Planning for Precise Contrasts: Tutorial for single factor designs

library(shiny)
library(devtools)
source_url("https://git.io/fpI1R")
shinyApp(ui = ui, server = server)

Examples 

Figure 1. Values for Target MoE, assurance and design

Figure 2: Standard contrasts for comparison of two conditions

The output is as follows:

The results give you the sample size for each condition (n), and information about target MoE (f), assurance (assu), the number of conditions (k), and the cross-condition correlation (cor; the value is zero, as it should be in the independent design). With n = 55, there is a 80% probability that f will not be larger than .40.

If you use 55 participants per group the expected MoE equals 0.38.

Of course, using 55 participants per group, makes the total sample size equal to 110.

The output also included a plot of the expected results (what you can expect to happen on average). See Figure 3.

Figure 3: Expected results using n = 55 participants per group in the two groups independent design

This output helps you to consider whether the Expected MoE is small enough. Suppose, for instance, that true difference equals .5 standard deviations, i.e. a medium effect. The figure shows that the expected contrast estimate is a medium effect, and the confidence interval shows that on average values ranging from small to large effects [.12, .88] will be included in the interval. If the difference between small, medium and large effects is important, an expected precision of f = .38 may not be enough, although small and large effects are at the limits of the confidence interval.

A four groups dependent design 

Technical Note: The app assumes that the sum of squares of the Error Variance can be decomposed in (k – 1) equal parts, where k is the number of conditions. I will change this restriction in a future version of the app. For a custom contrast it is assumed that the contrast is part of an orthogonal set.

Suppose your major interest is the comparison between the average of two groups and the average of two other groups. You have a dependent (repeated measures) design in which participants will be exposed to each of the four treatment conditions. Let’s plan for a target MoE of f = 0.25, with 80 % assurance and let’s suppose our cross-condition correlation equals r = .70. I choose a custom contrast with weights {1/2, 1/2, -1/2, -1/2} (see Figure 4).

Figure 4. Input for sample size planning

The output is as follows.

So, we need 26 participants to have 80% assurance that obtained MoE will not be larger than f = 0.25. Expected MoE is equal to .22. According to the guidelines above, this is a precise estimate.

If you choose “Helmert Contrasts” instead, and press the button without changing anything, the output is as follows.

Under Expected Moe you will see for each of the three contrasts c1, c2, and c3, the weights and expected MOE. The 46 participants give an expected MoE smaller than target MoE, for the least precise estimate (c3; the pairwise comparison) the other expected MoE’s are smaller than that. The Expected Results Figure will display the results for the contrasts with the largest expected MoE.