12.3 Effect size interpretation and practical significance
3 min read•august 7, 2024
Effect size interpretation and practical significance are crucial aspects of experimental design. They help researchers understand the magnitude and real-world impact of their findings beyond statistical significance.
Standardized effect size measures like and quantify the strength of relationships between variables. Practical significance measures, such as and , assess the real-world relevance of research outcomes.
Standardized Effect Size Measures
Measures of Standardized Mean Differences
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- Cohen's d expresses the difference between two means in standard deviation units
- Calculated as the difference between two means divided by the pooled standard deviation
- Commonly used benchmarks: 0.2 (), 0.5 (), 0.8 ()
- Eta squared () represents the proportion of variance in the dependent variable explained by the independent variable
- Ranges from 0 to 1, with higher values indicating a stronger effect
- Calculated as the ratio of the between-groups sum of squares to the total sum of squares
Measures of Association
- is a correlation coefficient that measures the strength and direction of a linear relationship between two continuous variables
- Ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation), with 0 indicating no correlation
- Squared value () represents the proportion of variance in one variable explained by the other variable
- (OR) compares the odds of an event occurring in one group to the odds of it occurring in another group
- An OR of 1 indicates no difference between groups, while values greater than 1 suggest higher odds in the first group compared to the second group
- Commonly used in case-control studies and logistic regression analyses
Measures of Risk
- (RR) compares the risk of an event in an exposed group to the risk in an unexposed group
- An RR of 1 indicates no difference in risk between groups, while values greater than 1 suggest a higher risk in the exposed group
- Often used in cohort studies and clinical trials to assess the impact of a risk factor or treatment on an outcome
Practical Significance Measures
Clinical Significance
- Number needed to treat (NNT) represents the average number of patients that need to be treated for one additional patient to benefit compared to a control
- Lower NNT values indicate a more effective treatment
- Calculated as the reciprocal of the absolute risk reduction (1/ARR)
- Clinical significance refers to the practical or real-world impact of a treatment effect on patient outcomes
- Considers factors such as the magnitude of the effect, the severity of the condition, and the risks and costs associated with the treatment
- Determined by clinicians and experts in the field based on their experience and judgment
Practical vs. Statistical Significance
- Practical significance assesses whether the observed effect is large enough to be meaningful or important in a real-world context
- Focuses on the magnitude and relevance of the effect rather than just its statistical significance
- A statistically significant result may not always be practically significant if the effect size is small or the outcome is not clinically relevant
- Statistical significance indicates the likelihood that the observed effect is due to chance alone
- Determined by the , which represents the probability of obtaining the observed results if the null hypothesis is true
- A statistically significant result (p < 0.05) suggests that the observed effect is unlikely to be due to chance, but does not necessarily imply practical significance
Key Terms to Review (14)
Clinical significance: Clinical significance refers to the practical importance of a treatment effect, indicating whether a treatment has a meaningful impact on patient outcomes in real-world settings. While statistical significance focuses on whether an observed effect is likely due to chance, clinical significance emphasizes the actual relevance of that effect in clinical practice, ensuring that results are not just statistically significant but also beneficial and applicable to patients' lives.
Cohen's d: Cohen's d is a measure of effect size that quantifies the difference between two group means in standard deviation units. It provides insight into the magnitude of an effect, allowing researchers to understand how meaningful their findings are beyond just statistical significance. This measure connects deeply with concepts like statistical power, sample size, and practical significance, making it vital for analyzing research outcomes effectively.
Eta squared: Eta squared is a measure of effect size that indicates the proportion of total variance in a dependent variable that can be attributed to a particular independent variable or factor. This statistic helps researchers understand the strength of relationships and the impact of different variables in analyses, especially within the context of ANOVA, power calculations, and assessing practical significance.
Hypothesis Testing: Hypothesis testing is a statistical method used to determine whether there is enough evidence in a sample of data to support a specific claim or hypothesis about a population parameter. This process involves formulating a null hypothesis and an alternative hypothesis, calculating a test statistic, and comparing it to a critical value to make a decision. It plays a crucial role in making statistical inferences, interpreting effect sizes, and choosing appropriate statistical tests.
Large Effect: A large effect refers to a substantial impact of an independent variable on a dependent variable, indicating that the difference observed is meaningful and significant. It highlights the strength of the relationship and suggests that the effect is not only statistically significant but also has practical implications, influencing real-world decisions or outcomes.
Mean Difference: Mean difference is the average difference between two groups in a study, calculated by subtracting the mean of one group from the mean of another. This value provides insights into the effect size, helping researchers understand the magnitude of differences observed in experimental results and its practical significance.
Medium effect: The medium effect is a measure of the strength of a relationship between variables, often expressed through effect size metrics like Cohen's d. It indicates that the impact of an intervention or treatment is moderate, which can be useful for understanding practical significance in research findings. A medium effect suggests that the difference or relationship is substantial enough to be meaningful in real-world applications, making it an important aspect to consider when evaluating research outcomes.
Number Needed to Treat: The number needed to treat (NNT) is a statistical measure that indicates the number of patients who need to be treated with a specific therapy or intervention in order for one patient to benefit from that treatment. This concept is essential for evaluating the practical significance of clinical interventions, as it provides a clear perspective on how effective a treatment is in real-world settings compared to merely looking at statistical significance.
Odds Ratio: An odds ratio is a statistical measure used to determine the odds of an event occurring in one group compared to another group. It is particularly useful in the context of case-control studies, where it helps assess the strength of association between exposure and an outcome. Understanding the odds ratio is essential for interpreting effect sizes and determining practical significance in research findings.
P-value: A p-value is a statistical measure that helps determine the significance of results obtained in hypothesis testing. It indicates the probability of observing data at least as extreme as the sample data, assuming the null hypothesis is true. Understanding p-values is crucial as they help researchers make decisions about rejecting or failing to reject the null hypothesis, and they are foundational to various statistical methods and analyses.
Pearson's r: Pearson's r is a statistical measure that evaluates the strength and direction of the linear relationship between two continuous variables. It provides a value between -1 and 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 indicates no correlation at all. Understanding Pearson's r is essential for interpreting the degree of association between variables, which is crucial for sample size calculations and determining the practical significance of research findings.
Relative risk: Relative risk is a measure used in epidemiology that compares the risk of a certain event occurring in two different groups, typically one exposed to a certain factor and one not exposed. It provides insight into the strength of the association between exposure and outcome, helping to determine whether a specific risk factor is linked to an increased chance of an adverse outcome. Understanding relative risk aids in evaluating the practical significance of research findings by indicating how much more (or less) likely an event is to occur in one group compared to another.
Small effect: A small effect refers to a modest impact or influence that an independent variable has on a dependent variable in research studies. Understanding the concept of small effects is crucial for interpreting effect sizes, which help researchers gauge how meaningful a finding is in real-world applications, beyond just statistical significance.
Variance Explained: Variance explained refers to the proportion of total variance in a dependent variable that can be attributed to the effects of one or more independent variables in a statistical model. This concept is crucial in evaluating how well a model fits the data, and it helps to measure the practical significance of findings by indicating the extent to which the independent variables account for variations in the outcome.