Respuesta :
Answer:
The degrees of freedom for the denominator on this case is given by [tex]df_{den}=df_{between}=N-K=3*15-3=42[/tex].
Step-by-step explanation:
Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample". Â
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean" Â
If we assume that we have [tex]3[/tex] groups and on each group from [tex]j=1,\dots,15[/tex] we have [tex]15[/tex] individuals on each group we can define the following formulas of variation: Â
[tex]SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 [/tex] Â
[tex]SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 [/tex] Â
[tex]SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 [/tex] Â
And we have this property Â
[tex]SST=SS_{between}+SS_{within}[/tex] Â
The degrees of freedom for the numerator on this case is given by [tex]df_{num}=df_{within}=k-1=3-1=2[/tex] where k =3 represent the number of groups.
The degrees of freedom for the denominator on this case is given by [tex]df_{den}=df_{between}=N-K=3*15-3=42[/tex].
And the total degrees of freedom would be [tex]df=N-1=3*15 -1 =44[/tex]
And the F statistic to compare the means would have 2 degrees of freedom on the numerator and 42 for the denominator. Â
