Part A-
Assignment 1: One-sample Chi-Square
Directions: Use the Chi-Square option in the Nonparametric Tests menu to answer the questions based on the following scenario. (Assume a level of significance of .05 and use information from the scenario to determine the expected frequencies for each category)
During the analysis of the district data, it was determined that one high school had substantially higher Graduate Exit Exam scores than the state average and the averages of high schools in the surrounding districts. To better understand possible reasons for this difference, the superintendent conducted several analyses. One analysis examined the population of students who completed the exam. Specifically, the superintendent wanted to know if the distribution of special education, regular education, and gifted test takers from the local high school differed from the statewide distribution. The obtained data is provided below.
|
|
Special Education*
|
Regular Education
|
Gifted
|
|
Number of student's from the local high school who took the Graduate Exit Exam
|
37
|
128
|
14
|
|
Percent of test taking students statewide who took the Graduate Exit Exam
|
19%
|
70%
|
11%
|
For purposes of testing, special education includes any student who received accommodations during the exam.
1. If the student distribution for the local high school did not differ from the state, what would be the expected percentage of students in each category?
2. What were the actual percentages of local high school students in each category? (Round answer to two decimal places)
3. State 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, was the population of test taking students at the local high school statistically significantly different from the statewide population?
8. Present the results as they might appear in an article. This must include a table and narrative statement that reports and interprets the results of the analysis.
Assignment 2: Chi-Square Test of Independence
Directions: Use the Crosstabs option in the Descriptives menu to answer the questions based on the following scenario. (Be sure to select Chi-square from the Statistics submenu and Observed, Expected, Row, and Column in the Cells submenu. Assume a level of significance of .05)
The superintendent is interested in determining if student participation in sports is related to performance on the Graduate Exit Exam of a local high school. The superintendent obtained the performance scores for the test-taking students and recorded their type of sports participation (none, one sport, multiple sports). The superintendent reported the performance scores as proficient or not proficient. The resulting data are provided below:
|
Proficient
|
Sports Participation
|
|
None
|
One Sport
|
Multiple Sports
|
1. Of the students that were proficient, what percent of the participates were in no sports, one sport, and multiple sports? (Round your answer to 1 decimal place).
2. State an appropriate null hypothesis for this analysis.
3. What is the value of the chi-square statistic?
4. What are the reported degrees of freedom?
5. What is the reported level of significance?
6. Based on the results of the chi-square test of independence, is there an association between sports participation and proficiency on the Graduate Exit Exam?
7. Present the results as they might appear in an article. This must include a table and narrative statement that reports and interprets the results of the analysis.
Part B-
Practice Exercise 1: 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 |
Thire 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 2: 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.
Practice Exercise 3: Chi-Square Test of Independence
When is it appropriate to use the chi-square test of independence instead of the one sample chi-square? (Hint: You can get information on this test through the SPSS Help menu by selecting Topics and searching for chi-square in the index)
Use the Crosstabs option in the Descriptives menu to answer the questions based on the following scenario. (Be sure to select Chi-square from the Statistics submenu and Observed, Expected, Row, and Column in the Cells submenu. Assume a critical level of significance of .05)
A school district is interested in determining if gender affects attitudes towards compulsory cooperative learning in schools. The gender of 110 students was reported as well as there answer to the following question: "Should cooperative learning be made compulsory in schools?" (Yes, Maybe, No). The distribution of responses is given below.
|
Yes |
Maybe |
No |
| Male |
18 |
2 |
34 |
| Female |
8 |
6 |
42 |
1. Write an appropriate null hypothesis for this analysis.
2. What is the value of the chi-square statistic?
3. What are the reported degrees of freedom?
4. What is the reported level of significance?
5. Based on the results of the chi- square test of independence, is there a statistically significant relationship between gender and attitude toward cooperative learning?
6. What percent of males favor compulsory cooperative learning in schools?
7. What percent of females favor compulsory cooperative learning in schools?
8. Based on the percent within gender, are males more likely, less likely, or equally likely to support compulsory cooperative learning in schools?
9. Report and interpret your findings as they might appear in an article.
Practice Exercise 4: Chi-Square Test of Independence
Use the Crosstabs option in the Descriptives menu to answer the questions based on the following scenario. (Be sure to select Chi-square from the Statistics submenu and Observed, Expected, Row, and Column in the Cells submenu. Assume a level of significance of .05)
You are interested in determining the existence of a significant interaction between three Preferred Instructional Strategies and Gender. Two hundred students from three introductory psychology classes were asked about their preferred instructional strategy. The results are shown below:
|
Computer-based Tecnology |
Video |
Lecture |
| Male |
8 |
17 |
42 |
| Female |
10 |
73 |
50 |
1. Write an appropriate null hypothesis for this analysis.
2. What is the value of the chi-square statistic?
3. What are the reported degrees of freedom?
4. What is the reported level of significance?
5. Based on the results of the chi- square test of independence, was there a statistically significant relationship between gender and the instructional strategy preference?
6. Based on the percentages within gender does there appear to be a clear instructional preference among males? If so, what strategy is preferred?
7. Based on the percentages within gender does there appear to be a clear instructional preference among females? If so, what strategy is preferred?
8. Were the preferred strategies identified by the males and females the same?
9. Report and interpret your findings as they might appear in an article.