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Statistics without maths for psychology
Sometimes the effect size is easy to calculate (as in the case of two conditions); at other
times it may be more diffi cult. Report the effect size, however, when you can. Sometimes
psychologists know the size of the effect that they are looking for, based on a knowledge of
previous work in the area. Statisticians have given us guidelines (remember – guidelines, not
rules) as to what constitutes a ‘small’ effect or a ‘large’ effect, as we learned in the previous
chapter. These are guidelines developed by Cohen (1988): 1
Effect size d Percentage of overlap
Small 0.20 85
Medium 0.50 67
Large 0.80 53
There are other measures of effect, and these are covered later. However, d is widely reported
and understood, so it is important that you understand how to calculate and interpret it. Robert
Rosenthal and his colleague Ralph Rosnow are still writing articles to show academics how
much better it is to report the test statistics, the exact p-value, the direction of the effect and
enough information that readers are given the fullest picture of the results. If you wish to learn
more about why you should use effect sizes, when to use them and how to use them, see
Rosnow and Rosenthal (2009).
8.3 Power
Sometimes you will hear people say things like ‘the t-test is more powerful than a Mann–
Whitney’ or ‘repeated-measures tests have more power’. But what does this really mean?
Power is the ability to detect a signifi cant effect, where one exists. And you have learned that
by ‘effect’ we mean a difference between means, or a relationship between variables. Power
is the ability of the test to fi nd this effect. Power can also be described as the ability to reject
the null hypothesis when false. Power is measured on a scale of 0 to +1, where 0 = no power
at all. If your test had no power, you would be unable to detect a difference between means,
or a relationship between variables; 0.1, 0.2 and 0.3 are low power values; 0.8 and 0.9 are high
power values.
What do the fi gures 0.1, 0.2, etc. mean?
0.1 means you have only a 10% chance of fi nding an effect if one exists. This is hopeless.
Imagine running a study (costing time and money!) knowing that you would be so unlikely
to fi nd an effect.
0.7 means that you have a 70% chance of fi nding an effect, where one exists. Therefore you
have a good chance of fi nding an effect. This experiment or study would be worth spending
money on.
0.9 means that you have a 90% chance of fi nding an effect. This rarely happens in psychological
research.
You can see, then, that if your power is 0.5, you have only a 50:50 chance of fi nding an effect,
if one exists, which is really not good enough.
1 A table giving the percentage overlap for d values 0.1 to 1.5 was given in Chapter 7, page 216.