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(b) Can an effect be both small and statistically significant? No, it is not possible for a small effect with no practical relevance or importance to be statistically significant if o is very small, more so if the sample size is very large. Yes, it is possible for a small effect with no practical relevance or importance to be statistically significant if o is very small, if the sample size is very large, or both. Yes, it is possible for a small effect with no practical relevance or importance to be statistically significant if o is very large, especially if the sample size is small. No, it is not possible for a small effect with no practical relevance or importance to be statistically significant if µ is very small, if the sample size is very small, or both.

(b) Can an effect be both small and statistically significant? No, it is not possible for a small effect with no practical relevance or importance to be statistically significant if o is very small, more so if the sample size is very large. Yes, it is possible for a small effect with no practical relevance or importance to be statistically significant if o is very small, if the sample size is very large, or both. Yes, it is possible for a small effect with no practical relevance or importance to be statistically significant if o is very large, especially if the sample size is small. No, it is not possible for a small effect with no practical relevance or importance to be statistically significant if µ is very small, if the sample size is very small, or both.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Can an effect be both small and statistically significant? How do sample size and sigma affect p-value?

**Title: Understanding Statistical Significance of Small Effects** **Question: Can an effect be both small and statistically significant?** - **Option 1**: No, it is not possible for a small effect with no practical relevance or importance to be statistically significant if σ (standard deviation) is very small, more so if the sample size is very large. - **Option 2**: Yes, it is possible for a small effect with no practical relevance or importance to be statistically significant if σ is very small, if the sample size is very large, or both. - **Option 3** (Selected Answer): Yes, it is possible for a small effect with no practical relevance or importance to be statistically significant if σ is very large, especially if the sample size is small. - **Option 4**: No, it is not possible for a small effect with no practical relevance or importance to be statistically significant if μ (mean) is very small, if the sample size is very small, or both. **Explanation:** The choice selected here highlights that small effects can be statistically significant when standard deviation (σ) is large and sample size is small, emphasizing the impact of variance and sample size on statistical outcomes.
Transcribed Image Text:**Title: Understanding Statistical Significance of Small Effects** **Question: Can an effect be both small and statistically significant?** - **Option 1**: No, it is not possible for a small effect with no practical relevance or importance to be statistically significant if σ (standard deviation) is very small, more so if the sample size is very large. - **Option 2**: Yes, it is possible for a small effect with no practical relevance or importance to be statistically significant if σ is very small, if the sample size is very large, or both. - **Option 3** (Selected Answer): Yes, it is possible for a small effect with no practical relevance or importance to be statistically significant if σ is very large, especially if the sample size is small. - **Option 4**: No, it is not possible for a small effect with no practical relevance or importance to be statistically significant if μ (mean) is very small, if the sample size is very small, or both. **Explanation:** The choice selected here highlights that small effects can be statistically significant when standard deviation (σ) is large and sample size is small, emphasizing the impact of variance and sample size on statistical outcomes.
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