Questions: Which one of the following is part of the underlying strategy behind ANOVA? Combining the samples and ranking the data from lowest to highest. Comparing the sample means using the z-statistic. Comparison of mean through two sample estimates of the population variance.

Which one of the following is part of the underlying strategy behind ANOVA? Combining the samples and ranking the data from lowest to highest. Comparing the sample means using the z-statistic. Comparison of mean through two sample estimates of the population variance.

Transcript text: Which one of the following is part of the underlying strategy behind ANOVA? Combining the samples and ranking the data from lowest to highest. Comparing the sample means using the $z$-statistic. Comparison of mean through two sample estimates of the population variance.

Solution

Solution Steps

Step 1: Understanding ANOVA

ANOVA, or Analysis of Variance, is a statistical method used to compare the means of three or more samples to determine if at least one sample mean is significantly different from the others. The underlying strategy involves comparing the variance between the sample means to the variance within the samples.

Step 2: Evaluating the Options

Combining the samples and ranking the data from lowest to highest: This is not a part of the ANOVA strategy. This method is more related to non-parametric tests like the Kruskal-Wallis test.
Comparing the sample means using the $z$-statistic: The $z$-statistic is typically used for comparing two sample means, not for ANOVA, which involves more than two groups.
Comparison of mean through two sample estimates of the population variance: This is the correct strategy behind ANOVA. ANOVA compares the variance between the groups to the variance within the groups to determine if the means are significantly different.