Question

Significance and sample size A study with $5000$ subjects reported a result that was statistically significant at the $5\%$ level. Explain why this result might not be particularly large or important.

Short answer

The sample size is too much large and for such large samples the value of the test statistic$t=\frac{\overline{x}-\mu }{s/\sqrt{n}}$

Step-by-step solution

Step-1 Given Information

Given In the question that A study with $5000$subjects reported a result that was statistically significant at the $5\%$level. we have to Explain why this result might not be particularly large or important.

Step-2 Explanation

The sample size is too much large and for such large samples the value of the test statistic

$t=\frac{\overline{x}-\mu }{s/\sqrt{n}}$

Would become very large too

Large values of test statistic then tends to very small P-values and therefore a statistically significant test even though the sample mean might not be very large and the difference between the assumed population mean.