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.

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.

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 = (μ₁-μ₂)/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).
   

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

• 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.

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:

= (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:

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 = (120 – 115)/4 = 1.3.

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.

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.

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