# Hypothesis testing (ANCOVA) • Null Hypothesis ..

The F statistic is computed by taking the ratio of what is called the "between treatment" variability to the "residual or error" variability. This is where the name of the procedure originates. In analysis of variance we are testing for a difference in means (H_{0}: means are all equal versus H_{1}: means are not all equal) by evaluating variability in the data. The numerator captures between treatment variability (i.e., differences among the sample means) and the denominator contains an estimate of the variability in the outcome. The test statistic is a measure that allows us to assess whether the differences among the sample means (numerator) are more than would be expected by chance if the null hypothesis is true. Recall in the two independent sample test, the test statistic was computed by taking the ratio of the difference in sample means (numerator) to the variability in the outcome (estimated by Sp).

## Null Hypothesis (H0): Write your null hypothesis here

### 1) Write a Null and Alternative Hypothesis

If you're doing a two-way anova, your statistical life will be a lot easier if you make it a balanced design. When there is only a single observation for each combination of the nominal variables, there are only two null hypotheses: that the means of observations grouped by one factor are the same, and that the means of observations grouped by the other factor are the same.

### you can’t reject the null hypothesis that the variances are equal.

Find: a) the variance between the different types of peppers, b) variance within each type of pepper, c) the F Test Statistic, d) the F critical value. Develop the Null and Alternative Hypothesis, and using a = 0.05 test your hypothesis. State your conclusion.