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 t-test

What is the key piece of information you must know in order to decide

 

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Part A

Some questions in Part A require that you access data from Statistics for People Who (Think They) Hate Statistics

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. What is your conclusion regarding the research hypothesis?

Gender N Mean Std. Deviation Std. Error Mean
hands up Boys 14 7.93 2.369 .633
Girls 16 5.31 2.387 .597

 

Independent Samples Test

Levene’s Test for Equality of Variances t-test for Equality of Means
F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference
Lower Upper
hands up Equal variances assumed .477 .495 3.006 28 .006 2.616 .870 .833 4.399
Equal variances not assumed 3.007 27.529 .006 2.616 .870 .833 4.399

 

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 different hypothesis (one is directional and the other is nondirectional). How do the results differ and why?

3.Practice the following problems by hand or in Excel just to see if you can get the numbers right. Using the following information, calculate the t-test statistic. (See page 192)

abc

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 null hypothesis 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. Is there a difference between urban and rural residents when it comes to gun control?

Group Statistics

Group N Mean Std. Deviation Std. Error Mean
Attitude Urban 16 6.5113 1.77221 .44305
Rural 14 5.3979 3.31442 .88582

 

Independent Samples Test

Levene’s Test for Equality of Variances t-test for Equality of Means
F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference
Lower Upper
Attitude Equal variances assumed 4.463 .044 1.168 28 .253 1.11339 .95311 -.83897 3.06576
Equal variances not assumed 1.124 19.273 .275 1.11339 .99044 -.95763 3.18442

 

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 outcome measures, same car seats, and so on. Dr. R’s results were marginally significant (recall Ch. 9) at the .051 level. Which result do you trust more and why?

 

7.In the following examples, indicate whether you would perform a t test of independent 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 quicker when some received additional in-home care whereas when others received the standard amount.

c.A group of adolescent boys was offered interpersonal skills counseling and then tested in September and May to see if there was any impact on family harmony.

d.One group of adult men was given instructions in reducing their high blood pressure whereas another was not given any instructions.

e.One group of men was provided access to an exercise program and tested two times over a 6-month period for heart health.

 

8.For the data represented below, 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. Report the exact probability of the outcome.

 

One-Sample Statistics

N Mean Std. Deviation Std. Error Mean
Before 20 5.480 2.2673 .5070
After 20 7.595 1.4155 .3165

 

One-Sample Test

Test Value = 0
t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference
Lower Upper
Before 10.809 19 .000 5.4800 4.419 6.541
After 23.996 19 .000 7.5950 6.933 8.257

 

9.Do this exercise by hand or in Excel. 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 grouping and the test variable.

design

 

11.When would you use a factorial ANOVA rather than a simple ANOVA to test the significance of the difference between the averages of two or more groups?

12.Create a drawing or plan for a 2 × 3 experimental design that would lend itself to a factorial ANOVA. Identify the independent and dependent variables.

 

 

Part B

Complete the questions below. Be specific and provide examples when relevant.

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 t-test?

 

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