QUESTION 1
- For questions 1-6, please use this data set: – Lab 3 Data Set – Q1-6.sav
You will need to complete a factorial ANOVA analysis and Bonferroni’s post hoc test. Don’t worry about doing any testing of assumptions for this. The IVs/factors used for these questions will be: parent’s graduation from college (parent_college) and life being exciting or dull (life). The DV will be: Number of hours worked last week (hrs1). Use the questions below to guide your interpretation of the output. (Hint: use steps outlined on pages 85-90 of the M&V text, 5th edition (pp. 87-93, 6th edition) to conduct this ANOVA. You can also use examples and screen shots provided in the Practice Exercises this week to help you guide this process.)
On my honor, I completed the ANOVA analysis and Bonferroni’s post hoc test, following the text book’s examples and directions. (1 point)
True
False
QUESTION 2
- Is there a significant main effect for “Is life exciting or dull” (life variable)?
| Yes, with significance level of p = .25 | ||
| Yes, with significance level of p = .004 | ||
| Yes, with significance level of p = .018 | ||
| Yes, with significance level of p < .001 | ||
| No, with significance level of p = .004 |
QUESTION 3
- Is there a significant main effect for a parent being a college graduate (parent_college)?
| Yes, with significance level of p = .25 | ||
| Yes, with significance level of p = .004 | ||
| Yes, with significance level of p = .006 | ||
| No, with significance level of p = .25 | ||
| No, with significance level of p = .004 |
QUESTION 4
- Is there a significant interaction effect for parent being a college graduate (parent_college) and life being dull or exciting (life)?
| Yes, with significance level of p = .25 | ||
| Yes, with significance level of p = .004 | ||
| Yes, with significance level of p < .001 | ||
| No, with significance level of p < .001 | ||
| No, with significance level of p = .154 |
QUESTION 5
- In looking at the Bonferroni’s post hoc test, were there any significant differences between the various pairwise comparisons?
| Yes, there was a significant difference between the group in which only one parent graduated from college and the group in which both parents graduated from college | ||
| Yes, there were two significant differences: 1) Between the group in which only one parent graduated from college and the group in which none of the parents graduated from college, and 2) Between the group in which both parents graduated from college and the the group in which only one of the parents graduated from college | ||
| Yes, there were two significant differences: 1) Between the group in which only one parent graduated from college and the group in which none of the parents graduated from college, and 2) Between the group in which both parents graduated from college and the the group in which none of the parents graduated from college | ||
| No, there were no significant differences among any of the comparison groups |
QUESTION 6
- According to your analysis of simple main effects, which of the following statements is true?
| Employees who reported that their life is dull and that none of their parents graduated from college worked the highest number of hours, as compared to all other groups | ||
| Employees who reported that their life is exciting and that none of their parents graduated from college worked the highest number of hours, as compared to other groups | ||
| Employees who reported that their life is exciting and that one of their parents graduated from college worked the lowest number of hours, as compared to other groups | ||
| Employees who reported that their life is dull and that both of their parents graduated from college worked the lowest number of hours, as compared to other groups |
QUESTION 7
- For questions 7-13, please use this data file: – Lab 3 Data Set – Q7-13.sav
For this ANOVA, your DV will be Current Salary (salnow), and your IVs will be Age of Employee (age – categorical variable with 4 categories) and Sex of Employee (sex).
Before you do any analyses, you will need to write out your research hypotheses for main effects and interactions here. You do not need to write corresponding null hypotheses this time.
| For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). Paragraph Open Sans,sans-serif 10pt P 0 WORDSPOWERED BY TINY |
QUESTION 8
- Instructions attached. To open, just click on the document and click Open. If that does not work, right click on the document, click Open in New Window, Open With, Microsoft Word, OK. You may save this document to your computer, print it out, etc.
Instructions file: Instructions for Lab 3 – Q8.doc
On my honor, I completed all of the steps in this document successfully.
True
False
QUESTION 9
- Were there any cases that you identified as outliers in this data set? (Use z score of more than 3SD’s from the mean as your standard for an outlier)
| No, I did not identify any outliers in this data set (there are 0 outliers) | ||
| I identified one outlier with ID# 1 (salary of $60,000) | ||
| I identified one outlier with ID# 56 (salary of $60,000) | ||
| I identified two outliers with IDs #56 and #403 (salaries of $60,000 and $45,000 respectively) | ||
| I identified 5 or more outliers in this data set |
QUESTION 10
- Did Levene’s Test indicate homogeneity of variance?
| Yes, it indicated homogeneity of variance and it was significant, F(7, 465) = 19.54, p < .001 | ||
| No, it did not indicate homogeneity of variance, because it was significant, F(7, 465) = 19.54, p < .001 | ||
| No, it did not indicate homogeneity of variance, because it was significant, F(3, 465) = 4.47, p = .004 | ||
| Yes, it indicated homogeneity of variance, and it was not significant, F(1, 465) = 3.04, p = .25 | ||
| No conclusions about homogeneity of variance can be drawn, because my ANOVA output did not produce a Levene’s Test |
QUESTION 11
- Based on the results of the ANOVA that you conducted for Question 11, which of the following conclusions is accurate?
| Age of employee significantly affected salary, but gender of employee did not have a significant effect on salary | ||
| Age of employee did not significantly affect salary, but gender of employee had a significant effect on salary | ||
| Both gender and age of employees significantly affected salary, but the interaction between gender and age was not significant | ||
| Neither gender nor age of employees significantly affected salary, but the interaction between gender and age was significant | ||
| Both gender and age of employees significantly affected salary, and the interaction between gender and age was significant |
QUESTION 12
- Based on your interpretation of the output, which of the following conclusions is correct?
| Males in the 31-40 age category earned the highest salary, and their earnings were significantly higher, as compared to most other groups (except for females in the same age group) | ||
| Males in the 31-40 age category earned significantly more, as compared to all other groups | ||
| Males in the 27-31 age category earned the lowest salary, and their earnings were significantly lower, as compared to most other groups (except for females in the same age group) | ||
| Females in the 20-27 age category earned the lowest salary, as compared to all other groups | ||
| Males in the “40 and older” age category earned the highest salary, and their earnings were significantly higher as compared to all other groups |
QUESTION 13
- Please fill in the blanks in the following Results section for the entire process of data screening and analysis that you completed for item 11.
Prior to analysis, sex of employees, age of employees, and current salary were examined through SPSS for accuracy of data entry, missing values, and fit between their distributions and the assumptions of univariate analysis. Preliminary examination of data indicated no data entry errors and missing values for either one of the studied variables. Then equality of groups was examined and split was found between the two gender groups or the four age categories.
Then data were examined for univariate outliers by analyzing frequency distribution and z-scores of the current salary variable (salnow). Analysis indicated that subject(s) with current salary of $ (ID# ) was considered outlier(s), because the z score of salnow variable for that case was outside of the acceptable range of z = +3 (z = ). This case was deleted from the dataset, leaving valid cases for analysis. After that, normality of the current salary variable (salnow) was examined using a frequency distribution table. Analysis of a frequency distribution table showed that skewness and kurtosis were within the acceptable range of -1 to +1 (skewness = , kurtosis = ), and therefore no transformations were needed.
A subsequent Levene’s test indicated that assumption of homogeneity of variances was , F(, ) = , p < . However, due to the insignificant number of outliers, the high number of participants, and a fairly even distribution of participants among all categories, it was concluded that continued analysis was acceptable.
Finally, a factorial ANOVA was conducted. The interaction between gender and age category was , F(, ) = , p = , partial η² = . Main effect results revealed that in this sample, salaries were significantly different for males, as compared to females, F(, ) = , p < , partial η² = . Similarly, salaries were different for different age categories as well, F(, ) = , p < , partial η² = .
Examination of simple main effects based on pairwise comparisons utilizing confidence intervals revealed that males in the 31-40 age category had the highest salary (M = ), and their earnings were significantly higher than earnings of employees in all other groups, except for females in the same age group (M = ) whose earnings were also significantly higher as compared the males and females in all other age categories. Males in the 20-27 age category had the lowest income (M = ) and their earnings were significantly lower than earnings of employees in other groups, except for females in the same age group (M = ) whose earnings were also significantly lower as compared the males and females in all other age categories.
Bonferroni post-hoc test was conducted as a follow up test for ANOVA in order to establish which age categories were significantly different in terms of salary. Results of the Bonferroni post-hoc test revealed that the salary of employees in the age category of 20-27 (M = ) was significantly lower as compared to salaries of employees in all other age categories. In addition, employees in the age category 27-31 made significantly less (M = ) as compared to the employees in the 31-40 age category (M = ). Further, employees in the “40 and over” age category (M = ) also made significantly less that employees in the 31-40 age category. Overall, within this sample, employees in the age range between 31 and 40 had the highest salary, which was significantly higher than that of employees in all other age groups. Finally, results of this study also indicated that males (M = ) are paid significantly more than females (M = ).
QUESTION 14
- How many interaction groups or “cells” would a 2 x 5 factorial Analysis of Variance contain?
| 2 | ||
| 5 | ||
| 7 | ||
| 10 |
QUESTION 15
How many hypotheses are tested simultaneously in a two-way Analysis of Variance?
| 1 | ||
| 2 | ||
| 3 | ||
| 4 |
