Q.94 - The Practice of Statistics for AP

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.

Step-by-Step Solution

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-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.