Effect Size Calculator

Q: Is an effect size of 0.8 good?

An effect size of 0.8 indicates a large difference between the control and experimental means. However, we cannot say whether this large difference is good or bad without context. If you are applying the effect size to analyze an LLM benchmark , for instance, this difference may be considered good if your experimental sample outperforms the control one.

Q: Is Cohen’s d the same as effect size f?

No, Cohen’s d and effect size f are used in different statistical contexts. Cohen’s d measures the difference between two means . Cohen’s f, on the other hand, is used mainly in ANOVA and is defined as the standard deviation of the group means divided by the common within-group standard deviation . Therefore, Cohen’s d is useful for making a direct comparison between the two groups, while Cohen’s f is used in statistical regression in analysis of variance (ANOVA).

Q: What is Rhea effect size?

The Rhea scale , or Rhea effect size , is a popular scale adopted mainly in medicine and biology. This scale was introduced in 2004 and defines small effects as d < 0.35 , medium as 0.35 – 0.80 , and large as 0.8 – 1.5 . The Rhea convention is widely adopted to assess the clinical meaningfulness of a given treatment, procedure, or analysis in health and biological applications.

Creators

João Rafael Lucio dos Santos, PhD

João Rafael Lucio dos SantosPhD, Federal University of Campina Grande

Website

Research Gate

João Rafael Lucio dos Santos, PhD, is a physicist, a researcher, and a professor at the Federal University of Campina Grande, Brazil. He earned his Ph.D. in Physics at the University of Rochester, NY in 2013. He has written several papers in international journals, mainly in field theory and cosmology. João is also a member of the BINGO telescope collaboration, which is building a state-of-the-art radio telescope that will operate in the Northeast of Brazil. He believes in the importance of spreading knowledge and high-quality information among society and the public in general. In his free time, he enjoys running, playing tennis, cooking, traveling, and having pleasant moments with his relatives and friends. See full profile

Check our editorial policy

Reviewers

Steven Wooding

Steven Wooding is a physicist by training with a degree from the University of Surrey specializing in nuclear physics. He loves data analysis and computer programming. He has worked on exciting projects such as environmentally aware radar, using genetic algorithms to tune radar, and building the UK vaccine queue calculator. Steve is now the Editorial Quality Assurance Coordinator here at Omni Calculator, making sure every calculator meets the standards our users expect. In his spare time, he enjoys cycling, photography, wildlife watching, and long walks. See full profile

Check our editorial policy

The effect size calculator is here to help you compute the magnitude of a phenomenon using statistical quantities. Along with this text, you will learn more about the effect size and the following subjects:

What is the effect size? Cohen’s d effect size definition;
How can I calculate the effect size? The effect size formula;
Effect size calculator — Example;
Is an effect size of 0.8 good?
Is Cohen’s d the same as effect size f?
How can I compute an effect size of 0.2?
What is Rhea’s effect size?
And much more.

Thus, stay with us and learn how to measure correlations between distributions using the effect size calculator.

🙋 You can learn more about statistical quantities by checking out our p-value calculator, confidence interval calculator, and z score calculator.

What is the effect size? Cohen’s d effect size definition

The effect size is a statistical quantity that determines the difference between two means and measures the magnitude of a phenomenon. The simplest form of the effect size considers two samples: the control and the experimental. The effect size interpretation depends on the scales considered. The most popular scale was defined by Jacob Cohen, and the formula associated with it is known as Cohen’s d (for difference).

In the table below, we present Cohen’s scale for the effect size and for the correlation coefficient:

Effect Size	Correlation	Interpretation
0.20	0.1	Small
0.50	0.3	Medium
0.80	0.5	Large

How can I calculate the effect size? The effect size formula

The Cohen’s d formula is given by:

d = \frac{x_{\mathrm{control}}-x_{\mathrm{exp}}}{sd_{\mathrm{pooled}}}

where:

$d$ — Effect size or Cohen’s d;
$x_{\mathrm{control}}$ — Control sample mean;
$x_{\mathrm{exp}}$ — Experimental sample mean; and
$sd_{\mathrm{pooled}}$ — Pooled standard deviation.

The pooled standard deviation is such that:

sd_{\mathrm{pooled}} = \sqrt{\frac{sd_{\mathrm{control}}^{\,2} + sd_{\mathrm{exp}}^{\,2}}{2}}

where:

$sd_{\mathrm{control}}$ — Control standard deviation; and
$sd_{\mathrm{exp}}$ — Experimental standard deviation.

The Cohen’s d can be used to determine another statistical quantity named the correlation coefficient $r$ and the variance $r^2$ , which are derived from the equation:

r = \frac{d}{\sqrt{d^{\,2}+4}}

The formula above is valid for two samples with the same size.

Effect size calculator — Example

Let us show you with an example that our tool is easy and intuitive to use. Suppose you are a teacher evaluating your students’ performance using two different methods. You split your students into two equal groups as follows:

Group A (control): 20 students learning with traditional approach;
Group B (experiment): 20 students learning with a tutorial software; and
Outcome: exams with scores between 0 and 150.

The results of the evaluation are the following:

Group	Mean	Standard deviation
Control	100	10
Experiment	105	12

Therefore, by filling the fields of our effect size calculator with the data above, we find that:

d = -0.45 \quad\ r = -0.22 \quad\ r^2 = 0.049

The absolute value of the effect size indicates a small difference between the two sample averages. The negative sign means the experimental group’s mean is 0.45 pooled standard deviations higher than the control group’s mean. The correlation coefficient corroborates the interpretation of the effect size. The variance reveals that only $4.9\%$ of the students’ performance is related to the use of the tutorial software.

In the end, this experiment shows a small-to-moderate improvement in scores with the tutorial software (d ≈ -0.45). Still, additional analysis would be needed to determine whether this difference is statistically or practically significant.

🙋 If you want to see another application of the effect size, access our article “Confidence Interval and Effect Size Applied to Clinical Meaningfulness in Sport”.

FAQs

Is an effect size of 0.8 good?

An effect size of 0.8 indicates a large difference between the control and experimental means. However, we cannot say whether this large difference is good or bad without context. If you are applying the effect size to analyze an LLM benchmark, for instance, this difference may be considered good if your experimental sample outperforms the control one.

Is Cohen’s d the same as effect size f?

No, Cohen’s d and effect size f are used in different statistical contexts. Cohen’s d measures the difference between two means. Cohen’s f, on the other hand, is used mainly in ANOVA and is defined as the standard deviation of the group means divided by the common within-group standard deviation. Therefore, Cohen’s d is useful for making a direct comparison between the two groups, while Cohen’s f is used in statistical regression in analysis of variance (ANOVA).

How can I compute an effect size of 0.2?

You can compute an effect size of 0.2 by following the steps below:

Take the control sample mean equal to 102.
Take the experimental sample mean equal to 100.
Take the control and the experimental standard deviations equal to 10.
Substitute in the formula for the effective size:

d = (102 − 100)/10 = 0.2
This corresponds to a small difference between the samples.

What is Rhea effect size?

The Rhea scale, or Rhea effect size, is a popular scale adopted mainly in medicine and biology. This scale was introduced in 2004 and defines small effects as d < 0.35, medium as 0.35 – 0.80, and large as 0.8 – 1.5. The Rhea convention is widely adopted to assess the clinical meaningfulness of a given treatment, procedure, or analysis in health and biological applications.