Question

1. A scientist is interested in whether the design of an air traffic control display affects how many airplanes an air traffic controller can manage at once. The scientist evaluates 2 different displays: A low information display (airplanes shown as uniform blips) and a high information display (airplanes shown as different blips depending on aircraft model, and color coded according to speed). The scientist recruits 20 air traffic controllers and randomly assigns 10 to each display condition. The researcher asks, do these display conditions impact how many aircraft air traffic controllers can manage?              

Low Information Display	High Information Display
11	12
12	12
12	9
11	10
14	11
12	10
11	10
14	8
12	8
10	9

What analysis could be used to answer the research question? Choose all answer choices that represent analyses that would be appropriate to use.

		one sample t-test
		independent samples t-test
		dependent samples t-test
		independent samples one-way ANOVA
		dependent samples one-way ANOVA
		factorial ANOVA

2. What are the Null and Research Hypotheses? Write them out in plain English. You do not need to use stats symbols.

3. What is the value of df between groups?

4. What is the value of df within groups?

5, What is the value of your total df for this analysis?

6. What is the value of Sum of Squares Between Groups (a.k.a. SSbetween?

7. What is the value of Sum of Squares Within Groups (a.k.a. SSwithin)?

8. What is the value of Sum of Squares Total (a.k.a. SStotal)? (Hint: Don't be fooled by SPSS labels)

9. What is the value of the Mean Square Between Groups (a.k.a. MSbetween)?

10. What is the value of the Mean Square Within Groups (a.k.a. MSwithin)?

11. What is the value of the F ratio?

12.

What can you conclude about the null hypothesis?

		You cannot make any decisions about the null hypothesis
		Fail to reject the null hypothesis
		Reject the null hypothesis

13.How do you know this conclusion about the null hypothesis is correct?

14. Do you need to conduct post hoc tests to figure out where the differences are?

		Yes. You always need to do post-hoc tests after a significant ANOVA to find out where the differences are.
		No. There are only 2 levels of the IV.
		No . There are no significant differences.
		Post who?

15.If you need to conduct post hoc tests, do so. Then answer this question: What can you conclude in plain English? Be specific about which groups (if any) are different and how.

16. What proportion of the variability in how many aircraft a controller can manage is accounted for (explained by) display condition?

Answer 1

1. Options: independent samples t-test, independent samples one-way ANOVA

2. Null hypothesis, H0: The two display conditions do not have any impact on how many aircraft air traffic controllers can manage

Alternative hypothesis, H1: The two display conditions do have an impact on how many aircraft air traffic controllers can manage

3. df between groups=2-1=1

4. df within groups=20-1-1=18

5, total df=20-1=19

6. SSbetween=20

7. SSwithin=33.8

8. SStotal=53.8

9. MSbetween=20

10. MSwithin=1.8778

11. F ratio=10.6509

12. Since p-value=0.0043<0.05, so Reject the null hypothesis.

13. p-value=0.0043<0.05

14. No. There are only 2 levels of the IV.

15. we do not need to conduct post hoc tests since there are only 2 levels of the IV.

16. Proportion of the variability=SSbetween/SStotal=20/53.8=0.3717

Excel output:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Low Information Display	10	119	11.9	1.655556
High Information Display	10	99	9.9	2.1
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	20	1	20	10.65089	0.004314	4.413873
Within Groups	33.8	18	1.877778
Total	53.8	19