QUESTION
ANOVA, ChiSquare, and Binomial Tests
Complete all of the following problems prior to the Adobe Connect session. Please use the Adobe Connection session to ask any questions you have and to check your answers.
 Analysis of Variance: A study was performed on five subjects to determine how environmental conditions such as temperature affect pulse. The five subjects were exposed to four different temperatures for 30 minutes before their pulse was taken. The data is recorded in the following table.
Perform an ANOVA test to determine whether or not pulse is affected by the external temperature. Use an α = 0.05. Reference Section 12.3 of Statistics for the Behavioral Sciences for assistance.
Temperature 
Pulse (bpm) 

40° F 
82 
81 
98 
90 
75 
60° F 
68 
74 
92 
88 
72 
80° F 
71 
69 
90 
87 
70 
100° F 
78 
75 
97 
92 
73 
 State the null hypothesis.
 State the alternative hypothesis.
 Calculate df_{between} (also known as df_{Numerator}).
 Calculate df_{within} (also known as df_{Denominator}).
 Use the values for df_{N} and df_{D} you calculated with an α = 0.05 to determine the expected Fration. (Use Table B.4 “The F Distribution.”)
 Calculate the total (∑x) for each treatment condition (T).
 Calculate the sum of all scores in the research study (G = ∑T).
 Calculate the sum of squares (SS) for each treatment conditions where: .
 Calculate SS_{TOTAL} where: .
 Calculate SS_{WITHIN} where SS_{WITHIN }= ∑SS_{inside each treatment}.
 Calculate SS_{BETWEEN} where .
 Calculate df_{TOTAL}. (Remember that you calculated df_{BETWEEN} and df_{WITHIN} in parts c and d.)
 Calculate MS_{BETWEEN} where MS_{BETWEEN} = .
 Calculate MS_{WITHIN} where MS_{WITHIN} = .
 Calculate the actual Fration where F = .
 Based on the values you have calculated in this problem, should you accept or reject the null hypothesis?
 Based on your conclusion in part p, does temperature affect pulse rate based on this experiment?
 ChiSquare: Friedman and Roseman (1974) have suggested that personality type is related to heart disease. Specifically, Type A people, who are competitive, driven, pressured, and impatient, are more prone to heart disease. On the other hand, Type B individuals, who are less competitive and more relaxed, are less likely to have heart disease. The data is reported in the following table.
Perform a Chisquare test to determine whether or not there is a relationship between personality and heart disease. Use an alpha value of α = 0.05. Reference Section 17.3 and Demonstration 17.1 of Statistics for the Behavioral Sciences for assistance.
Heart 
Vascular 
Hypertension 
None 

Type A Personality 
38 
27 
43 
70 
Type B Personality 
22 
23 
17 
120 

 State the null hypothesis.

 State the alternative hypothesis.

 Calculate the degrees of freedom (df).

 Locate the critical region (Use Table B.8 “The ChiSquare Distribution.”)

 Calculate the row and column totals. Record your results in the following table:
Heart 
Vascular 
Hypertension 
None 
f_{c} 

Type A Personality 
38 
29 
43 
60 

Type B Personality 
18 
22 
14 
126 

f_{r} 

 Calculate n.

 Calculate the expected frequencies (f_{c}) and record in the following table:

Personality
Disease
Type A Personality
Heart
Vascular
Hypertension
None
Type B Personality
Heart
Vascular
Hypertension
None

 Perform the calculations in the following table to calculate: .






Type A: Heart 
38 

Type A: Vascular 
29 

Type A: Hypertension 
43 

Type A: None 
60 

Type B: Heart 
18 

Type B: Vascular 
22 

Type B: Hypertension 
14 

Type B: None 
126 

 Calculate the chisquare statistic: .

 Based on the chisquare statistic you calculated above and the critical region that you determined earlier, should you accept or reject the null hypothesis?

 Based on your conclusion in part j, is there a connection between personality type and disease?
 Binomial Test: A new medication that is designed to decrease anxiety was tested on 87 individuals that have been diagnosed with chronic depression. After the study, 36 of the test subjects reported a noticeable decrease in their anxiety and the other 51 subjects reported that they had noticed no change in their anxiety levels.
Perform a binomial test on this dataset to determine whether or not the drug decreases anxiety in people with chronic depression. Reference Sections 18.1 and 18.2 of Statistics for the Behavioral Sciences for assistance.

 State the value on n (the total number of subjects).

 State the value X (the number of subjects who reported a decrease in anxiety).

 State the null hypothesis.

 State the alternative hypothesis.

 Find the critical region using an alpha value of 0.05. (Use Table B.1 “The Unit Normal Table.”)

 Calculate the zscore. (Use equation 18.1.)

 Given this result, do you reject the null hypothesis?

 Based on your conclusions, does this medication help to reduce the anxiety of patients with chronic depression?
ANSWER
ANOVA, ChiSquare, and Binomial Tests
Complete all of the following problems prior to the Adobe Connect session. Please use the Adobe Connection session to ask any questions you have and to check your answers.

Analysis of Variance: A study was performed on five subjects to determine how environmental conditions such as temperature affect pulse. The five subjects were exposed to four different temperatures for 30 minutes before their pulse was taken. The data is recorded in the following table.
Perform an ANOVA test to determine whether or not pulse is affected by the external temperature. Use an α = 0.05. Reference Section 12.3 of Statistics for the Behavioral Sciences for assistance.
Temperature 
Pulse (bpm) 

40° F 
82 
81 
98 
90 
75 
60° F 
68 
74 
92 
88 
72 
80° F 
71 
69 
90 
87 
70 
100° F 
78 
75 
97 
92 
73 

State the null hypothesis.
H_{0}: μ_{1} = μ_{2} = μ_{3} … = μ_{k}

State the alternative hypothesis.
H_{1}: Means are not all equal.

Calculate df_{between} (also known as df_{Numerator}).
1.7

Calculate df_{within} (also known as df_{Denominator}).
2.3

Use the values for df_{N} and df_{D} you calculated with an α = 0.05 to determine the expected Fration. (Use Table B.4 “The F Distribution.”)
1.3

Calculate the total (∑x) for each treatment condition (T).
76

Calculate the sum of all scores in the research study (G = ∑T).
65

Calculate the sum of squares (SS) for each treatment conditions where: .
44

Calculate SS_{TOTAL} where: .
1843

Calculate SS_{WITHIN} where SS_{WITHIN }= ∑SS_{inside each treatment}.
1213

Calculate SS_{BETWEEN} where .
554

Calculate df_{TOTAL}. (Remember that you calculated df_{BETWEEN} and df_{WITHIN} in parts c and d.)
4

Calculate MS_{BETWEEN} where MS_{BETWEEN} = .
3.3

Calculate MS_{WITHIN} where MS_{WITHIN} = .
3.1

Calculate the actual Fration where F = .
1.1

Based on the values you have calculated in this problem, should you accept or reject the null hypothesis?
reject

Based on your conclusion in part p, does temperature affect pulse rate based on this experiment?

ChiSquare: Friedman and Roseman (1974) have suggested that personality type is related to heart disease. Specifically, Type A people, who are competitive, driven, pressured, and impatient, are more prone to heart disease. On the other hand, Type B individuals, who are less competitive and more relaxed, are less likely to have heart disease. The data is reported in the following table.
Perform a Chisquare test to determine whether or not there is a relationship between personality and heart disease. Use an alpha value of α = 0.05. Reference Section 17.3 and Demonstration 17.1 of Statistics for the Behavioral Sciences for assistance.
Heart 
Vascular 
Hypertension 
None 

Type A Personality 
38 
27 
43 
70 
Type B Personality 
22 
23 
17 
120 


State the null hypothesis.

H0: Personality and heart disease are independent.


State the alternative hypothesis.


H1: Personality and heart disease are not independent.


Calculate the degrees of freedom (df).

3


Locate the critical region (Use Table B.8 “The ChiSquare Distribution.”)



Calculate the row and column totals. Record your results in the following table:

Heart 
Vascular 
Hypertension 
None 
f_{c} 

Type A Personality 
38 
29 
43 
60 
170 
Type B Personality 
18 
22 
14 
126 
180 
f_{r} 
56 
51 
57 
186 
350 


Calculate n.

350


Calculate the expected frequencies (f_{c}) and record in the following table:


Personality
Disease
Type A Personality
Heart
27.2
Vascular
24.78
Hypertension
27.68
None
90.34
Type B Personality
Heart
28.8
Vascular
26.22
Hypertension
29.31
None
95.65


Perform the calculations in the following table to calculate: .







Type A: Heart 
38 
27.2 
10.8 
116.64 
4.288235294 
Type A: Vascular 
29 
24.78 
4.22 
17.8084 
0.71866021 
Type A: Hypertension 
43 
27.68 
15.32 
234.7024 
8.479132948 
Type A: None 
60 
90.34 
30.34 
920.5156 
10.1894576 
Type B: Heart 
18 
28.8 
10.8 
116.64 
4.05 
Type B: Vascular 
22 
26.22 
4.22 
17.8084 
0.679191457 
Type B: Hypertension 
14 
29.31 
15.31 
234.3961 
7.997137496 
Type B: None 
126 
95.65 
30.35 
921.1225 
9.630135912 


Calculate the chisquare statistic: .

46.03195092


Based on the chisquare statistic you calculated above and the critical region that you determined earlier, should you accept or reject the null hypothesis?

We have statistically significant evidence at α=0.05 to show that H_{0} is false.


Based on your conclusion in part j, is there a connection between personality type and disease?

In the χ^{2} goodnessoffit test, we conclude that either the distribution specified in H_{0} is false (when we reject H_{0}) or that we do not have sufficient evidence to show that the distribution specified in H_{0} is false

Binomial Test: A new medication that is designed to decrease anxiety was tested on 87 individuals that have been diagnosed with chronic depression. After the study, 36 of the test subjects reported a noticeable decrease in their anxiety and the other 51 subjects reported that they had noticed no change in their anxiety levels.
Perform a binomial test on this dataset to determine whether or not the drug decreases anxiety in people with chronic depression. Reference Sections 18.1 and 18.2 of Statistics for the Behavioral Sciences for assistance.


State the value on n (the total number of subjects).

87


State the value X (the number of subjects who reported a decrease in anxiety).

36


State the null hypothesis.

the drug has no effect on people.


State the alternative hypothesis.

the drug has effect on people.


Find the critical region using an alpha value of 0.05. (Use Table B.1 “The Unit Normal Table.”)



Calculate the zscore. (Use equation 18.1.)

1.645 (taking from the left )


Given this result, do you reject the null hypothesis?

accept


Based on your conclusions, does this medication help to reduce the anxiety of patients with chronic depression?

yes
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