Chapter 6: Analysing the Data Part III: Common Statistical Tests

# Example 3

A group of college students is asked to answer the following multiple-choice question in a values inventory:

What do you believe is the true nature of God?

1. I believe in a personal God who has revealed Himself in the Bible.

2. There is a God, Father of all men, who is common to all religious faiths. It is not particularly important whether a man is a Christian, Jew, Moslem, Hindu, and so on.

3. I believe in a Supreme Being or First Cause, but I cannot believe in a personal God.

4. The nature of God is not (or cannot) be known by man.

5. There is no God.

The respondents were identified by gender and the research question becomes: Is there an association between the types of responses students give and gender? Or, equally, are gender and type of response independent? The following bivariate frequency table resulted. The observed numbers are the actual numbers of students that chose that response option. E stands for the Expected number in each cell.

 1 2 3 4 5 Totals Males E=18 E=40 7 4 1 70 observed=12 observed=33 17 8 0 Females E=36 80 14 8 2 140 observed=42 87 4 4 3 Totals 54 120 21 12 3 210

## Steps in hypothesis testing

### Step 1

Ho: Sex of respondent and response on survey are independent.

H1: Response on survey is dependent upon the sex of the respondent.

### Step 2

Expected values in any cell > 5.

[Note, 3 cells do not satisfy this requirement!
Perhaps Response 5 would be better removed from the analysis or combined with Response 4.
However, for illustration purposes we let things remain as they are!]

### Step 3

The calculation of the expected frequencies will be illustrated for cell11:

Note, these expected values can also be determined intuitively. 54 students out of the total of 210 (= .257) chose Response 1. Therefore, if males and females were independent in their choice of response we would expect .257 of the males to choose Response 1 ( = .257 X 70 = 18) and .257 of the females to choose Response 1 ( = .257 X 140 = 36).

The calculation of the chi-square is as follows:

### Step 4

df=Number of categories minus 1 for one variable multiplied by the Number of categories minus one for the other variable [i.e., (r-1)(c-1)]

=4 (inventory variable) X 1 (sex variable)

=4

Enter the Chi-square table (in Howell, p. 672) at df = 4 and travel along until the calculated value is exceeded. In this case the largest tabled value is 14.86 and our calculated value easily exceeds this, hence we can associate a p-value to the above data of "p < 0.005". This is obviously significant. Reject the null hypothesis.

### Step 5

There is a significant relationship between sex of the respondent and response to the question (2(4) = 33.77, p < 0.005). While the test of independence does not specifically identify the difference between the responses of the two groups, an examination of the available responses and of the bivariate frequency table suggests that the females are more inclined to believe in a personal God than are the males. (There are statistical ways of determining exactly which cells are significantly different and which ones aren't, but we are not going to deal with them in this unit).

Unfortunately, we cannot get SPSS to do the above calculations for us very easily. SPSS requires individual cases and the category scores for those cases. In other words we need the raw data not the totals as shown above.