Describe about F test in ANOVA.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Describe about F test in ANOVA.

Expert Solution
Step 1

Null Hypothesis:

H0: There is no significant difference between means of three populations.

Alternative Hypothesis:

H1: At least one mean is different.

Decision rule:

If F test statistic is greater than its critical value then reject the null hypothesis. Otherwise fail to reject the null hypothesis.

Decision rule:

If P-value ≤ α, then reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

 

Step 2

P-value for right-tailed test (greater than-type alternative):

The F-statistic is given by:

F = MSbetween / MSwithin

The F-statistic would follow the F-distribution with degrees of freedom (dfbetween, dfwithin), if the null hypothesis is true.

The P-value is the probability of obtaining a test statistic value as extreme as or more extreme than (in this case, “extreme” implies “greater than”) the observed test statistic value, given that the null, H0 is true. Thus, P-value = PHo (test statistic ≥ observed value of test statistic).

That is p-value =P(F> observed value of test statistic).

Based on decision rule, decide whether to reject the null hypothesis or not.

 

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