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Hello! I will take number 3. I consider these self-explanatory, being a 1-1 and a 2-2 definition. Thus, one-way is used according to one factor of the sample data, while two-way is used according to two different factors of the sample data.

Explanation / Answer

1. what is one-way analysis of variance?
The analysis of variance is one of the method of testing the equality of more than two population means. The test of significance based on t distribution is a procedure only for testing the significance of the difference between two sample means. In situation when we have three or more samples, then we need an alternative procedure for testing the hypothesis that all the sample are drawn from same population that is the they have same means.
For example five fertilizers are applied to four plots is of wheat and yeild of wheat on each of the plot is given so here we may be interested in finding out wheather the effects of these fertilizers on the yeild is significantly difference. The answer to this problem is provided by ANOVA and the basic purpose of ANOVA is to testing the homogeneity of several means.

2) See when number of groups increases the number of test increases this implies that the probability of making

a Type I error increases as the number of tests increase.

here If we consider three t test and the probability of a Type I error for the analysis is set at 0.10 and 3 t-tests are

done, then the overall probability of a Type I error for the set of tests = 1 – (0.90)^3 = 0.27 instead of 0.10.

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