# Explore The Relationships Between Variables

Assignment: Explore Relationships Between Variables Using Correlation, Regression, and Chi-Square
Instructions
This assignment has two parts. Part I is about correlation and regression. Part II is about chi-square. Include both parts in a single document.
Part I. Correlation and Regression
Imagine a researcher is interested in examining the relationship of 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 theteacherdata.savdataset available in this weeks resources (and Table 3) to conduct the analysis involvingSelf_estm,Prod, andExperience. Use these data to answer the questions.
Table 3
Datasetteacherdata.sav
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 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 of the other. (Hint: Level of measurement of the variables.)
Determine if a Pearson correlation or Spearman correlation will be used and explain why.
Which is the measure for effect size used in a 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 result. Only the statistical analysis results are needed; no additional discussion or explanation needed.)
What decision can be made from these results regarding the null hypothesis?
2. Produce an SPSS analysis using regression to examine the impact of participants years of experience on their productivity.
Provide the null and alternative hypotheses. (Hint: This is related to prediction.)
Which is the measure for effect size used in a regression analysis?
What is the effect size in this 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? Be sure to consider possible study limitations and provide recommendations for future research.
Given only two variables were examined, how does testing the significance of the regression equation relate to testing the significance of the Pearson correlation?
Part II. Chi-Square
You will be entering and analyzing in SPSS the data in Table 4. When entering the data, please use 1 for Red, 2 for , 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 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 valuenfor Red.
Please provide the observed valuenfor Yellow.
Please provide the expected value for each of the colors.
Please 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 Supplemental Resources available for each week in the Course Resources linked at the top of your course.
Length: Complete responses for all parts of all questions in both parts. In addition to a WORD (.doc) file with the answers to the assignment questions, also include 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.).

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