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.
Table of contents
- 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 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 deviationStandard DeviationStandard deviation (SD) is a popular statistical tool represented by the Greek letter 'σ' to measure the variation or dispersion of a set of data values relative to its mean (average), thus interpreting the data's reliability. 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:
- 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).
- 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
- Correlation Coefficient: The correlation coefficientCorrelation CoefficientCorrelation Coefficient, sometimes known as cross-correlation coefficient, is a statistical measure used to evaluate the strength of a relationship between 2 variables. Its values range from -1.0 (negative correlation) to +1.0 (positive correlation). 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:
- 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
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.
= (155 – 163)/4 = -2
In the above case, a negative effect size represents the increase in flight fares in February compared to January.
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.
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:
- Small Size (0.2): Such an effect between the two groups is negligible and cannot be spotted with naked eyes.
- 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.
- 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 methodPearson's Coefficient MethodPearson correlation coefficient measures the strength between the different variables and their relationships. Therefore, whenever any statistical test is conducted between the two variables, it is good to analyze the correlation coefficient value to know how strong the relationship between the two variables is., where the values range between -1 and 1, there can be two interpretations:
- Positive Value: A value between 0 to 1 shows a direct relationship between the two variables.
- Negative Value: A value between -1 to 0 indicates an inverse relationship between the two variables.
- 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 researchQuantitative ResearchQuantitative Research refers to the systematic investigation in which a person collects the data from the different respondents based on numerical figures. Data obtained is then analyzed to get the results using various mathematical, statistical, and computational tools.. 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 significanceStatistical SignificanceStatistical significance is the probability of an observation not being caused by a sampling error., 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)
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.
A size of 0.25 or more is considered favorable. However, its relevance depends on the purpose of the study.
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.
This article has been a guide to what is Effect Size & Meaning. We discuss effect size definition, Cohen’s D statistics, calculator, formula, and interpretation. You can learn more about excel modeling from the following articles –
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