Final answer:
If we have a large effect size but no statistical significance, it means that there is a notable difference between two groups or variables, but this difference is not considered statistically significant. This could be due to variations in the data or a small sample size. Both the effect size and statistical significance should be considered when interpreting research findings.
Step-by-step explanation:
If we have a large effect size but no statistical significance, it means that even though there is a notable difference between two groups or variables, this difference is not considered statistically significant. This could happen due to variations in the data or a small sample size, which can affect the p-value and make it larger than the threshold for significance.
An effect size measures the magnitude of the difference between groups or variables, while statistical significance determines whether this difference is likely due to chance or not. It is important to consider both the effect size and the statistical significance when interpreting research findings.
For example, let's say we are comparing the test scores of two groups of students. Group A has a mean score of 90 and Group B has a mean score of 95. The effect size is the difference between the means, which is 5. If the p-value is larger than the threshold for significance (e.g., 0.05), we cannot confidently conclude that the 5-point difference is not due to chance. In this case, we have a large effect size (5 points), but no statistical significance.