Write a short answer for each question. You may include figures or references if

Question

Write a short answer for each question. You may include figures or references if need be.

1. The ANOVA model has three main assumptions:

1. Independences of observations

2. Normality - each group is normally distributed

3. Homoscedasticity - the variance of each group is equal

Choose one of the assumptions and explain why it is important. How might the results of the test be impacted if the assumption was violated?

2. In your own words, explain what a z-score is, and why it is important in statistics. 3. In your own words, explain what a p-value is, and how this is obtained from statistical testing? Suppose you ran a test, and got a p-value of 0.031. What does this mean?

Explanation / Answer

Answer to both question is as follows:

1. Assumption 1 explanation:You should have independence of observations, which means that there is no relationship between the observations in each group or between the groups themselves. For example, there must be different participants in each group with no participant being in more than one group. This is more of a study design issue than something you can test for, but it is an important assumption of the one-way ANOVA.

If your study fails this assumption, you will need to use another statistical test instead of the one-way ANOVA (e.g., a repeated measures design)

2. Z score or the number of deviations the point is away from the mean is the standardized score. For example, a Z of 2 means that the point is at 2 deviation more than mean.

p-value is defined as probability of finding the observed, or more extreme, results when the null hypothesis (H 0) of a study question is true.

A p-value of .031 means that there is very less probability of finding a more extreme value result when Ho is true. We will have to reject Ho in this case if alpha was .05 (or confidence level was 95%)

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