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 the “teacher’data.sav” dataset to conduct the analysis involving Self_estm, Prod, and Experience. Use these data to answer the questions below (these data have already been entered into the “teacher’data.sav” SPSS file).
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:
- Produce an SPSS analysis for a correlation between participants’ self-esteem and productivity.
a. Provide the null and alternative hypotheses. (Hint: The relationship between variables.)
b. 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.)
c. Determine if a Pearson correlation or Spearman correlation will be used and explain why.
d. Which is the measure for effect size used in a correlation analysis?
e. What is the effect size in this correlation analysis? Explain whether it is small, medium, or large.
f. Report the results in APA format. (Hint: Follow the guidelines in the APA manual to report statistical results.)
g. What decision can be made from these results regarding the null hypothesis? - Produce an SPSS analysis using regression to examine the impact of participants’ years of experience on their productivity.
a. Provide the null and alternative hypotheses. (Hint: This is related to prediction.)
b. Which is the measure for effect size used in a regression analysis?
c. What is the effect size in this regression analysis? Explain whether it is small, medium, or large.
d. Report the results in APA format. (Hint: Follow the guidelines in the APA manual to report statistical results.)
e. 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.
f. 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 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.
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
provide the null and alternative hypothesis for this variable.
provide the observed value n for Red.
provide the observed value n for Yellow.
provide the observed value n Green.
provide the expected value for each of the colors.
provide the value of the chi-square test.
Sample Solution