Stats & Methodology

# What's an Effect Size? | Statistics

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## What’s an Effect Size? | Statistics

Effect size is a way to measure the strength of the statistical relationship between two variables. It is a standardized measure that is used to indicate the magnitude of the effect of an intervention or treatment. In other words, how big the effect is.

### Large vs small effect sizes

In physiotherapy, effect sizes can be used to determine the effectiveness of different treatments for conditions such as non-specific chronic low back pain or knee osteoarthritis. For example, if an exercise program for back pain results in large effect size, it means that the treatment has a strong positive effect on reducing pain. On the other hand, if the effect size is small, the treatment has a minimal effect on reducing pain.

The effect size is independent of the sample size, so a small sample size does not necessarily imply a small effect size. Small samples can have big effects and vice versa.

### Comparing different studies

Effect sizes can be especially useful in medical research because they allow for the comparison of treatment effects across different studies, populations, and outcome measures. For example, two studies may find that a treatment has a statistically significant result. Still, one study may show a larger effect size than the other, indicating that the treatment may be more effective in certain contexts or populations.

The effect size is independent of the sample size, so a small sample size does not necessarily imply a small effect size. Small samples can have big effects and vice versa.

### Cohen’s d

A common effect size statistic used in physiotherapy research is Cohen’s d, which compares the mean change in an outcome measure (e.g. pain score) between two groups (e.g. treatment and control group) and expresses it in standard deviation units. Depending on the particular study, other effect size statistics such as Hedge’s g, or r may also be used.

### Low p-value ≠ large effect size

Moreover, effect sizes can help to overcome the limitations of p-values, which are often used to determine statistical significance in medical studies. P-values only indicate whether an observed effect is statistically significant, but do not provide any information about the size of the effect. In contrast, effect sizes provide a measure of the practical or clinical significance of an effect, which can be more relevant for making medical decisions.

It is crucial to understand that a p-value does not show the size of an effect. Some readers think that when a given p-value is low, it means that the effect is large. This is not true. A huge sample with a tiny difference between groups can create a small p-value.

### Easy calculation

Some researchers do not report effect sizes in their papers. A back-of-the-envelope calculation will show you the effect size:

Cohen’s d formula:

(M1 – M2)/SDpooled

M1: mean 1

M2: mean 2

SDpooled: pooled standard deviation

It is important to note that this formula works best for samples bigger than n = 50 and equal group sizes. Effects will appear larger than they truly are in smaller groups. This is due to data noise.

## Reference

Kamper S. J. (2019). Interpreting Outcomes 2-Statistical Significance and Clinical Meaningfulness: Linking Evidence to Practice. The Journal of orthopaedic and sports physical therapy49(7), 559–560.

Nuzzo R. (2014). Scientific method: statistical errors. Nature506(7487), 150–152.

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