Glass's estimator of effect size and related estimators.” journal of Educational Statistics, 6(2), 107–128.

Lecoutre B (2007). “Another look at confidence intervals from the noncentral T distribution.” Journal of Modern Applied Statistical Methods, 6, 107 – 116. doi:10.22237/jmasm/1177992600.

Morris SB (2000). “Distribution of the standardized mean change effect size for meta-analysis on repeated measures.” British Journal of Mathematical and Statistical Psychology, 53, 17 – 29. doi:10.1348/000711000159150.

Examples

# example in which the means are 114 vs. 101 with sds of 14.3 and 12.5 respectively
Cohensdp( statistics = list( m1= 101, m2= 114, s1= 12.5, s2= 14.3, n1= 12, n2= 12 ), 
          design     = "between")

# example in a repeated-measure design
Cohensdp(statistics =list( m1= 101, m2= 114, s1= 12.5, s2= 14.3, n= 12, rho= 0.53 ),
         design     ="within" )

# example with a single-group design where mu is a population parameter
Cohensdp( statistics = list( m = 101, m0 = 114, s = 12.5, n = 10 ), 
          design     = "single")

# The results can be displayed in three modes
res <- Cohensdp( statistics = list( m = 101, m0 = 114, s = 12.5, n = 10), 
                 design     = "single")

# a raw result of the Cohen's d_p and its confidence interval
res              

# a human-readable output
summarize( res ) 

# ... and a human-readable ouptut with additional explanations.
explain( res )   

# example in a repeated-measure design with a different method than piCI
Cohensdp(statistics =list( m1= 101, m2= 114, s1= 12.5, s2= 14.3, n= 12, r= 0.53 ),
         design     ="within", method = "adjustedlambdaprime")