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Last updated on 2024年6月7日

How do effect size and statistical significance differ?

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When delving into statistics, you'll encounter two pivotal concepts: effect size and statistical significance. They may seem intertwined, but they serve different purposes in research. Effect size quantifies the magnitude of a difference or relationship, while statistical significance assesses whether a result is likely due to chance. Understanding the distinction is crucial because a statistically significant result doesn't always mean the effect is substantial, and conversely, a large effect size may not always be statistically significant due to sample size or variability.

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Prof. Dr. yaser awad

Vice President, Sakhnin College. Applied Statistics and Actuarial Science at Haifa UN
??Ali Khreiss??

Founder @ Bands Consultancy |Statistician| Statistics Specialist|Trainer|Consultant|Machine Learning Master Thesis 2010

1 Effect Size

Effect size is a measure of the strength of the relationship between two variables, or the magnitude of the difference between groups. It's a standardized value that helps you understand the practical significance of your findings, irrespective of sample size. For example, a large effect size indicates a strong relationship or a substantial difference, which could be of practical importance in real-world applications. In contrast, a small effect size suggests a weaker relationship or a minor difference that may not be practically significant.

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Prof. Dr. yaser awad

Vice President, Sakhnin College. Applied Statistics and Actuarial Science at Haifa UN
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The main difference between the two concepts lies in their focus: statistical significance deals with the probability and reliability of an effect, while effect size deals with the magnitude and practical importance of an effect. It is better in data analysis; both should be considered. For example, many of the studies, might find statistically significant results even for trivially small effects that are not practically meaningful, emphasizing why it's essential to report effect size next to statistical significance to give a complete picture of the study findings.

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??Ali Khreiss??

Founder @ Bands Consultancy |Statistician| Statistics Specialist|Trainer|Consultant|Machine Learning Master Thesis 2010
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When talking about the effect size, it is very important to show the strength of the relationship or significance difference, when a difference is statistically significant, it does not necessarily mean that it is big, important or helpful in decision-making, it simply means you can be confident that there is a difference. Just noted that the higher the effect size, the fewer samples needed.

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2 Statistical Significance

Statistical significance is determined through hypothesis testing and indicates whether the observed effect is unlikely to have occurred by chance. This is typically assessed using a p-value, which compares the observed data to a distribution of data that would be expected if no effect were present. If the p-value is below a predetermined threshold (often 0.05), the result is considered statistically significant. However, this does not necessarily mean the effect is large or important; it merely implies that it is not likely due to random variation.

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??Ali Khreiss??

Founder @ Bands Consultancy |Statistician| Statistics Specialist|Trainer|Consultant|Machine Learning Master Thesis 2010
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The theory of statistical test of significance essentially involves setting of a null hypothesis and competing alternative hypothesis so the null hypothesis H0 is a hypothesis of no difference, no effect or correlation while the alternative hypothesis H1 is the competing alternative to H0 and is usually the research hypothesis set out to investigate.

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3 P-Value Explained

The p-value is a probability that measures the evidence against a null hypothesis, which posits no effect or no difference. A low p-value suggests that your data are unlikely under the null hypothesis and thus provides evidence in favor of the alternative hypothesis. It's important to note that the p-value does not tell you the size of the effect or its importance; it only indicates whether the effect is statistically significant.

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??Ali Khreiss??

Founder @ Bands Consultancy |Statistician| Statistics Specialist|Trainer|Consultant|Machine Learning Master Thesis 2010
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The p-value indicates how probable the results are due to chance, if p=0.05 it means that there is a 5% probability that the results are due to random chance

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4 Sample Size Impact

Sample size plays a crucial role in determining both effect size and statistical significance. Larger samples tend to provide more precise estimates of the effect size and can detect smaller effects as statistically significant. Conversely, smaller samples may yield larger effect sizes by chance and may fail to detect true effects as statistically significant. Thus, the reliability of your results is heavily dependent on choosing an appropriate sample size for your study.

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??Ali Khreiss??

Founder @ Bands Consultancy |Statistician| Statistics Specialist|Trainer|Consultant|Machine Learning Master Thesis 2010
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Note that the magnitude of the p-value depends on the sample size, with a sufficiently large sample size, even an extremely small difference could be detected as significant

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5 Practical vs. Statistical

It's essential to distinguish between practical significance and statistical significance. Practical significance refers to the real-world importance or relevance of an effect, which is often related to effect size. An effect can be statistically significant but have little practical significance if the effect size is small. Conversely, an effect can be practically significant with a large effect size but not reach statistical significance if the sample size is too small or the data are too variable.

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??Ali Khreiss??

Founder @ Bands Consultancy |Statistician| Statistics Specialist|Trainer|Consultant|Machine Learning Master Thesis 2010
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Statistical significance reflects the improbability of our findings while practical significance is concerned with meaning, this is why we must interpret not only the statistical significance of our results but their practical, or real-world significance as well.

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6 Misinterpretations Avoided

Misinterpretation of statistical results can lead to incorrect conclusions. Assuming that statistical significance equates to a meaningful effect can be misleading. Similarly, overlooking a large effect size because it did not achieve statistical significance can dismiss potentially important findings. Understanding the difference between effect size and statistical significance helps you make informed decisions about the implications of your research and avoid common pitfalls in statistical analysis.

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7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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How do effect size and statistical significance differ?

1

2

3

4

5

6

7

1 Effect Size

2 Statistical Significance

3 P-Value Explained

4 Sample Size Impact

5 Practical vs. Statistical

6 Misinterpretations Avoided

7 Here’s what else to consider

Statistics

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How do effect size and statistical significance differ?

1

2

3

4

5

6

7

1 Effect Size

2 Statistical Significance

3 P-Value Explained

4 Sample Size Impact

5 Practical vs. Statistical

6 Misinterpretations Avoided

7 Here’s what else to consider

Statistics

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