When interpreting F(7.31) = 4.78, p > 0.05. how many subjects were tested in this simple one-way ANOVA?

ANOVA or analysis of variance is a statistical test to find whether two different groups or categories are significantly different by testing their means and variance.
There are two types of ANOVA tests - one-way and two-way tests.

A one-way ANOVA test has one independent variable (categorical/factor) and a dependent variable that is normally distributed and continuous.
The F value in one-way ANOVA helps us to find if the variance between the means of two populations is significantly different or not.

A two-way ANOVA test has more than one independent variable (categorical/factor) and a dependent variable that is normally distributed and continuous.

It refers to the number of independent values in statistical analysis.
df = n - p, where n = sample size and p = the number of parameters.
In the one-way ANOVA test, since there is only one parameter (one independent variable), df = n-1.

We are given that:

F(7 , 31) = 4.78

Step 1: Find the total degrees of freedom.

The treatment df = 7

The error df = 31

[tex]df_{treatment} &\ +df_{error} &\ = df_{total}[/tex]

Hence, the total df = 7+31 = 38.

Step 2: Find the number of subjects tested.

We know that in a one-way ANOVA test:

df = n-1

⇒ 38 = n-1

⇒ n = 39.

Hence, 39 subjects were tested in this simple one-way ANOVA.

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