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# Statistics - ANOVA - Family planning agency

1. Please explain in simplest terms F statistic and F test?

2. Under what situations can or could you use the ANOVA? Your answer should at least comment on the type of data needed.

3. A family planning agency wants to know if a religion's emphasis on family and child bearing has any influence on family size. Specifically, they are interested in any possible differences in family size between Catholic, Mormon, Protestant and Other families. You draw a random sample from census data and find that the mean sizes of the four groups are indeed different. How might you test the significance of this difference? What information would you need to know before using this approach?

4. A farmer is interested in knowing if added water and fertilizer would increase crop yield. Since this involves added work and expense, he does not want to do it unless he can see a payback. He divides his fields into 4 sections and adds additional water to two of them and additional fertilizer to two of them - giving one field with no changes, one with more water, one with more fertilizer, and one with more water and fertilizer. How could he analyze the results to determine what, if any, impact the added work produced?

5. Can nonparametric tests be used in measuring how some populations are more at risk of been contaminated by aids than others for example? Are these statistics better measured through parametric tests such as the T-Test?

#### Solution Preview

1. Please explain in simplest terms F statistic and F test?

We use F-statistic in F-test.
F-statistic is a characteristic of the sample which is used in F-test.
F-test is statistical process which help us determine if the sample is true representation of the population

2. Under what situations can or could you use the ANOVA? Your answer should at least comment on the type of data needed.
If there are more than two samples to be tested if there is any significant difference between means we use ANOVA. The data should be quantitative.
For example we wish to test the sales in three outlets we use ANOVA

Outlet A Outlet B Outlet C
10 14 31
12 15 14
64 21 6

3. A family ...

#### Solution Summary

An explanation of the F test along with an application of ANOVA tests and some case questions on a family planning agency and a farmer.

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