Simone Lawson
Effect size is a critical component in evaluating the strength of a statistical claim. It is a measure of the amount of change in a sample of patients who undergo a treatment or a comparison of the amount of change between patients who undergo a treatment and a control group. Effect size is independent of sample size, and it is used to quantitatively compare the results of studies done in different settings. A large effect size means that a research finding has practical significance and that the difference is important. Cohen's criteria categorise effect sizes into small, medium, and large, with a large effect size indicated by a Cohen's d value of 0.8 or above.
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What You'll Learn
Cohen's criteria
Cohen's d can be used in conjunction with Pearson's r, which measures the strength of the relationship between two variables. Researchers typically use Cohen's guidelines of Pearson's r = .10, .30, and .50, and Cohen's d = 0.20, 0.50, and 0.80 to interpret observed effect sizes as small, medium, or large, respectively. However, these guidelines were not based on quantitative estimates and are only recommended if field-specific estimates are unknown.
The standard deviation of the effect size is critical, as it indicates the uncertainty included in the measurement. A standard deviation that is too large will render the measurement meaningless. SMD values of 0.2 to 0.5 are considered small, 0.5 to 0.8 are considered medium, and above 0.8 are considered large.
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Standard deviation
Cohen's d is a widely used measure of effect size, especially when comparing two groups. It quantifies the difference between two means in terms of standard deviation units. Cohen's d is calculated by taking the difference between the means of two groups and dividing it by the standard deviation of the control group or the pooled standard deviation of both groups. This allows for a standardised comparison, as Cohen's d represents the magnitude of the unstandardised effect relative to the variability in the data.
For example, if the unstandardised effect size is 10 and the standard deviation is 2, Cohen's d would be 5, indicating a substantial effect. However, if the standard deviation is also 10, Cohen's d would be 1, suggesting a less significant effect. Cohen suggested that a Cohen's d of 0.2 represents a "small" effect size, 0.5 is "medium", and 0.8 or above indicates a "large" effect size.
It is important to note that the standard deviation should not be too large, as it can render the measurement meaningless. Additionally, effect sizes can be measured in relative or absolute terms, and both can be used together as they convey different information. While relative effect sizes compare two groups directly, absolute effect sizes indicate that a larger absolute value signifies a stronger effect.
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Sample size
Effect size is independent of sample size. It is calculated using only the data. However, sample size is crucial when determining statistical significance, which is distinct from practical significance or effect size. Increasing the sample size makes it more likely to find a statistically significant effect, regardless of the real-world impact of the finding.
The minimum sample size required for sufficient statistical power depends on the expected effect size. A power analysis can be used to determine the sample size needed for a certain power level, using a set effect size and significance level.
In some cases, a large sample size can lead to guaranteed statistical significance, even when there is no significant relationship between the variables. This is known as a Type I error. To avoid this issue, it is important to report the practical significance or effect size in addition to the p-value or statistical significance.
The concept of a large sample size is relative and can vary depending on the field or discipline. For example, Lin, Lucas, and Shmueli (2013) considered sample sizes over 10,000 cases to be large.
In summary, while sample size is important for determining statistical significance, effect size provides a measure of the magnitude or practical significance of the relationship between variables, and it is independent of the sample size.
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Practical significance
Effect sizes are used to quantify practical significance. They measure the size or magnitude of the difference or relatedness between variables. Effect sizes can be categorised as small, medium, or large, according to criteria such as Cohen's, which suggests that a Cohen's d of 0.2 is a "small" effect size, 0.5 represents a "medium" effect size, and 0.8 is a "large" effect size. However, the criteria for a small or large effect size may depend on the specific field of research.
Effect sizes are calculated using statistical software, and they are independent of sample size. They are widely used in meta-analyses and are essential for evaluating the strength of a statistical claim. Reporting effect sizes in research papers is considered good practice and is required by guidelines such as the APA guidelines. By reporting effect sizes, researchers can communicate the practical significance of their findings and avoid the potential biases associated with only reporting statistical significance.
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Statistical significance
While statistical significance is important, it does not always equate to practical significance. Practical significance, represented by effect sizes, indicates the magnitude or importance of a research outcome in the real world. Effect sizes can be measured in relative or absolute terms. Relative effect sizes compare two groups directly, while absolute effect sizes indicate that a larger absolute value represents a stronger effect.
Effect sizes can be categorised as small, medium, or large. Cohen's criteria for these categories differ based on the specific effect size measurement used. For Cohen's d, a widely used measure, a value of 0.2 is considered a small effect size, 0.5 represents a medium effect size, and 0.8 or above indicates a large effect size. It is important to note that the criteria for small or large effect sizes may vary depending on the specific research field.
In research, it is crucial to report both statistical significance and effect sizes. Statistical significance alone can be misleading, as it is influenced by sample size. Increasing the sample size makes it more likely to find a statistically significant result, regardless of its practical significance. Effect sizes, on the other hand, are independent of sample size and provide a more meaningful interpretation of the research findings.
By considering both statistical and practical significance, researchers can better evaluate the strength and importance of their findings. This helps ensure that research outcomes are not only statistically significant but also have meaningful implications in the real world.
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Frequently asked questions
Effect size is a measure of the amount of change in a sample of patients who undergo a treatment, or a measure of the amount of change in a sample of patients who undergo a treatment compared to a control group. It indicates the practical significance of a research outcome.
Effect size helps to evaluate the strength of a statistical claim. While statistical significance shows that an effect exists in a study, practical significance (represented by effect size) shows that the effect is large enough to be meaningful in the real world.
Cohen's criteria categorise effect sizes into small, medium, or large. Cohen suggested that d = 0.2 be considered a “small” effect size, 0.5 represents a “medium” effect size and 0.8 a “large” effect size. However, the criteria for a small or large effect size may depend on what is commonly found in research in a particular field.
