# How to Calculate Effect Sizes

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An effect size is an important, if somewhat underutilized, value in statistical analysis. Often, many analysts will test for statistical significance, ignoring the question of practical significance. Effect sizes provide the answer to that question and are not difficult to calculate. Including effect sizes in your research will strengthen the rigor of your studies and lend greater weight to your analysis, conclusions, and recommendations. Effect sizes are useful in the range of disciplines, including natural and social sciences, education, and business.

### Things You'll Need

• Statistical software
• Data
• Calculator
• Statistics book

## FInding Practical Significance: Computing the Effect Size

• Examine the statistical significance of the statistics you are analyzing. This may be from an analysis of variance (ANOVA), regression, or other statistical procedure. You need a statistically significant association, such as between income and level of education, to give only one example, before calculating an effect size to determine the strength or practical significance of that association.

• Locate the mean values of the two groups or samples you are studying. You'll need these to calculate an effect size. The two groups are usually referred to as the experimental or intervention group and the control group. The results of your statistical procedure will display the mean values in the descriptive statistics section or table.

• Combine your two groups into one and compute a standard deviation. This is known as the pooled standard deviation because it results from pooling the two separate groups. A standard deviation shows the level of spread in a distribution of values or scores.

• Calculate your effect size. One of the best-known measures of effect size is "Cohen's d", named for the American statistician and psychologist Jacob Cohen. To calculate the value of "d", you subtract the mean of the control group from the mean of the experimental group and divide by the pooled standard deviation.

• Interpret the results of your calculation in Step 4. Effect sizes in value are less than 1. Interpretations vary, but in general, a "d" value of 0.2 indicates only a small effect; 0.5, a medium effect; and 0.8 or greater, a large effect. The "d" score indicates the practical significance of the association you are exploring.

## Tips & Warnings

• Remember that it is possible to have strong statistical significance and a low effect size at the same time. Such a result would suggest that an association exists between the two variables in question, but that the relationship is small and not of great practical significance.
• Despite the popularity of this effect size measure, Cohen's d is not available on many statistical programs such as SPSS or on the Excel spreadsheet program. However, the statistic is easy to compute on a regular calculator or in a spreadsheet.

## References

• How to Calculate Effect Sizes
• SPSS For Windows: An Introduction to Use and Interpretation in Research George Morgan, Orlando Griego, and Gene Gloeckner, 2001
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