Final answer:
The question involves ANOVA with five groups and four values in each group. The degrees of freedom for among-group variation, within-group variation, and total variation are provided. The sum of squares (SS) values and mean squares (MS) are given, along with the F statistic.
Step-by-step explanation:
The question pertains to the analysis of variance (ANOVA), which is a statistical test used to compare means of multiple groups. In this case, there are five groups and four values in each group.
The degrees of freedom are important in ANOVA calculations. It is given that the degrees of freedom for the among-group variation is 4, and for the within-group variation, it is 15. The total degrees of freedom is stated as 19.
The question also provides the sum of squares (SS) values for the factor (between) variation, error (within) variation, and the total variation. These values are 344.16, 1,219.55, and 1,563.71 respectively.
To compute the mean squares (MS), the sum of squares is divided by its respective degrees of freedom. For the factor variation, MS = SSbetween / df = 344.16 / 3 = 114.72. For the error variation, MS = SSw / df = 1,219.55 / 15 = 81.30.
The F statistic is computed by dividing the mean square for the factor by the mean square for the error. FSTAT = MSbetween / MSw = 114.72 / 81.30 = 1.41.