# ind.twoway.second: A two-way design with independent samples using published... In rpsychi: Statistics for psychiatric research

## Description

`ind.twoway.second` conducts a two-way design with independent samples, namely two-way randomized-group analysis of variance, using published work.

## Usage

 ```1 2``` ``` ind.twoway.second(m, sd, n, unbiased = TRUE, sig.level = 0.05, digits = 3) ```

## Arguments

 `m` a matrix contains the means `sd` a matrix contains the sample/unbiased standard deviations `n` a matrix contains the sample size `unbiased` `sd` contains unbiased standard deviations (`unbiased` = TRUE, default) or sample standard deviations (`unbiased` = FALSE) `sig.level` a numeric contains the significance level (default 0.05) `digits` the specified number of decimal places (default 3)

## Details

This function conducts a two-way design with independent samples, namely two-way randomized-group analysis of variance, using published work. Statistical power is calculated using the following specifications:

(a) small (η^2 = 0.01), medium (η^2 = 0.06), and large (η^2 = 0.14) population effect sizes, according to the interpretive guideline for effect sizes by Cohen (1992)

(b) sample size specified by `n`

(c) significance level specified by `sig.level`

## Value

The returned object of `ind.oneway.second` contains the following components:

 `anova.table` returns a ANOVA table containing sums of squares, degrees of freedom, mean squares, F values `omnibus.es` returns a omnibus effect sizes which is a partial η^2, and its' confidence interval for each main and interaction effect `power` returns statistical power for detecting small (η^2 = 0.01), medium (η^2 = 0.06), and large (η^2 = 0.14) population effect sizes

## Author(s)

Yasuyuki Okumura
Department of Social Psychiatry,
National Institute of Mental Health,
National Center of Neurology and Psychiatry
yokumura@blue.zero.jp

## References

Cohen B (2000) Calculating a factorial ANOVA from means and standard deviations. Understanding Statistics, 1, 191-203.

Cohen J (1992) A power primer. Psychological Bulletin, 112, 155-159.

Kline RB (2004) Beyond significance testing: Reforming data analysis methods in behavioral research. Washington: American Psychological Association.

Tabachnick BG, Fidell LS (2007) Experimental designs using ANOVA. Belmont, CA: Thomson.

`ind.twoway`
 ``` 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``` ```##Cohen (2000) Table 1 m.mat <- matrix(c(37.13, 39.31, 39.22, 32.71), ncol=2) #2 * 2 sd.mat <- matrix(c(13.82, 9.42, 9.43, 9.62), ncol=2) n.mat <- matrix(c(9, 13, 8, 14), ncol=2) ind.twoway.second(m = m.mat, sd = sd.mat, n = n.mat) ##Tabachnick and Fidell (2007) #5.7 Complete example of two-way randomized-groups ANOVA (p.221-236) m.mat <- matrix(c(837.9, 573.6, 354.9, 699.0, 112.0, 852.2, 781.6, 683.3, 1193.9, 130.0), ncol=2) #5 * 2 sd.mat <- matrix(c(189.87449, 61.31195, 147.93351, 128.51891, 43.36922, 227.17042, 104.81221, 116.25934, 198.36692, 37.64158), ncol=2) #5 * 2 n.mat <- matrix(rep(10, 10), ncol=2) ind.twoway.second(m = m.mat, sd = sd.mat, n = n.mat) ##Kline (2004) Table 7.5 dat <- data.frame( y = c(2,3,4,1,3,1,3,4,5,5,6,6,6,7), A = factor(c(rep("A1",5), rep("A2", 9))), B = factor(c(rep("B1",3), rep("B2",2), rep("B1",2), rep("B2",7))) ) ind.twoway.second(m = tapply(dat\$y, list(dat\$A,dat\$B), mean), sd = tapply(dat\$y, list(dat\$A,dat\$B), sd), n = tapply(dat\$y, list(dat\$A,dat\$B), length) ) ```