Question

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

Answer 1

Let

`$k_1$` = number of levels for the factors 'flavors' = 4

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

The degree of freedom for the factor 'flavors' =
`$k_1$` - 1

= 4 - 1

= 3

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

F test statics =
`$=\frac{Ms\text{ (factor falvor)}}{Ms \text{ (errors)}}$` , Ms = mean square

where F =
`$F_(k_1-1)$`, error df.

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

= 4 - 1

= 3