The meanDiff function compares the means between two groups. It computes Cohen's d, the unbiased estimate of Cohen's d (Hedges' g), and performs a t-test. It also shows the achieved power, and, more usefully, the power to detect small, medium, and large effects.

```
meanDiff(x, y=NULL, paired = FALSE, r.prepost = NULL, var.equal = "test",
conf.level = .95, plot = FALSE, digits = 2, envir = parent.frame())
```

x

Dichotomous factor: variable 1; can also be a formula of the form y ~ x, where x must be a factor with two levels (i.e. dichotomous).

y

Numeric vector: variable 2; can be empty if x is a formula.

paired

Boolean; are x & y independent or dependent? Note that if x & y are dependent, they need to have the same length.

r.prepost

Correlation between the pre- and post-test in the case of a paired samples t-test. This is required to compute Cohen's d using the formula on page 29 of Borenstein et al. (2009). If NULL, the correlation is simply computed from the provided scores (but of course it will then be lower if these is an effect - this will lead to an underestimate of the within-groups variance, and therefore, of the standard error of Cohen's d, and therefore, to confidence intervals that are too narrow (too liberal). Also, of course, when using this data to compute the within-groups correlation, random variations will also impact that correlation, which means that confidence intervals may in practice deviate from the null hypothesis significance testing p-value in either direction (i.e. the p-value may indicate a significant association while the confidence interval contains 0, or the other way around). Therefore, if the test-retest correlation of the relevant measure is known, please provide this here to enable computation of accurate confidence intervals.

var.equal

String; only relevant if x & y are independent; can be "test" (default; test whether x & y have different variances), "no" (assume x & y have different variances; see the Warning below!), or "yes" (assume x & y have the same variance)

conf.level

Confidence of confidence intervals you want.

plot

Whether to print a dlvPlot.

digits

With what precision you want the results to print.

envir

The environment where to search for the variables (useful when calling meanDiff from a function where the vectors are defined in that functions environment).

An object is returned with the following elements:

Input variables

Levels of the x variable, the dichotomous factor

Confidence of confidence intervals

Number of digits for output

Values of dependent variable in first group

Values of dependent variable in second group

Type of t-test (independent or dependent, equal variances or not)

Sample sizes of the two groups

Means of the two groups

Standard deviations of the two groups

Objects used; the t-test and optionally the test for equal variances

Variance of the difference score

Difference between the means

Cohen's d

Variance of Cohen's d

Standard error of Cohen's d

Correction for Cohen's d to get to the unbiased Hedges g

Achieved power with current effect size and sample size

Power to detect small effects with current sample size

Power to detect medium effects with current sample size

Power to detect large effects with current sample size

Hedges' g

Variance of Hedges' g

Standard error of Hedges' g

Z value used to compute confidence intervals

Lower bound of confidence interval around Cohen's d

Upper bound of confidence interval around Cohen's d

Lower bound of confidence interval around Hedges' g

Upper bound of confidence interval around Hedges' g

Lower bound of confidence interval around raw mean

Upper bound of confidence interval around raw mean

Student t value for Null Hypothesis Significance Testing

Degrees of freedom for t value

p-value corresponding to t value

Note that when different variances are assumed for the t-test (i.e. the null-hypothesis test), the values of Cohen's d are still based on the assumption that the variance is equal. In this case, the confidence interval might, for example, not contain zero even though the NHST has a non-significant p-value (the reverse can probably happen, too).

This function uses the formulae from Borenstein, Hedges, Higgins & Rothstein (2009) (pages 25-32).

Borenstein, M., Hedges, L. V., Higgins, J. P., & Rothstein, H. R. (2011). Introduction to meta-analysis. John Wiley & Sons.

```
# NOT RUN {
### Create simple dataset
dat <- PlantGrowth[1:20,];
### Remove third level from group factor
dat$group <- factor(dat$group);
### Compute mean difference and show it
meanDiff(dat$weight ~ dat$group);
### Look at second treatment
dat <- rbind(PlantGrowth[1:10,], PlantGrowth[21:30,]);
### Remove third level from group factor
dat$group <- factor(dat$group);
### Compute mean difference and show it
meanDiff(x=dat$group, y=dat$weight);
# }
```

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