meanDiff: meanDiff

In userfriendlyscience: Quantitative Analysis Made Accessible

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, r.prepost = NULL, var.equal = "test",
         conf.level = .95, plot = FALSE, 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.
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).

Details

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

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).

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);

Example output

sh: 1: cannot create /dev/null: Permission denied
Input variables:

  group (grouping variable)
  weight (dependent variable)
  Mean 1 (ctrl) = 5.03, sd = 0.58, n = 10
  Mean 2 (trt1)= 4.66, sd = 0.79, n = 10

Independent samples t-test (tested for equal variances, p = .372, so equal variances)
  (pooled standard deviation used, 0.7)

95% confidence intervals:
  Absolute mean difference: [-0.28, 1.03] (Absolute mean difference: 0.37)
  Cohen's d for difference: [-0.36, 1.42] (Cohen's d point estimate: 0.53)
  Hedges g for difference:  [-0.34, 1.36] (Hedges g point estimate:  0.51)

Achieved power for d=0.53: 0.2038 (for small: 0.0708; medium: 0.1851; large: 0.3951)

(secondary information (NHST): t[18] = 1.19, p = .249)
Input variables:

  group (grouping variable)
  weight (dependent variable)
  Mean 1 (ctrl) = 5.03, sd = 0.58, n = 10
  Mean 2 (trt2)= 5.53, sd = 0.44, n = 10

Independent samples t-test (tested for equal variances, p = .424, so equal variances)
  (pooled standard deviation used, 0.52)

95% confidence intervals:
  Absolute mean difference: [-0.98, -0.01] (Absolute mean difference: -0.49)
  Cohen's d for difference: [-1.88, -0.03] (Cohen's d point estimate: -0.95)
  Hedges g for difference:  [-1.8, -0.03] (Hedges g point estimate:  -0.91)

Achieved power for d=-0.95: 0.5238 (for small: 0.0708; medium: 0.1851; large: 0.3951)

(secondary information (NHST): t[18] = -2.13, p = .047)

userfriendlyscience documentation built on May 2, 2019, 1:09 p.m.