Question

Suppose we want to test whether or not three means are equal. We want to perform this test with a 7% significance level.

If we perform an ANOVA test, what is the probability of the test producing accurate results (avoiding a Type I error)?

Suppose we, instead, run three separate hypothesis tests (t-tests), each with 7% significance level.

• Mean 1 = Mean 2
• Mean 1 = Mean 3
• Mean 2 = Mean 3

What is the probability that all three tests would be accurate? Hint: use principles of probability to help your calculations: P(accurate AND accurate AND accurate))  (Write your answer accurate without rounding.)

Why would we use ANOVA instead of three separate tests?

Why would we want to use three separate tests instead of ANOVA?

Answer 1

ANSWER:

Given that,

Level of significance is the probability of making type I error in the test.

So alpha = 7% means that, we will make an error in the test with probability of 0.07, at the same time it means that we will get the accurate result with a probability of 0.93.

1)

if we perform ANOVA  test to compare the three means, we are conducting one single test for all the three means, and thus the probability of accurate result is 0.93

2)

Now, if instead of ANOVA we use three different test for three pairwise comparison of mean, then accurate result will be produced if all the three test are accurate.

So the probability for accuracy of the three test will become

P(accurate result) =

3)

we use ANOVA instead of multiple test when we just want to see that if the means of the group different or not.

Why ANOVA Instead of three different test.

1) we need to perform more test if we do not use ANOVA.

2) Using the multiple test will increase the probability of making Type I error.

Why would we want to use three separate tests instead of ANOVA,

We use the multiple test when we want to see which group of mean exactly differ from each other.