Educational Statistics

Practice Exercise 20: One-sample Chi-Square

1. When is it appropriate to use the one-sample chi-square test to analyze data?

2. What name is commonly used for the one-sample chi-square test?

3. What does the degrees of freedom in a one-sample chi-square test approximate?

4. How would you explain the procedure for determining the degrees of freedom for

a one-sample chi-square test?

Use the Chi-Square option in the Nonparametric Tests menu to answer the questions

based on the following scenario.

Some researchers believe that abnormal behavior is more likely to occur during a full moon. To test this belief, a one-year study was conducted that categorized new clients at a mental health unit by lunar phases. The following data concerning the number of admissions during each phase was recorded. (Assume a critical level of significance of .05 and the expected frequencies are equally distributed across phases)

Full Moon New Moon First Quarter Third Quarter

31 25 30 28

5. Write an appropriate null hypothesis for this analysis.

6. What is the value of the chi-square statistic?

7. What are the reported degrees of freedom?

8. What is the reported level of significance?

9. Based on the results of the one-sample chi-square test, is there a statistically

significant difference in the percentage of clients admitted during each moon

phase?

10. Report and interpret your findings as they might appear in an article.

Practice Exercise 21: One-sample Chi-Square

Use the Chi-Square option in the Nonparametric Tests menu to answer the questions based on the following scenario. (Assume a critical level of significance of .05 and use information from the scenario to determine the expected frequencies for each category). A superintendent in interested in determining if the graduating seniors at the local high school are performing better than expected on the state approved exit examination. The examination classifies students into one of four categories: not proficient, approaching proficiency, basic proficiency, and advanced proficiency. The frequency of classifications for the 100 students from the most recent graduating class and the percent of students statewide placed in each category are reported below. Not Proficient Approaching

Proficiency Basic

Proficiency Advanced

Proficiency High School 13 18 45 24

Statewide 21% 27% 39% 13%

1. Based on the percentages that were observed statewide, if the percent of students

in each category at the high school did not differ from the statewide percentages,

what would be the expected values for each classification?

2. What are the observed percentages for each category at the local high school?

(Note: SPSS does not include this information in the output. It must be manually

calculated by dividing the number in each category by the total number of

students and multiplying by 100.)

3. Write an appropriate null hypothesis for this analysis.

4. What is the value of the chi-square statistic?

5. What are the reported degrees of freedom?

6. What is the reported level of significance?

7. Based on the results of the one-sample chi-square test, is there a statistically

significant different between the distribution of students at the local high school

and the statewide distribution?

8. Report and interpret your findings as they might appear in an article.