Question

I am doing a research paper in statistics on how college degrees effect quality of life. I came up with the below data. What statistical test would I use to compare the variables? How would I set up the data in SPSS? I am using the null hypothesis that there is no significant change in quality of life with degrees and the alternative hypothesis is that there is significant change in quallife with college degrees.

Level	Total	Poor	Fair	Good	Excellent
Highschool	719	22	128	366	203
College	477	7	40	187	243

Answer 1

The data here is on the level of the degree i.e. high school or college and the effect of the same on the quality of life. Since the goal is to check if there is any relation between the two variables, we can perform a goodness of fit chi-square test on this data.

The given data is:

Level	Total	Poor	Fair	Good	Excellent	TOTAL
Highschool	719	22	128	366	203	1438
College	477	7	40	187	243	954
TOTAL	1196	29	168	553	446	2392

The alternate hypothesis is that there is a relation between the two variables and the null hypothesis is that there is no relation between the two variables.

If there is a relation between the two variables, we can get an expected value for each of the cells by multiplying the total of the row and the total of the column and then dividing this value by the grand total. Doing so, we get an expected table as:

Level	Total	Poor	Fair	Good	Excellent	TOTAL
Highschool	719	17.4339	100.9967	332.4473	268.1221	1438
College	477	11.5661	67.0033	220.5527	177.8779	954
TOTAL	1196	29	168	553	446	2392

Next we compute the ratio:

Doing so, we get:

Level	Total	Poor	Fair	Good	Excellent
Highschool	0	1.1959	7.2198	3.3864	15.817
College	0	1.8026	10.8827	5.1044	23.8416

The chi-square statistic is given by the formula:

Summing the values, we get:

The number of rows in the table is n1 = 2 and the number of columns in the table are n2 = 5. Hence, the degrees of freedom become: df = (n1 - 1) + (n2 - 1) = (2 - 1) + (5 - 1) = 1 + 4 = 5.

Let the significance level be 0.01. Using a chi-square table, we get a critical value of 15.086.

Since the chi-square statistic is greater than the critical value, we can reject the null hypothesis and conclude that there is a significant relation between the two variables.