Discuss a situation in your home life, work life, school life, or that you found in the media where the correct analysis would be to conduct a goodness of fit, one-way chi-square. Set up the proper chi-square contingency table for the one-way chi-square. Then, include the expected frequencies and observed frequencies using both the textbook and the Blackboard weekly materials as guides. Report the calculated chi square statistic (you don't have to show all your work) and interpret your results.

For one of your peer-replies, check the calculations of at least one of your peers. Let them know if you agree with their calculations and interpretation. For the second peer-reply, suggest a way in which their described one-way chi-square could be made into a study design utilizing a second independent variable so that a two-way chi-square test of independence would be the appropriate test. No need to do create scores/do calculations in the second peer-reply.

Reminder: All replies to discussion postings are due by 11:59pm, CT on Saturday this week, since the course ends on Saturday.

INSTRUCTOR TIPS:

I thought I would provide an example of the calculations for a one-way chi-square. The data:

Black White Pink Red Blue

Observed 45 25 20 35 25

Expected 30 30 30 30 30

First, add across all observed scores and divide by the number of scores (5) to find the average score of 30.

Observed frequency is each of the actual 5 scores (45, 25 20, 35, & 25).Fo= each of the actual scores.

The expected frequency is the average score of 30. Fe = 30.

1) Find the difference between the observed scores and the expected score. 2) Square the difference.

• 45 - 30 = 15 --> 15*15 = 225
• 25 - 30 = -5 --> -5*-5 = 25
• 20 - 30 = -10 --> -10*-10 = 100
• 35 - 30 = 5 --> 5 *5 = 25
• 25 - 30 = -5 --> -5*-5 = 25

Now add all of the squared scores --> 225 + 25 + 100 + 25 + 25 = 400

To obtain the chi square statistic, divide by the expected score, Fe of 30: 400/30 = 13.33

Since the obtained chi square statistic of 13.33 exceeds the chi square critical value of 9.49, a relationship exists. The groups are said to be dependent on each other.

**Note that the chi square of 9.49 is specific to using 5 categories! See Blackboard notes to learn how to look up the critical chi square value if you use more or less than 5 categories being compared.