Conduct a one-way ANOVA to investigate the relationship between hair color and social extroversion. Conduct appropriate post hoc tests.
Part A
Some questions in Part A require that you access data from Statistics for People Who (Think They) Hate Statistics. This data is available on the student website under the Student Text Resources link.
1. Using the data in the file named Ch. 11 Data Set 2, test the research hypothesis at the .05 level of significance that boys raise their hands in class more often than girls. Do this practice problem by hand using a calculator. What is your conclusion regarding the research hypothesis? Remember to first decide whether this is a one- or two-tailed test.
2. Using the same data set (Ch. 11 Data Set 2), test the research hypothesis at the .01 level of significance that there is a difference between boys and girls in the number of times they raise their hands in class. Do this practice problem by hand using a calculator. What is your conclusion regarding the research hypothesis? You used the same data for this problem as for Question 1, but you have a differenthypothesis (one is directional and the other is nondirectional). How do the resultsdiffer and why?
3. Practice the following problems byhand just to see if you can get the numbersright. Using the following information, calculate the ttest statistic.
a.
b.
c.
4. Using the results you got from Question 3 and a level of significance at .05,what are the two-tailed critical values associated with each? Would the nullhypothesis be rejected?
5. Using the data in the file named Ch. 11 Data Set 3, test the null hypothesis that urban and rural residents both have the same attitude toward gun control. UseIBM^{®}SPSS^{®}software to complete the analysis for this problem.
6. A public health researcher tested the hypothesis that providing new car buyers with child safety seats will also act as an incentive for parents to take other measures to protect their children (such as driving more safely, child-proofing the home, and so on). Dr. L counted all the occurrences of safe behaviors in the cars and homes of the parents who accepted the seats versus those who did not. The findings:a significant difference at the.013 level. Another researcher did exactly the same study; everything was the same—same type of sample, same outcomemeasures, same car seats, and so on. Dr. Rs results were marginally significant(recallCh. 9) at the .051 level. Whichresult do you trustmore and why?
7. In the following examples, indicate whether you would perform a t test ofindependent means or dependent means.
a. Two groups were exposed to different treatment levels for ankle sprains.Which treatment was most effective?
b. A researcher in nursing wanted to know if the recovery of patients was quickerwhen some received additional in-home care whereas when others received thestandard amount.
c. A group of adolescent boys was offered interpersonal skills counseling andthen tested in September and May to see if there was any impact on familyharmony.
d. One group of adult men was given instructions in reducing their high bloodpressure whereas another was not given any instructions.
e. One group of men was provided access to an exercise program and tested twotimes over a 6-month period for heart health.
8. For Ch. 12 Data Set 3, compute the t value and write a conclusion on whether there is a difference in satisfaction level in a group of families use of service centers following a social service intervention on a scale from 1 to 15. Do this exercise using IBM^{®}SPSS^{®}software, and report the exact probability of the outcome.
9. Do this exercise by hand. A famous brand-name manufacturer wants to know whether people prefer Nibbles or Wribbles. They sample each type of cracker and indicate their like or dislike on a scale from 1 to 10. Which do they like the most?
Nibbles rating | Wribbles rating |
9 | 4 |
3 | 7 |
1 | 6 |
6 | 8 |
5 | 7 |
7 | 7 |
8 | 8 |
3 | 6 |
10 | 7 |
3 | 8 |
5 | 9 |
2 | 8 |
9 | 7 |
6 | 3 |
2 | 6 |
5 | 7 |
8 | 6 |
1 | 5 |
6 | 5 |
3 | 6 |
10. Using the following table, provide three examples of a simple one-way ANOVA, two examples of a two-factor ANOVA, and one example of a three-factor ANOVA. Complete the table for the missing examples.Identify the groupingand the test variable.
Design | Grouping variable(s) | Test variable |
Simple ANOVA | Four levels of hours of training—2,4,6,and8hours | Typing accuracy |
Enter Your Example Here | Enter Your Example Here | |
Enter Your Example Here | Enter Your Example Here | |
Enter Your Example Here | Enter Your Example Here | |
Two-factor ANOVA | Two levels of training and gender(two-way design) | Typing accuracy |
Enter Your Example Here | Enter Your Example Here | |
Enter Your Example Here | Enter Your Example Here | |
Three-factor ANOVA | Two levels of training, two of gender, and three of income | Voting attitudes |
Enter Your Example Here | Enter Your Example Here |
11. Using the data in Ch. 13 Data Set 2 and the IBM^{®}SPSS^{®}software, compute the F ratio for a comparisonbetween the three levels representing the average amount of time thatswimmers practice weekly (<15, 15–25, and >25 hours) with the outcome variablebeing their time for the 100-yard freestyle. Does practicetime make a difference?Use the Options feature to obtainthe meansfor the groups.
12. When would you use a factorial ANOVA rather than a simple ANOVA to test thesignificance of the difference between the averages of two or more groups?
13. Create a drawing or plan for a 2 × 3 experimental design that would lend itself toa factorial ANOVA. Identify the independent and dependent variables.
From Salkind (2011). Copyright © 2012 SAGE. All Rights Reserved. Adapted with permission.
Part B
14. John is interested in determining if a new teaching method, the involvement technique, iseffective in teaching algebra to first graders. John randomly samples six first graders from allfirst graders within the Lawrence City School System and individually teaches them algebra withthe new method. Next, the pupils complete an eight-item algebra test. Each item describes aproblem and presents four possible answers to the problem. The scores on each item are 1 or 0,where 1 indicates a correct response and 0 indicates a wrong response. The IBM^{®}SPSS^{®} data file containssix cases, each with eight item scores for the algebra test.
Conduct a one-sample t test on the total scores. On the output, identify the following:
a. Mean algebra score
b. T test value
c. Pvalue
The data for Exercise 15 isin thedata file named Lesson 25 Exercise File 1.
15. Marvin is interested in whether blonds, brunets, and redheads differ with respect to their extrovertedness. He randomly samples 18 men from his local college campus: six blonds, six brunets, and six redheads. He then administers a measure of social extroversion to each individual.
Conduct a one-way ANOVA to investigate the relationship between hair color and social extroversion. Conduct appropriate post hoc tests. On the output, identify the following:
a. F ratio for the group effect
b. Sums of squares for the hair color effect
c. Mean for redheads
d. Pvalue for the hair color effect
From Green &Salkind (2011).Copyright © 2012 Pearson Education. All Rights Reserved.Adapted with permission.
Part C
Complete the questions below. Be specific and provide examples when relevant.
Citeany sources consistent withAPA guidelines.
Question | Answer | |
What is meant by independent samples? Provide a research example of two independent samples. | ||
When is it appropriate to use a t test for dependent samples? What is the key piece of information you must know in order to decide? | ||
When is it appropriate to use an ANOVA? What is the key piece of information you must know in order to decide? | ||
Why would you want to do an ANOVA when you have more than two groups, rather than just comparing each pair of means with a ttest? | ||