Question

The distribution of the test statistic for analysis of variance is the F-distribution. true or false

Answer 1

Answer:

True. See explanation below

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

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"  

If we assume that we have $k$ groups and on each group from $j=1,\dots,k$ we have $k$ individuals on each group we can define the following formulas of variation:  

$SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2$  

$SS_{between=Treatment}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2$  

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2$  

And we have this property  

$SST=SS_{between}+SS_{within}$  

The degrees of freedom for the numerator on this case is given by $df_{num}=k-1$ where k represent the number of groups.  

The degrees of freedom for the denominator on this case is given by $df_{den}=df_{between}=N-k$.  

And the total degrees of freedom would be $df=N-1$

And the we can find the F statistic $F=\frac{MSR}{MSE}$