Question

Describe a scenario where a researcher could use a One-Way ANOVA to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use? Please do not provide answer with "Goodness of fit" scenario.

Answer 1

A scenario where a researcher could use a one way ANOVA is when researcher wants to compare more than two means. One way is ANOVA is best to use when we need to compare more than two means. Using One way for compairing more than two Means is better than t test because the chances of errors might increase if t-test is used when we have to compare more than two means of the populations concurrently, that is why one way ANOVA is used.

Suppose we want to compare the mean scores obtained by three different study technique.

Our null hypothesis for this will be

H0:

and alternative hypothesis is

Ha: At least one mean is different.

Our three different study technique will be independent variables or you can say treatments

and the scores obtaind by three different study techiniques will be our dependent variable.

Now we will calculate sum of squares due to treatments , sum of squares due to error , total sum of squares, Mean sum of  squares due to treatments and Mean sum of  squares due to errors.

Then we calculate test statistic which is

F = Mean sum of  squares due to treatments/ Mean sum of  squares due to errors

Then we will compare this F statistic with Fcritical.

Reject H0 if F cal>F crit otherwise fail to reject H0.

I hope this much will be sufficient. Please comment for any doubt. Thank you.