userfriendlyscience (version 0.1-2)

meanDiff: meanDiff

Description

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.

Usage

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

Arguments

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.

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.

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).

Value

• An object is returned with the following elements:
• variables
  Input variables
• groups
  Levels of the x variable, the dichotomous factor
• ci.confidence
  Confidence of confidence intervals
• digits
  Number of digits for output
• x
  Values of dependent variable in first group
• y
  Values of dependent variable in second group
• type
  Type of t-test (independent or dependent, equal variances or not)
• n
  Sample sizes of the two groups
• mean
  Means of the two groups
• sd
  Standard deviations of the two groups
• objects
  Objects used; the t-test and optionally the test for equal variances
• variance
  Variance of the difference score
• meanDiff
  Difference between the means
• meanDiff.d
  Cohen's d
• meanDiff.d.var
  Variance of Cohen's d
• meanDiff.d.se
  Standard error of Cohen's d
• meanDiff.J
  Correction for Cohen's d to get to the unbiased Hedges g
• power
  Achieved power with current effect size and sample size
• power.small
  Power to detect small effects with current sample size
• power.medium
  Power to detect medium effects with current sample size
• power.largel
  Power to detect large effects with current sample size
• meanDiff.g
  Hedges' g
• meanDiff.g.var
  Variance of Hedges' g
• meanDiff.g.se
  Standard error of Hedges' g
• ci.usedZ
  Z value used to compute confidence intervals
• meanDiff.d.ci.lower
  Lower bound of confidence interval around Cohen's d
• meanDiff.d.ci.upper
  Upper bound of confidence interval around Cohen's d
• meanDiff.g.ci.lower
  Lower bound of confidence interval around Hedges' g
• meanDiff.g.ci.upper
  Upper bound of confidence interval around Hedges' g
• meanDiff.ci.lower
  Lower bound of confidence interval around raw mean
• meanDiff.ci.upper
  Upper bound of confidence interval around raw mean
• t
  Student t value for Null Hypothesis Significance Testing
• df
  Degrees of freedom for t value
• p
  p-value corresponding to t value

Warning

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).

Details

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

References

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

Examples

### 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);