    Chapter 6: Analysing the Data Part III: Common Statistical Tests # Example 1

Suppose the relative frequencies of marital status for the population of adult Australian females under 40 years of age are as follows:

 General Population Sample (N=200) Marital status Relative Freq Observed Frequencies Married 0.55 100 Single 0.21 44 Separated 0.09 16 Divorced 0.12 36 Widowed 0.03 4

Figure 6.11 Data for first one-sample chi-square example.

Then suppose an investigator wanted to know whether a particular sample of 200 adult females under age 40 was drawn from a population that is representative of the general population as described above. The observed frequencies (i.e., actual numbers out of 200) for the sample are also given above.

By applying the procedures described below we can decide whether the sample distribution is close enough to the population distribution to be considered representative of it. We calculate Expected frequencies for each of the cells in our sample distribution. If in our general population, 55% of such women are married then we would expect 55% of 200  = 110 in our sample to be married. Similarly for each of the other categories. Therefore the expected number of Single women would be 21% of 200 = 42, for Separated 9% of 200 = 18, Divorced = 12% of 200 = 24, and Widowed 3% of 200 = 6. We then get the difference between each Expected and each Observed, square this, and then divide this result by the Expected.

## Steps in hypothesis testing

### Step 1

Ho: The sample follows the hypothesised distribution.

H1: The sample does not follow the hypothesised distribution.

### Step 2

Expected frequencies should not be below 5 in any cell

Observations should be independent of each other

### Step 3 =0.91 + 0.10 + 0.22 + 6.00 + 0.67

=7.90

### Step 4

You then refer to your 2 tables (see Howell, p. 672, under .050 heading) with df = C-1 = 4 (i.e., the number of categories minus 1 and find a critical value of 9.49 and hence our calculated value is not significant. We do not reject Ho.

### Step 5

We conclude that our sample distribution is not significantly different to our population distribution ( 2 (4) = 7.90, p> 0.05).

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