Standardized Effect Size

Basic Concepts

In Effect Size, we introduce the notion of a standardized effect size and briefly mention Cohen’s d effect size. We now explain this concept further.

Definition 1: Cohen’s d for two independent samples is defined as

Cohens d effect size

where m1 and m2 represent the means of the two samples and σpooled is some combined value for the standard deviations of the two samples.

The effect size represented by d is conventionally viewed as small, medium, or large as follows:

  •  small effect: d = 0.20
  •  medium effect: d = 0.50
  •  large effect: d = 0.80

Note that Cohen’s d is a statistic that is independent of the sample sizes of the two samples.

For single sample hypothesis testing of the mean, we use the following value for Cohen’s d

Cohens d one sample

Example

Example 1: National norms for a school mathematics proficiency exam are normally distributed with a mean of 80 and standard deviation of 20.  A random sample of 60 students from New York City is taken showing a mean proficiency score of 75 (as in Example 1 of Single Sample Hypothesis Testing). Find the effect size for the sample mean.

Per Definition 1,

image413

which indicates a small effect. Note that the effect size is independent of the sample size. We should interpret d to mean that the sample mean is a quarter of a population standard deviation below the population mean.

Reference

Howell, D. C. (2010) Statistical methods for psychology, 7th Ed. Wadsworth. Cengage Learning
https://labs.la.utexas.edu/gilden/files/2016/05/Statistics-Text.pdf

16 thoughts on “Standardized Effect Size”

  1. hello, ANOVA analysis was used in the studies I have for meta-analysis. only the difference of squares, F value and P value are given in the anova tables. how can I calculate the effect size (cohen d) with these values. i would be very happy if you give information. thank you very much

    Reply

  3. HI Charles

    I have been reading that cohen’s d works well for sample sizes over 50 and that samples below that result in effect sizes being over inflated. Is there a real stats function that corrects for this?

    Demos.

    Reply

  5. Hi Charles,

    Is there any tool in the Statistics Resource Pack that you can use to calculate Effect Size using Cohen’s D w/ excel?

    Thank you

    Reply

    • Hi Jonathan,
      The effect size (Cohen’s d) is included in a number of data analysis tools. E.g. see T Tests and Non-parametric Equivalents data analysis tool.
      Charles

      Reply

  6. Do you only need to calculate effect size on those who are significantly different to each other?

    Also on calculating some effect size a few of my answers were negative i.e. -3.065 and -0.385 is that ok? and if so then how do you interpret it?

    Thank you

    Reply

    • Helen,
      In my view, you should calculate an effect size in any case, but it is probably most useful when you have a significant result.
      Depending on the effect size measure that you use, you could get a negative value. This just indicates the direction of the effect. E.g. in calculating the effect size for the difference between the means of sample A and sample B where A has a higher mean, you will get a positive value if you subtract A from B and a negative value if you do the subtraction in the opposite order. Often it is the absolute value that is used and so the negative sign goes away.
      Charles

      Reply

  7. Thank you so much Mr. All of your explanation so clear and good. That’s very helpful for my thesis. And I want to say, again. Many thanks. I don’t have many word to say because I’m very happy I get what I want from this web.

    Reply

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