Understanding Effect Sizes: Cohen’s d and Cohen’s h Explained

What is it? 

Cohen’s d is a measure of effect size. It tells us how much of a difference there is between two groups. In simple terms, it helps us understand if a treatment, like probiotics, has a big or small effect on IBS symptoms compared to no treatment (placebo) or a different treatment.

How is it calculated? 

It’s the difference between the means (average scores) of two groups, divided by the standard deviation (a measure of the spread of scores) of those groups.

Example: 

Imagine a study comparing IBS patients taking probiotics with those taking a placebo. If the probiotic group has an average symptom score of 4 (on a scale of 1 to 10) and the placebo group has an average score of 6, and the standard deviation for both groups is 2:

A Cohen’s d of 1.0 indicates a large effect, suggesting that probiotics significantly reduce IBS symptoms compared to the placebo.

What is it?

Cohen’s h is another measure of effect size, but it’s used specifically for comparing proportions or probabilities. It helps us understand the difference between two proportions, such as the proportion of IBS patients who feel better after taking probiotics versus those who feel better after taking a placebo.

How is it calculated? 

It’s the difference between two proportions transformed into arcsine values (a mathematical function), which adjusts for the proportions being bounded between 0 and 1.

Example

Consider a study where 70% of IBS patients taking probiotics report improvement, while only 50% of those taking a placebo report improvement. Here’s how we calculate it:

A Cohen’s h of 0.22 indicates a small effect, suggesting that probiotics have a noticeable but not huge impact on the proportion of IBS patients who report improvement.

When researchers report Cohen’s d or Cohen’s h, they’re giving us a sense of how effective a treatment is in a way that’s more meaningful than just saying “it works” or “it doesn’t work.” By quantifying the effect, we can better compare results across different studies and decide whether a treatment is worth trying.

• Cohen’s d: Helps us understand the magnitude of the difference in IBS symptom scores between those taking probiotics and those not.
• Cohen’s h: Helps us understand the difference in the proportion of patients reporting improvement between those taking probiotics and those not.

Both metrics give us valuable insights into how well probiotics might help manage IBS symptoms, making it easier for clinicians and patients to make informed decisions.