# wp.rmanova: Statistical Power Analysis for Repeated Measures ANOVA In WebPower: Basic and Advanced Statistical Power Analysis

## Description

Repeated-measures ANOVA can be used to compare the means of a sequence of measurements (e.g., O'brien & Kaiser, 1985). In a repeated-measures design, evey subject is exposed to all different treatments, or more commonly measured across different time points. Power analysis for (1) the within-effect test about the mean difference among measurements by default. If the subjects are from more than one group,the power analysis is also available for (2) the between-effect test about mean difference among groups and (3) the interaction effect test of the measurements and groups.

## Usage

 ```1 2``` ```wp.rmanova(n = NULL, ng = NULL, nm = NULL, f = NULL, nscor = 1, alpha = 0.05, power = NULL, type = 0) ```

## Arguments

 `n` Sample size. `ng` Number of groups. `nm` Number of measurements. `f` Effect size. We use the statistic f as the measure of effect size for repeated-measures ANOVA as in Cohen(1988, p.275). `nscor` Nonsphericity correction coefficient. The nonsphericity correction coefficient is a measure of the degree of sphericity in the population. A coefficient of 1 means sphericity is met, while a coefficient less than 1 means not met. The samller value of the coefficient means the further departure from sphericity. The lowest value of the coefficient is 1/(nm-1) where nm is the total number of measurements. Two viable approaches for computing the empirical nonsphericity correction coefficient are sggested. One is by Greenhouse and Geisser (1959), the other is by Huynh and Feldt (1976). `alpha` significance level chosed for the test. It equals 0.05 by default. `power` Statistical power. `type` Type of analysis (`0` or `1` or `2`). The value "0" is for between-effect; "1" is for within-effect; and "2" is for interaction effect.

## Value

An object of the power analysis

## References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed). Hillsdale, NJ: Lawrence Erlbaum Associates.

Greenhouse, S. W., & Geisser, S. (1959). On methods in the analysis of profile data. Psychometrika, 24(2), 95-112.

Huynh, H., & Feldt, L. S. (1976). Estimation of the Box correction for degrees of freedom from sample data in randomized block and split-plot designs. Journal of educational statistics, 1(1), 69-82.

O'brien, R. G., & Kaiser, M. K. (1985). MANOVA method for analyzing repeated measures designs: an extensive primer. Psychological bulletin, 97(2), 316.

Zhang, Z., & Yuan, K.-H. (2018). Practical Statistical Power Analysis Using Webpower and R (Eds). Granger, IN: ISDSA Press.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66``` ```#To calculate the statistical power for repeated-measures ANOVA: wp.rmanova(n=30, ng=3, nm=4, f=0.36, nscor=0.7) # Repeated-measures ANOVA analysis # # n f ng nm nscor alpha power # 30 0.36 3 4 0.7 0.05 0.2674167 # # NOTE: Power analysis for between-effect test # URL: http://psychstat.org/rmanova #To generate a power curve given a sequence of sample sizes: wp.rmanova(n=seq(30,150,20), ng=3, nm=4, f=0.36, nscor=0.7) # Repeated-measures ANOVA analysis # # n f ng nm nscor alpha power # 30 0.36 3 4 0.7 0.05 0.2674167 # 50 0.36 3 4 0.7 0.05 0.4386000 # 70 0.36 3 4 0.7 0.05 0.5894599 # 90 0.36 3 4 0.7 0.05 0.7110142 # 110 0.36 3 4 0.7 0.05 0.8029337 # 130 0.36 3 4 0.7 0.05 0.8691834 # 150 0.36 3 4 0.7 0.05 0.9151497 # # NOTE: Power analysis for between-effect test # URL: http://psychstat.org/rmanova #To plot the power curve: plot(res) #To calculate the required sample size given power and effect size: wp.rmanova(n=NULL, ng=3, nm=4, f=0.36, power=0.8, nscor=0.7) # Repeated-measures ANOVA analysis # # n f ng nm nscor alpha power # 109.2546 0.36 3 4 0.7 0.05 0.8 # # NOTE: Power analysis for between-effect test # URL: http://psychstat.org/rmanova #To calculate the minimum detectable effect size given power and sample size: wp.rmanova(n=30, ng=3, nm=4, f=NULL, power=0.8, nscor=0.7) # Repeated-measures ANOVA analysis # # n f ng nm nscor alpha power # 30 0.716768 3 4 0.7 0.05 0.8 # # NOTE: Power analysis for between-effect test # URL: http://psychstat.org/rmanova # To generate a power curve given a sequence of effec sizes: wp.rmanova(n=30, ng=3, nm=4, f=seq(0.1,0.5,0.05), nscor=0.7) # Repeated-measures ANOVA analysis # # n f ng nm nscor alpha power # 30 0.10 3 4 0.7 0.05 0.06442235 # 30 0.15 3 4 0.7 0.05 0.08327886 # 30 0.20 3 4 0.7 0.05 0.11101678 # 30 0.25 3 4 0.7 0.05 0.14853115 # 30 0.30 3 4 0.7 0.05 0.19640404 # 30 0.35 3 4 0.7 0.05 0.25460008 # 30 0.40 3 4 0.7 0.05 0.32223192 # 30 0.45 3 4 0.7 0.05 0.39746082 # 30 0.50 3 4 0.7 0.05 0.47757523 # # NOTE: Power analysis for between-effect test # URL: http://psychstat.org/rmanova ```

WebPower documentation built on May 1, 2019, 8:19 p.m.