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Scale vs Scale paired

2b: Effect size

From the example on the previous pages we got the impression that a commercial had an effect on the opinion of a brand, since overall the difference was positive between the before and after score.

The last part would be to determine how big the difference can be classified as. For this we can make use of an effect size, but there are many options and different authors suggest different ones. Cohen's is probably the most frequently used one, but there are several variations on Cohen's d. I'll use the one that is based on the differences (sometimes denoted as d_z), but with a correction proposed by Hedges for small sample sizes.

In the example from that we started with d_z* = .48. Unfortunately there is no formal way to determine if 0.48 (you can ignore the negative sign) is high or low (although almost everyone would agree this is high), and the rules of thumb floating around on the internet vary quite a lot, often depending on the field (e.g. biology, medicine, business, etc.). I would the following rule of thumb (combining Cohen (1988) and Sawilowsky (2009)):

0.00 < 0.20 - Very weak (Sawilowsky)
0.20 < 0.50 - Weak (Cohen)
0.50 < 0.80 - Moderate (Cohen)
0.80 < 1.20 - Strong (Cohen)
1.20 < 2.00 - Very strong (Sawilowsky)
2 or more - extremely strong (Sawilowsky)

These rule of thumb are however for Cohen's d, not d_z. Luckily though, you can simply multiply a Cohen d_z with the square root of 2, to convert it to a Cohen d (Cohen, 1988, p. 48). In this example we could therefor speak of a medium effect. The results could be reported as:

A paired samples t-test showed that there was a significant but weak difference in scores on opinion about the brand before and after seeing the commercial, t(23) = 2.40, p = .025, Cohen's d (based on differences) with Hedges correction = 0.48.

We can now complete the report by combining all the results, which will be done on the next page.

Scale vs Scale paired

Introduction

Impression

Visualisation

Test

Effect size

Reporting

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