The Independent Samples T-Test s1

The Chi Square Test of Homogeneity The Chi Square Test of Homogeneity tests whether it is reasonable to believe that a population is broken down into categories they have the same number of members in each category. If so the population is said to be homogeneous. In other words, each cell is the same as every other cell in the table.

Assumptions and Conditions (They are still the same!!!!)

Counted Data Condition –

Random Condition –

Expected Counts Condition –

Hypotheses

H0 = The proportion that falls into each category is the same for both populations.

H A = For at least category the proportion for one population is different from the other.

The test statistic ( c 2 ) needs the following:

1. Make a Chi Square Table! This time the table will be a 2 way table though!

Variable Observed Total Division Expected of Observed Variable Expected

Total Grand Total

2. Calculate Expected Frequencies (A.K.A Expected Counts) (row total)( column total ) f = e grand total 3. Test Statistic:

The same!!

4. Degrees of Freedom:

df = (r – 1) (c – 1)

5. The P-Value for your data is the probability of getting a value of c 2 as extreme as or even more extreme than the one in the sample, assuming the null is true. Approximate the P-Value by comparing the value of c 2 to the appropriate value of c 2 in the table in the back of the book or by using your calculator.

Conclusion in Context

If the P-Value is smaller than the alpha level or if the c 2 value is larger than the value in the back of the book then reject the null hypothesis. If not, there is no evidence that the null is false and you don’t reject it.

Example: This question is done out on page 599. Do the problem first on your own using the guide you just filled in. Check in the book to see that you carried out the test correctly.

In November 1997 Gallup released the results of a poll on family values for different nations of the world. One question asked is “Do you think it is necessary to have a child at some point in your life in order to feel fulfilled?” The number of adults in some large countries who gave various answers are given in a 2 way table below. Test the hypothesis that the proportion of adults who would give each answer is the same for each country.

U.S. India Mexico Canada Germany Total Yes 460 930 610 590 490 3080 No 510 60 380 370 450 1770 Undecided 30 10 10 40 60 150 Total 1000 1000 1000 1000 1000 5000