Inferential Statistics in Decision-making

Final practice test

Select the correct test, apply the test, and communicate the answer according to the handbook.

1. What effect does noise pollution have on helpfulness? A person with a cast on one arm gets out a car and drops an armload of books in front of pedestrians. Will the pedestrians help? Maybe. Sometimes there was a loud gasoline lawn mower operating nearby when the books were dropped and sometimes the mower was not operating. Of the 25 pedestrians who could have helped when the mower was operating, four did so. Of the 25 who could have helped when the mower was quiet, 20 did so. Of the 25 who could have helped when the mower was operating, four did so.

The chi square test is the best choice. The results were significant, (, (X2 [1, N=50] = 20.51, p < .001). Reject the null hypothesis. Pedestrians are significantly less likely to help in the presence of a loud noise.

	Observed	Expected	(O-E)2	(O-E)2 /E
noise helped	4	12	64	5.333333
no noise helped	20	12	64	5.333333
noise did not help	21	13	64	4.923077
no noise did not help	5	13	64	4.923077
			X2	20.51282

2. A leader wanted to know if there was a difference in employee attendance rates based on the shift that employees work.

Here is the data:

First shift	Second shift	Third shift
0	2	3
1	1	2
1	2	4
1	1	1
1	1	3
0	1	2
1	2	4
2		1
1		3

Perform the test, report the results, and complete any additional tests.

Answer: The ANOVA is the best choice. There was a significant difference between the employee attendance based on shift, (f [2,22] = 9.60, p < .01). Post hoc independent sample t-tests were conducted. There was a significant difference between attendance between first (M = .89) and second shift (M=1.42), (t [14] = 1.87, p < .05). There was a significant difference between first (M = .89) and third shift (M= 2.56), (t [16] = 3.91, p < .01). There was a significant difference between second shift (M=1.42) and third shift (M= 2.56), (t [14] = 2.42, p < .05).

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
First shift	9	8	0.888889	0.361111
Second shift	7	10	1.428571	0.285714
Third shift	9	23	2.555556	1.277778
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	12.9346	2	6.467302	9.597088	0.001008	3.443357
Within Groups	14.8254	22	0.673882
Total	27.76	24
	First shift	Second shift
Mean	0.888888889	1.428571429
Variance	0.361111111	0.285714286
Observations	9	7
Pooled Variance	0.328798186
Hypothesized Mean Difference	0
df	14
t Stat	-1.867600341
P(T<=t) one-tail	0.041446865
t Critical one-tail	1.761310136
P(T<=t) two-tail	0.082893729
t Critical two-tail	2.144786688
	First shift	Third shift
Mean	0.888888889	2.555556
Variance	0.361111111	1.277778
Observations	9	9
Pooled Variance	0.819444444
Hypothesized Mean Difference	0
df	16
t Stat	-3.905667329
P(T<=t) one-tail	0.000629328
t Critical one-tail	1.745883676
P(T<=t) two-tail	0.001258656
t Critical two-tail	2.119905299
	Second shift	Third shift
Mean	1.428571429	2.555555556
Variance	0.285714286	1.277777778
Observations	7	9
Pooled Variance	0.85260771
Hypothesized Mean Difference	0
df	14
t Stat	-2.421884652
P(T<=t) one-tail	0.014800274
t Critical one-tail	1.761310136
P(T<=t) two-tail	0.029600549
t Critical two-tail	2.144786688

3. A researcher wanted to know if two educator created assessments assessed the same skills. Students were given both assessments. The data are below:

	Assessment A	Assessment B
Student 1	10	11
Student 2	10	12
Student 3	10	13
Student 4	10	14
Student 5	20	19
Student 6	15	18
Student 7	25	18
Student 8	25	18
Student 9	25	18
Student 10	14	18
Student 11	14	18
Student 12	14	18

Answer: The best choice for this scenario is the regression, because the data is paired and you are looking for similarities. There was a significant relationship between the assessments, (r [10] = .70, p < .05). According to Cohen, this would be a large effect size.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.701889326
R Square	0.492648626
Adjusted R Square	0.441913488
Standard Error	4.594106787
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	1	204.9418	204.9418	9.710205796	0.010946026
Residual	10	211.0582	21.10582
Total	11	416

4. With the same data from question #9, what if the researcher wanted to know if the students performed differently on two assessments?

Answer: The paired samples t-test would determine if the scores for each student were different. There was no difference in the student’s performance on assessment A (M = 16) and assessment B ( M = 16.25), (t [11] =.19, p > .05). (Practical note- it was a huge hint here that the previous answer was highly correlated, which means that there couldn’t be a significant difference here).

t-Test: Paired Two Sample for Means
	Assessment A	Assessment B
Mean	16	16.25
Variance	37.81818182	8.204545455
Observations	12	12
Pearson Correlation	0.701889326
Hypothesized Mean Difference	0
df	11
t Stat	-0.187666682
P(T<=t) one-tail	0.427277438
t Critical one-tail	1.795884819
P(T<=t) two-tail	0.854554876
t Critical two-tail	2.20098516