A doughnut shop wants to determine if there is a difference in donut sales at different times of the day and for different types of doughnuts. They are open in the morning, afternoon, and night, and offer the following flavors: vanilla, chocolate, red velvet, and marbled. There were a total of 48 sales recorded. The shop conducted a two-way ANOVA test and found an F test statistic for Flavor of 14.87. What would be the numerator degree of freedom for the F test statistic to determine if the factor flavor was significant

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AbsorbingMan AbsorbingMan · Answer 1 · 2021-04-14T13:43:28+02:00

Solution :

Let

[tex]$k_1$[/tex] = number of levels for the factors 'flavors' = 4

(4 levels vanilla, chocolate, red velvet and marbled)

The degree of freedom for the factor 'flavors' = [tex]$k_1$[/tex] - 1

= 4 - 1

= 3

Now defining the F test statistics for testing the significance of the factors, 'flavors' :

F test statics = [tex]$=\frac{Ms\text{ (factor falvor)}}{Ms \text{ (errors)}}$[/tex] , Ms = mean square

where F = [tex]$F_{k_1-1}$[/tex], error df.

Thus the numerator degrees of the freedom for the F test statistics to determine if the factor flavor was significant is = [tex]$k_1$[/tex] - 1

= 4 - 1

= 3