Question

In your own words, explain in detail why the expected value for an F-ratio is equal to 1.00 when there is no treatment effect. Can F have a negative value? Explain (in your own words). Can SS have a negative value? Explain (in your own words). What can you take from these answers in preparing you for catching errors/mistakes when completing homework problems?
Note: While all answers above should be in your own words, they should be based on the textbook and other course resources.

Answer 1

The expected value for an F-ratio is equal to 1.00 when there is no treatment effect because the variance due to the treatment is equivalent to the variance due to the error.

F=(Mean Sum of Square due to treatment)/(Mean Sum of Square due to Error)

=(Variance due to treatment)/(Variance due to error)

No, F value can not have a negative value because the minimum value of both the Mean Sum of Square due to treatment and error is greater than zero. Whereas, these values may be zero when all the values are equal to each other.

No, SS can not have a negative value. It may be zero when all the values are equal otherwise it is greater than zero.

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What can you take from these answers in preparing you for catching errors/mistakes when completing homework problems?

Ans: In reality case, the F-ratio is equal to 1.00 is not happen in almost. It may be less than or greater than one. So, we can say that there may be a mistake on the calculation steps for F-test statistic.