Part I. Correlation and Linear Regression
Imagine a researcher is interested in examining the relationship between self-esteem (Self_Estm) and productivity (Prod). The researcher is also interested in the ability to predict the productivity of teachers using years of teaching (Experience) as the predicting variable.
Use the “teacher’data.sav” dataset to conduct the analysis involving Self_estm, Prod, and Experience. Use this data to answer the questions below (these data have already been entered into the “teacher’data.sav” SPSS file).
Table 3
“teacher’data.sav” Dataset
| Sex | Self_Estm | Experience | Prod |
| M | 64 | 25 | 25 |
| M | 68 | 14 | 28 |
| F | 74 | 10 | 36 |
| M | 75 | 20 | 38 |
| F | 76 | 30 | 34 |
| F | 79 | 3 | 36 |
| F | 82 | 13 | 42 |
| M | 68 | 29 | 22 |
| M | 70 | 19 | 38 |
| F | 74 | 22 | 39 |
| F | 76 | 6 | 34 |
| F | 78 | 16 | 38 |
| M | 81 | 15 | 45 |
| M | 85 | 2 | 46 |
| F | 71 | 15 | 30 |
| M | 73 | 12 | 34 |
| F | 76 | 18 | 33 |
| M | 77 | 10 | 36 |
| M | 78 | 21 | 38 |
| M | 80 | 5 | 42 |
| F | 83 | 18 | 46 |
| F | 86 | 21 | 49 |
| F | 74 | 15 | 38 |
| M | 77 | 18 | 32 |
| M | 77 | 12 | 35 |
| F | 78 | 8 | 36 |
| F | 84 | 32 | 49 |
| F | 87 | 16 | 48 |
| F | 77 | 29 | 36 |
| M | 71 | 19 | 33 |
| F | 75 | 4 | 33 |
| F | 76 | 17 | 36 |
| M | 79 | 30 | 38 |
| M | 83 | 20 | 48 |
| F | 89 | 11 | 48 |
| F | 92 | 14 | 49 |
In this assignment, you will expand your understanding of inferential statistics involving correlation and linear regression. Complete the following:
1. Produce an SPSS analysis for a correlation between participants’ self-esteem and productivity.
- Provide the null and alternative hypotheses. (Hint: The relationship between variables.)
- Discuss the difference between the Pearson correlation and the Spearman correlation. Explain when it is appropriate to use one or the other. (Hint: Level of measurement of the variables.)
- Determine if a Pearson correlation or Spearman correlation will be used by conducting the assumptions tests. Explain what correlation analysis was conducted and explain why that test was conducted.
- What is the measure for effect size in a correlation analysis?
- Conduct the correlation analysis. What is the effect size in this correlation analysis? Explain whether it is small, medium, or large.
- Report the results in APA format. (Hint: Follow the guidelines in the APA manual to report statistical results.)
- What decision can be made from these results regarding the null hypothesis?
2. Produce an SPSS analysis using linear regression to examine whether participants’ years of experience predict their productivity.
- Provide the null and alternative hypotheses. (Hint: This is related to prediction.)
- What is the measure for effect size in a linear regression analysis?
- Test assumptions of a linear regression analysis and copy/paste results.
- Conduct the linear regression analysis. What is the effect size in this linear regression analysis? Explain whether it is small, medium, or large.
- Report the results in APA format. (Hint: Follow the guidelines in the APA manual to report statistical results.)
- What decision can be made from these results regarding the null hypothesis? Given only two variables were examined in the linear regression analysis, how does testing the significance of the linear regression equation relate to testing the significance of the Pearson correlation analysis?
- Discuss how you could turn this example into a multiple regression analysis instead of a linear regression analysis.
Part II. Chi-Square
You will be entering and analyzing the following data in SPSS. When entering the data, please use 1 for Red, 2 for Yellow, and 3 for Green. Make sure that you go to the variable view window and enter these values in the label box.
Twenty senior students were asked to choose the color they preferred for their senior-class shirt. Conduct a chi-square goodness-of-fit test to test the null hypothesis that says there is no true difference in the population from which the sample was drawn.
Table 4
Red, Yellow, and Green Data
| Student | Color | Color Code |
| 1 | Red | 1 |
| 2 | Yellow | 2 |
| 3 | Green | 3 |
| 4 | Red | 1 |
| 5 | Red | 1 |
| 6 | Yellow | 2 |
| 7 | Yellow | 2 |
| 8 | Yellow | 2 |
| 9 | Yellow | 2 |
| 10 | Red | 1 |
| 11 | Yellow | 2 |
| 12 | Green | 3 |
| 13 | Red | 1 |
| 14 | Yellow | 2 |
| 15 | Yellow | 2 |
| 16 | Yellow | 2 |
| 17 | Yellow | 2 |
| 18 | Yellow | 2 |
| 19 | Yellow | 2 |
| 20 | Green | 3 |
- Please provide the null and alternative hypothesis for this variable.
- Please provide the observed value n for Red.
- Please provide the observed value n for Yellow.
- Please provide the observed value n for Green.
- Please provide the expected value for each of the colors.
- Are the assumptions met for this test?
- Conduct test and provide the value of the chi-square test.
- Please provide the value of the associated probability (sig.). Are the results significant at the .05 level?
- Write a statement of the results of the significance test in APA style (make sure to include your decision based on the statistical hypothesis).
Remember that there are additional resources available in the Supplemental Resources under Course Resources from the course home page.
Length: There is not a set number of pages required for this assignment. All questions in the assignment need to be answered. In addition to the answers to the assignment questions, also submit the output (.spv) file. (Note. SPSS automatically generates the .spv file as you work in SPSS. When you close your SPSS main window, SPSS will ask you if you want to save the output file. Click ‘yes’, then save to your computer and upload with your assignment.)
References: No references are required, though any sources used other than those provided within the assignment should be cited and referenced in APA format
Your responses should demonstrate thoughtful consideration of the ideas and concepts presented in the course and provide new thoughts and insights relating directly to this topic. Your response should reflect scholarly writing and current APA standards. Be sure to adhere to National University’s Academic Integrity Policy.