CK-12 Probability and Statistics - Advanced

http://www.ck12.org Chapter 10. Chi-Square

Lesson Summary

1. The Chi-Square Test of Independence is used to assess if 2 factors are related. It is commonly used in social
   science research to examine behaviors, preferences, measurements, etc.


2. As with the Chi-Square Goodness-if-Fit test, tables help capture and display relevant information.


3. For each cell in the table constructed to run a chi-square test, we need to calculate theexpected frequency.The
   formula used for this calculation is:

Expected Frequency=

(Row Total)(Column Total)

Total Number of Observations

4. To calculate the Chi-Square statistic for theTest of Independence,we use the same formula as the Goodness-of-
   Fit test. If the calculated Chi-Square value is greater than the critical value, we reject the null hypothesis.


5. We perform theTest of Homogeneityto examine the randomness of a sample. The Test of Homogeneity tests
   whether various populations are homogeneous or equal with respect to certain characteristics.

Review Questions

1. What is the Chi-Square Test of Independence used for?


2. True or False: In the Test of Independence, you can test if two variables are related but you cannot test the
   nature of the relationship itself.


3. When calculating the expected frequency for a cell in a contingency table, you use the formula:
   (a)

Expected Frequency=

(Row Total)(Column Total)

Total Number of Observations

(b)

Expected Frequency =

(Total Observations)(Column Total)

Row Total

(c)

Expected Frequency=

(Total Observations)(Row Total)

Column Total

Please use the table below to answer the following review questions.

TABLE10.11: Research Question: Are females at UC-Berkeley more likely to study abroad than
males?

Studied Abroad Did Not Study Abroad

Females 322 460

Males 128 152

4. What is the total number of females in the sample?