Question

A counselor used a single-factor ANOVA to study the effects of different types of student involvement on students' feeling of belonging at the university. After the study, the report contained the following test statistic: F(2,27)=5.625, p<.05.

a.Given the results of the test, which error was potentially made? (type 1, type II, no error, cannot be determined)

b. If the study was replicated multiple times, what is the probability that each of the subsequent studies would result in differences among groups at least as extreme as the one displayed in this study? (0.0, Less than 0.05, More than 0.05, 1.00, Cannot be determined).

Answer 1

a)

Here we are given with the fact that the report contained the test statistic F(2,27) = 5.625

level of significance considered here is 0.05.

Also, we know that p value of the test is less than the level of significance. Hence, the null hypothesis under this one factor ANOVA set up is rejected.

The null hypothesis considered here was:

all the effect of different types of student involvement on sudents' feeling of belonging at the university is same.

Based on the sample taken, we can conclude that we reject the null hypothesis at level of significance 0.05.

When a hypothesis testing occurs, we can make type I error or type II error.

Here we don't know if the null hypothesis is true or the alternate one. (which is at least one effect is not equal from that of others)

So, it can not be determined that what type of error is potentially made here, because we have no information on actually which hypothesis(null or alternative) is true.

b)

Here testing of hypothesis is done based on a random sample. If we take a different sample, then the conclusion of the hypothesis thesis may not remain same. Based on the given sample the hypothesis was rejected at the level of significance alpha = 0.05 .

But it may happen that, based on some other sample, the hypothesis of interest is failed to be rejected at the given level of significance. This is because the F statistic value is dependent on the sample taken, so as the sample changes, sample value changes and hence the F statistic value also changes. Hence we may end up with some different conclusion, if the experiment of testing is repeated multiple times.

We are given p value < 0.05

=>

Suppose the hypothesis is repeated n times, then probability that all the test are resulting in difference, then, if the observed value of F statistics are found to be

then the required probability is

as they are independent.

Hence the required probability is less than 0.05