## Null and Alternative Hypothesis | Real Statistics Using …

where k is the number of comparison groups and N is the total number of observations in the analysis. If the null hypothesis is true, the between treatment variation (numerator) will not exceed the residual or error variation (denominator) and the F statistic will small. If the null hypothesis is false, then the F statistic will be large. The rejection region for the F test is always in the upper (right-hand) tail of the distribution as shown below.

In the survey study example given the data showed tea drinkers had fewer health problems. Imagine the experimenter's hypothesis (explanation) is, "This proves tea prevents health problems."

## In hypotheses tests can you make assumptions under …

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).

## 0 is false and that the alternative hypothesis Ha is ..

Psychologists would have a problem with this statement. First psychologists don't use the term "prove" which is more a philosophical or math (cf. proofs) term. We would use the terms the hypothesis to be more logically correct.

## Alternative hypothesis HA- question explored by the investigator

The technique to test for a difference in more than two independent means is an extension of the two independent samples procedure discussed previously which applies when there are exactly two independent comparison groups. The ANOVA technique applies when there are two or more than two independent groups. The ANOVA procedure is used to compare the means of the comparison groups and is conducted using the same five step approach used in the scenarios discussed in previous sections. Because there are more than two groups, however, the computation of the test statistic is more involved. The test statistic must take into account the sample sizes, sample means and sample standard deviations in each of the comparison groups.

## reject Ho and accept the Alternative, Ha.

If one is examining the means observed among, say three groups, it might be tempting to perform three separate group to group comparisons, but this approach is incorrect because each of these comparisons fails to take into account the total data, and it increases the likelihood of incorrectly concluding that there are statistically significate differences, since each comparison adds to the probability of a type I error. Analysis of variance avoids these problemss by asking a more global question, i.e., whether there are significant differences among the groups, without addressing differences between any two groups in particular (although there are additional tests that can do this if the analysis of variance indicates that there are differences among the groups).

## (Ho) in favor of the alternative hypothesis (Ha).

If you have done Critical Thinking programs you may have read how another explanation for the data is called an "alternative explanation". However, the advantage of using the acronym PRAH instead of alternative explanation is it is more precise and, if your class requires you to come up with examples, PRAH will guide you to better examples. You can use the initials to help develop and test the quality of your own alternative explanations. Let's work through developing a PRAH for the tea study.