Question

A researcher conducted a test to determine how sleep influenced learning. He had three conditions: normal sleep, reduced sleep, and no sleep. Mean performance scores for the Normal Sleep, Reduced Sleep, and No Sleep groups were 18.0, 16.6, and 15.6, respectively. His F ratio was 0.97. Therefore, he concluded that those who sleep perform better than those who have reduced sleep, who perform better than those with no sleep.

List two problems with this scenario, why are they problems.

Answer 1

The first problem is that -

when we compare more than 2 samples for equality of their means we use ANOVA which finally gives F-ratio based on which we reject or accept the claim of equal means. Now ANOVA use ratio of mean squares within and mean square error to calculate the F which involves knowledge of degrees of freedom.

So degrees of freedom are not given

secondly,

we also don't have the level of significance it might happen that some hypothesis is rejected based on a specific level of significance but when we change the level of significance it might be accepted.

So clarity about the level of significance is must for deciding whether to reject or accept the hypothesis.

so a combined knowledge of degrees of freedom and level of significance allows one to look for a specific critical F value which helps in deciding the result and both these things are not given so we cannot say in the above problem that the conclusion drawn by the researcher is appropriate statistically.  

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