Which condition is listed as an assumption of ANOVA regarding sampling?

Which condition is listed as an assumption of ANOVA regarding sampling?

• A. Randomly sampled data
• B. Non-random sampling
• C. No sampling is required
• D. Large sample only

Answer: (A)

The key idea is that ANOVA relies on data collected by random sampling from the populations being compared. Random sampling helps ensure observations are independent and the sample is representative, which makes the estimated group means and variances valid for testing with the F-statistic. If sampling is non-random, bias and dependencies can creep in, distorting the results and undermining the test assumptions. It isn’t correct to say no sampling is required because ANOVA compares group means based on collected data. It also isn’t required that samples be large; smaller samples can still be analyzed with ANOVA if the assumptions about normality and equal variances are reasonably met.

The key idea is that ANOVA relies on data collected by random sampling from the populations being compared. Random sampling helps ensure observations are independent and the sample is representative, which makes the estimated group means and variances valid for testing with the F-statistic. If sampling is non-random, bias and dependencies can creep in, distorting the results and undermining the test assumptions. It isn’t correct to say no sampling is required because ANOVA compares group means based on collected data. It also isn’t required that samples be large; smaller samples can still be analyzed with ANOVA if the assumptions about normality and equal variances are reasonably met.