# ANOVA, P-Value and Equality of Mean

1) An agronomist wants to compare the crop yield of three varieties of chickpea seeds. She plants 15 fields, five with each variety. She then measures the crop yield in bushels per acre. The results are presented in the table (see attachment).

Use the following computer printout to test for the equality of mean crop yields of the three different seeds at 0.01 significance level. What is the p-value for this test. Explain the meaning of the p-value.

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#### Solution Preview

Good morning from Cleveland, Ohio...

Glad to help you out with your stats question. Presented below is an explanation to your question regarding the "p" value.

1. Always keep in mind the F Test or ANOVA is basically a multiple "t" test wherein you are seeking to determine differences between multiple goups; i.e., statistically significant differences between "mean" or "average" measurement values -- in your case chickpea yield of three different types of chickpeas.

2. Although the ANOVA will determine for you whether or not there are statistically significant differences between the mean measurement values of more than two groups or variables being measured, it will not permit you to say which one is more significant (or produces a better yield) than the other. When you have a statistically significant F value it is up to you, the research investigator, to determine which single comparison has caused the overall statistical significance.

3. F tests or ANOVA/Analysis of Variance tests can only function when you, the research investigator, have established a null hypothesis to test for statistically significant differences. In your situation, the null hypothesis would be stated as such: There exists no statistically significant difference in the yield factor of the three types of chickpeas under examination." From this point you compare the 3 mean values of chickpea yield all at once. The resulting F value is then calculated. From here you look at the between and within degrees of freedom, take these co-ordinates to the stat. table at the end of any stat. text book, and locate what ...

#### Solution Summary

This solution is provided in 1,124 words. It discusses what an ANOVA means and what the p-value of a study means.