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Effect Size

Updated on March 12, 2024
Article byWallstreetmojo Team
Edited byAshish Kumar Srivastav
Reviewed byDheeraj Vaidya, CFA, FRM

What is Effect Size?

Effect size measures the intensity of the relationship between two sets of variables or groups. It is calculated by dividing the difference between the means pertaining to two groups by standard deviation. It is a statistics concept.

It can be measured in three ways—the odd Ratio method, the standardized mean difference method, and the correlation coefficient method. It is applied in statistical analysis to ascertain the viability or relevance of findings. This measurement is more practical than statistical significance.

Key Takeaways

  • An effect size is an analytical concept that studies the strength of association between two groups.
  • It is commonly evaluated using Cohen’s D method, where the standard deviation is divided by the difference between the means pertaining to two groups of variables.
  • If the value is 0.2, it is considered a small effect, if it is 0.5, the effect is medium, and if 0.8 or more, it is a large effect.
  • This parameter is not dependent on sample size and, therefore, very practical.

Effect Size in Statistics Explained

Effect-Size-Formula

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Effect size measures the strength of the relation between two variables. It is computed as the fraction of the difference between two groups’ means and the standard deviation. The statistics parameter is standard for all research involving two variables.

For example, the average or mean percentage scored by the students of two different sections, A and B, are 72% and 67%, respectively. If the standard deviation is 2.5, the difference between the average percentages is 5%. Now to compute the effect size, we divide 5% by 2.5%. Therefore, the effect size of sections A and B is 2. Based on the result, we infer that there is a visible difference between the two sections.

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Types

Correlation between two variables can be measured in the following ways:

  1. Odds Ratio: The odds ratio helps determine an event’s causation based on the other event. It evaluates the relationship strength of the two events. The odds ratio formula is as follows:
    Odds Ratio = (a*d)/(b*c).
  2. Standardized Mean Difference: Cohen’s D is the most common method. It measures the standardized mean difference. It is computed as follows:
    Effect Size = (μ12)/σ
  3. Correlation Coefficient: The correlation coefficient is another method of finding the intensity of the relationship between given variables. The findings range between -1 to 1, where -1 shows an intense negative relation, 1 depicts a strong positive connection, and 0 means no relationship. The formula for Pearson’s Coefficient is as follows:
    p_xy = Cov(x,y)/(σ_x × σ_y).

Effect Size Formula

We use the Cohen’s D method to compute how closely two variables are related:

Cohen's D Formula
  • Here, μ1 is the mean of the first population group,
  • μ2 is the mean of the second population group, and
  • σ is the standard deviation.

Examples with Calculation

Example #1

Let us assume that the average fare of a flight between New York and San Francisco for two different months, January and February, were $155 and $163. If the standard deviation for the two months is 4, ascertain the effect size.

Solution:

Effect Size Formula 1

= (155 – 163)/4 = -2

In the above case, a negative effect size represents the increase in flight fares in February compared to January.

Example #2

In a class of 24 students, there are an equal number of girls and boys, i.e., 12. And the mean height of boys in the class is 120 cm. The mean height of girls in that class is 115 cm. If the standard deviation for the two populations is 4, calculate the effect size.

Solution:

Correlation Example 1

To identify the effect of the difference between the two variables, we need to divide the difference between the two means from the standard deviation. The calculation is as follows:

Effect Size Example 1-1

Effect Size = (120 – 115)/4 = 1.3.

Effect Size Example 1-2

With the help of this value, we can find out the shape of the distribution to ascertain the percentage of the population falling under this percentage.

Interpretation

Under the Cohen’s D effect size method, we can consider the following three interpretations:

  1. Small Size (0.2): Such an effect between the two groups is negligible and cannot be spotted with naked eyes.
  2. Medium Size (0.5): This level of correlation is usually identified when the researcher goes through the data—medium size can have a reasonable overall impact.
  3. Large Size (0.8 or greater): A large effect can be observed without using any calculator—the impact is significant in real-world scenarios.

In Pearson’s Coefficient method, where the values range between -1 and 1, there can be two interpretations:

  1. Positive Value: A value between 0 to 1 shows a direct relationship between the two variables.
  2. Negative Value: A value between -1 to 0 indicates an inverse relationship between the two variables.
  3. Zero Value: When the result is 0, there is no relationship between the two variables.

Relevance and Uses

Correlation parameters are vital statistics tools; they are regularly employed in quantitative research. Using the results, we can find out the shape of the distribution—we can ascertain the percentage of the population falling under the distribution.

This measurement is widely employed in educational research, medical research, quantitative analysis, planning, and reporting of data. Compared to statistical significance, this measurement is more practical and more scientific.

You can download this Effect Size Formula Excel Template from here – Effect Size Formula Excel Template

Frequently Asked Questions (FAQs)

What is Cohen’s D?

The Cohen’s D method was proposed by the American statistician Jacob Cohen. The method determines standardized mean difference by dividing the difference between the mean values pertaining to two groups by the standard deviation value.

What is a good effect size?

A size of 0.25 or more is considered favorable. However, its relevance depends on the purpose of the study.

Why is effect size important?

The parameter analyzes the differential effect between the two variables. It determines the magnitude of this difference. The effect can be small, medium, or large. For this measurement, sample size doesn’t matter; therefore, it is very practical.

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