PU Application of The ANOVA T

Please respond to two students 

Student 1

Why would you use ANOVA when you could just run many sets of t-tests? [Think about practical considerations, as well as statistical considerations.]

The major reason we would use ANOVA is that we can make an unsatisfactory Type I error .   When testing the equality of three or more population means, the analysis of variance (ANOVA) technique is used and the F-statistic is used as the test statistic. Using ANOVA to test the equality of three or more population means requires that three assumptions are true: 1. The populations,  follow the normal distribution, 2. The populations have equal standard deviations (?), 3. The populations are independent.  When these conditions are met, F is used as the distribution of the test statistic.  Using the t distribution to compare the four population means, we would have to conduct six different t tests.  For each t test, suppose we choose an ? = .05.  Therefore, the probability of a Type I error, rejecting the null when it is true, is .05. The complement is the probability of .95 that we do not reject the null when it is true.  The ANOVA technique allows us to compare population means simultaneously at a selected significance level.  It avoids the buildup of Type I error associated with testing many hypotheses.  I like the ANOVA technique, since it cuts down the probability of making a Type I error.

Luis

Reference:

Lind, D., Marchal, W., & Wathen, S. (2019). Basic Statistics for Business and Economics (9th ed.). McGraw-Hill (Pages 341 – 342). Retrieved from https://newconnect.mheducation.com

Student 2

Good Afternoon,

-Why would you use ANOVA when you could just run many sets of t-tests? [Think about practical considerations, as well as statistical considerations.]

ANOVA would be used for t-testing even though we can use many other tests for t-testing, but ANOVA provides accurate results to simultaneously compare the mean population; when samples are categorized into two different factors. ANOVA reduces errors and generates accurate results. ANOVA allows us to simultaneously compare and contrast the means of populations when the samples are categorized into two obvious and different factors. There’s a clear differentiation between 2 population means that can be done, and that variance in results is more or less removed to a great extent by Anova. Dependency on one variable over the other can be studied more precisely; how the changes in 1 variable affect the other variable can be accurately analyzed using Anova. Lesser assumptions are required to be taken in Anova, which makes the results more precise. The error rate is significantly less, and wholesome results are achieved.

Resource

Lind, D., Marchal, W., & Wathen, S. (2021). Basic Statistics for Business and Economics (9th ed.). McGraw-Hil.

Sincerely,

Molly Collins


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