Please make up and discuss research examples corresponding t

Please make up and discuss research examples corresponding to the various techniques from statistics known. Describe a plausible study for each of the following statistical procedures, indicating how it would apply and what results you would predict. Also include information about the number of participants you would assess and how you would go about estimating effect size and statistical power (when relevant).

a.   correlation

b.   multiple regression

c.   t test for independent means

d.   t test for dependent means

e.   ANOVA

f.   chi square for goodness of fit

Solution

a. correlation

We can test whether gpa and age are related to each other.

b. multiple regression

We can check whether gpa can be predicted using age, family income.

c. t test for independent means

We can check whether there is any significant difference in the gpa with respect to male and female students.

d. t test for dependent means

We can check whether there is any significant increase in the gpa this year with respect to last year.

e. ANOVA

We can check whether gpa is different among different racial groups.

f. chi square for goodness of fit

We can check whether there is any significant difference in student proportion with respect to different racial groups.