Question

Suppose that a one-way ANOVA is being performed to compare the means of three populations and that the sample sizes are $10$,$12$ , and $15$. Determine the degrees of freedom for the $F$-statistic.

Short answer

$F$-statistic $(2,34)$degrees of freedom

Step-by-step solution

-Introduction 

One way ANOVA:

One-way ANOVA (“ANOVA”) compares the means of two or more independent groups to see if there is statistical evidence of single-factor ANOVA with significantly different relevant population means.

Single Factor ANOVA:

Judge. Analysis of variance (ANOVA) is one of the most commonly used techniques in life and environmental sciences.

Step 2- Information

The $3$populations to consider is $k=3$, and the number of observation islocalid="1654190826907" $37$, or localid="1654190834085" $n=37$.

Step 3- Explanation

Therefore, the degrees of freedom of the $F$ statistics are as follows:

$df=(k-1,n-k)$

$=(3-1,37-3)$

$=(2,34)$