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The F ratio in a completely randomized ANOVA is the ratio ofGroup of answer choicesMSE/MSTMSE/MSTRMST/MSEMSTR/MSE

Question

The F ratio in a completely randomized ANOVA is the ratio ofGroup of answer choicesMSE/MSTMSE/MSTRMST/MSEMSTR/MSE

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Solution

The F ratio in a completely randomized ANOVA is the ratio of MSTR/MSE.

Here's a step-by-step explanation:

  1. ANOVA (Analysis of Variance) is a statistical method used to test differences between two or more means. It may seem odd that the technique is called "Analysis of Variance" rather than "Analysis of Means."

  2. In an ANOVA test, we compare the ratio of two variances, Between-group variability, and Within-group variability. If the null hypothesis is true, we expect F to have a value close to 1.0 most of the time. A large F ratio means that the variation among group means is more than you'd expect to see by chance.

  3. MSTR (Mean Square Between) and MSE (Mean Square Error) are two components of a one-way ANOVA.

  4. MSTR is the mean of the group variances, i.e., the variance within each group, averaged over all the groups. It estimates the common variance assuming the null hypothesis is true.

  5. MSE is the mean of the group means, i.e., the mean within each group, averaged over all the groups. It estimates the variance of the population from which the groups were sampled.

  6. The F ratio is the ratio of MSTR to MSE. If the null hypothesis is true, this ratio is expected to be close to 1. If the group means are very different, MSTR will be larger than MSE, and the F ratio will be larger than 1.

So, the correct answer is MSTR/MSE.

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