# wp.anova: Statistical Power Analysis for One-way ANOVA In WebPower: Basic and Advanced Statistical Power Analysis

## Description

One-way analysis of variance (one-way ANOVA) is a technique used to compare means of two or more groups (e.g., Maxwell & Delaney, 2003). The ANOVA tests the null hypothesis that samples in two or more groups are drawn from populations with the same mean values. The ANOVA analysis typically produces an F-statistic, the ratio of the bewteen-group variance to the within-group variance.

## Usage

 ```1 2``` ```wp.anova(k = NULL, n = NULL, f = NULL, alpha = 0.05, power = NULL, type = c("overall", "two.sided", "greater", "less")) ```

## Arguments

 `k` Number of groups. `n` Sample size. `f` Effect size. We use the statistic f as the measure of effect size for one-way ANOVA as in Cohen (1988). Cohen defined the size of effect as: small 0.1, medium 0.25, and large 0.4. `alpha` Significance level chosed for the test. It equals 0.05 by default. `power` Statistical power. `type` Type of test (`"overall"` or `"two.sided"` or `"greater"` or `"less"`). The default is "two.sided". The option "overall" is for the overall test of anova; "two.sided" is for a contrast anova; "greater" is testing the between-group vairance greater than the within-group, while "less" is vis versus.

## 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.

Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: A model comparison perspective (Vol. 1). Psychology Press.

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 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81``` ```#To calculate the statistical power for the overall test of one-way ANOVA: wp.anova(f=0.25,k=4, n=100, alpha=0.05) # Power for One-way ANOVA # # k n f alpha power # 4 100 0.25 0.05 0.5181755 # # NOTE: n is the total sample size (overall) # URL: http://psychstat.org/anova #To calculate the power curve with a sequence of sample sizes: res <- wp.anova(f=0.25, k=4, n=seq(100,200,10), alpha=0.05) res # Power for One-way ANOVA # # k n f alpha power # 4 100 0.25 0.05 0.5181755 # 4 110 0.25 0.05 0.5636701 # 4 120 0.25 0.05 0.6065228 # 4 130 0.25 0.05 0.6465721 # 4 140 0.25 0.05 0.6837365 # 4 150 0.25 0.05 0.7180010 # 4 160 0.25 0.05 0.7494045 # 4 170 0.25 0.05 0.7780286 # 4 180 0.25 0.05 0.8039869 # 4 190 0.25 0.05 0.8274169 # 4 200 0.25 0.05 0.8484718 # # NOTE: n is the total sample size (overall) # URL: http://psychstat.org/anova #To plot the power curve: plot(res, type='b') #To estimate the sample size with a given power: wp.anova(f=0.25,k=4, n=NULL, alpha=0.05, power=0.8) # Power for One-way ANOVA # # k n f alpha power # 4 178.3971 0.25 0.05 0.8 # # NOTE: n is the total sample size (overall) # URL: http://psychstat.org/anova #To estimate the minimum detectable effect size with a given power: wp.anova(f=NULL,k=4, n=100, alpha=0.05, power=0.8) # Power for One-way ANOVA # # k n f alpha power # 4 100 0.3369881 0.05 0.8 # # NOTE: n is the total sample size (overall) # URL: http://psychstat.org/anova #To conduct power analysis for a contrast one-way ANOVA: wp.anova(f=0.25,k=4, n=100, alpha=0.05, type='two.sided') # Power for One-way ANOVA # # k n f alpha power # 4 100 0.25 0.05 0.6967142 # # NOTE: n is the total sample size (contrast, two.sided) # URL: http://psychstat.org/anova #To calculate the power curve with a sequence of sample sizes: res <- wp.anova(f=seq(0.1, 0.8, 0.1), k=4, n=100, alpha=0.05) res # Power for One-way ANOVA # # k n f alpha power # 4 100 0.1 0.05 0.1128198 # 4 100 0.2 0.05 0.3452612 # 4 100 0.3 0.05 0.6915962 # 4 100 0.4 0.05 0.9235525 # 4 100 0.5 0.05 0.9911867 # 4 100 0.6 0.05 0.9995595 # 4 100 0.7 0.05 0.9999908 # 4 100 0.8 0.05 0.9999999 # # NOTE: n is the total sample size (overall) # URL: http://psychstat.org/anova ```

### Example output ```Loading required package: MASS
Loading required package: lme4
Loading required package: Matrix
Loading required package: lavaan
This is lavaan 0.6-3
lavaan is BETA software! Please report any bugs.
Loading required package: parallel
Loading required package: PearsonDS
Power for One-way ANOVA

k   n    f alpha     power
4 100 0.25  0.05 0.5181755

NOTE: n is the total sample size (overall)
URL: http://psychstat.org/anova
Power for One-way ANOVA

k   n    f alpha     power
4 100 0.25  0.05 0.5181755
4 110 0.25  0.05 0.5636701
4 120 0.25  0.05 0.6065228
4 130 0.25  0.05 0.6465721
4 140 0.25  0.05 0.6837365
4 150 0.25  0.05 0.7180010
4 160 0.25  0.05 0.7494045
4 170 0.25  0.05 0.7780286
4 180 0.25  0.05 0.8039869
4 190 0.25  0.05 0.8274169
4 200 0.25  0.05 0.8484718

NOTE: n is the total sample size (overall)
URL: http://psychstat.org/anova
Power for One-way ANOVA

k        n    f alpha power
4 178.3971 0.25  0.05   0.8

NOTE: n is the total sample size (overall)
URL: http://psychstat.org/anova
Power for One-way ANOVA

k   n         f alpha power
4 100 0.3369881  0.05   0.8

NOTE: n is the total sample size (overall)
URL: http://psychstat.org/anova
Power for One-way ANOVA

k   n    f alpha     power
4 100 0.25  0.05 0.6967142

NOTE: n is the total sample size (contrast, two.sided)
URL: http://psychstat.org/anova
Power for One-way ANOVA

k   n   f alpha     power
4 100 0.1  0.05 0.1128198
4 100 0.2  0.05 0.3452612
4 100 0.3  0.05 0.6915962
4 100 0.4  0.05 0.9235525
4 100 0.5  0.05 0.9911867
4 100 0.6  0.05 0.9995595
4 100 0.7  0.05 0.9999908
4 100 0.8  0.05 0.9999999

NOTE: n is the total sample size (overall)
URL: http://psychstat.org/anova
```

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