ANOVA Analysis of Depression Scores

This assignment involves analyzing the results of an ANOVA conducted on depression scores. The analysis examines the effects of two factors: group (healthy people vs. those with chronic health conditions) and state. The output provides detailed statistics including Sum, Average, Variance, and ANOVA results for each source of variation. Students are tasked with interpreting these results, stating null hypotheses, drawing conclusions about significant differences between groups and states, and providing relevant comments on the findings.

Running Head: HI6007 GROUP ASSİGNMENT
Student Name:
Partner(s) Name:
Course:
Professor Name:
Date Submitted:
HI6007 Group Assignment

HI6007 Group Assignment
Task 1
1. Descriptive Statistics summary for the sampled data of 50 credit card users:
Income
($1000s)
Household
Size
Amount
Charged ($)
Mean 43.48 3.42 3963.86
Standard Error 2.058 0.246 132.023
Median 42 3 4090
Mode 54 2 3890
Standard Deviation 14.55 1.74 933.55
Sample Variance 211.72 3.02 871508.74
Kurtosis -1.25 -0.72 -0.74
Skewness 0.01 0.53 -0.13
Range 46 6 3814
Minimum 21 1 1864
Maximum 67 7 5678
Sum 2174 171 198193
Count 50 50 50
Confidence Level (95.0%) 4.14 0.50 265.31
Comments
 The average household size was computed to be 3.42. The data values are
likely to deviate by 1.739 around this mean value. Further, as read from the
median value, about 50% of the sampled customers had a household size of 3
or more. The minimum & maximum household sizes are 1 and 7, respectively.
 The mean annual Income of sampled customers is $43,480. The data values are
likely to deviate within $14,550 around this mean value. Moreover, about 50%
of the customers have an annual income of $42,000 or above, while the
remaining 50% below this. The maximum and minimum recorded annual
incomes for the sampled data are $21,000 and $67,000, respectively.
 The average annual amount charged to the credit card holders is $3963.8. The
data values are likely to deviate by $933.55 around this mean value. Further,
the median value suggests that about 50% of the credit card holders were
charged $4,090 or over while the remaining 50% below this. The minimum
Page | 1

HI6007 Group Assignment
and maximum amounts charged to credit card holders are $1,864 and $5,678,
respectively.
 The kurtosis and skewness factors for all the three variables further indicate
that distribution is approximately normal (with some measure of skewness).
2. Following regression models and equations were obtained for the 2 cases:
Case 1: Income as the Independent variable
The regression equation is given as:
y=β0 +β1 ( x )
Amount charged ( $ )=2204.24+ 40.47 ( Income ( $ 1000 s ) )
Excel Regression Output:
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.6308
R Square 0.3979
Adjusted R Square 0.3853
Standard Error 731.9025
Observations 50
ANOVA
df SS MS F Sig. F
Regression 1 16991228.91 16991228.91 31.72 0.0000
Residual 48 25712699.11 535681.23
Total 49 42703928.02
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 2204.24 329.13 6.697 0.0000 1542.47 2866.01
Income ($1000s) 40.47 7.19 5.632 0.0000 26.02 54.92
Comments
 The overall model and the individual slope coefficient are statistically
significant (Sig. F and p-value are less than the assumed significance level of
0.05).
 However, the model is a poor fit as it explains only about 39.79% of the
variation in the dependent variable (annual amount charged).
Page | 2

HI6007 Group Assignment
Case 2: Household size as the Independent variable
The regression equation is given as:
Amount charged ( $ )=2581.64+404.16 ¿
Excel Regression Output:
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.7529
R Square 0.5668
Adjusted R Square 0.5578
Standard Error 620.8163
Observations 50
ANOVA
df SS MS F Sig. F
Regression 1 24204112.28 24204112.28 62.80 0.0000
Residual 48 18499815.74 385412.83
Total 49 42703928.02
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 2581.64 195.27 13.221 0.0000 2189.03 2974.26
Household size 404.16 51.00 7.925 0.0000 301.61 506.70
Comments
 Here as well, the overall model and the individual slope coefficient (household
size) are statistically significant.
 Further, the model is a moderate fit as it explains about 56.68% of the variation
in the dependent variable (amount charged) by the predictor variable
(household size).
Conlcusion
As evident from the above models, the variable ‘household size’ is a better predictor
of annual credit card charges at it explains about 56.68% of the variation in the
dependent variable (more than that by the variable Income).
Page | 3

HI6007 Group Assignment
3. Predictor Variables: Income, Household size
The regression equation is given as:
y=β0 +β1 ( x1 ) + β2 ( x2 )
Amount charged ( $ ) =1305.03+33.12 ( Income ( $ 1000 s ) ) +356.34 ¿
Excel Regression Output:
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.9085
R Square 0.8254
Adjusted R Square 0.8179
Standard Error 398.3249
Observations 50
ANOVA
df SS MS F Significance F
Regression 2 35246778.72 17623389.36 111.07 0.0000
Residual 47 7457149.30 158662.75
Total 49 42703928.02
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 1305.03 197.77 6.599 0.0000 907.17 1702.90
Income ($1000s) 33.12 3.97 8.343 0.0000 25.13 41.11
Household size 356.34 33.22 10.727 0.0000 289.51 423.17
Comments
 The overall model and the two individual slope coefficients (Income and
household size) are statistically significant and therefore, are included in the
final model.
 The overall model is a good fit as it explains about 81.79% of the variation in
the dependent variable (amount charged by the credit card company to its
users) using Income level and household size of the user.
4. Household size = 3 Annual Income = $40,000
Amount charged ( $ ) =1305.03+33.12 ( Income ( $ 1000 s ) ) +356.34 ¿
Substituting values gives:
Amount charged ( $ ) =1305.03+33.12 ( 40 ) +356.34 ( 3 )
Amount charged ( $ ) =$ 3,698.85
Page | 4

HI6007 Group Assignment
5. The regression model obtained in part 4 above is not a perfect fit and therefore, fails to
explain 100% variation in values of the dependent variable ‘amount charged’. For an
even better fit than this model, following variables could be added to the model:
 Gender of the customer (qualitative: categorical)
 Age of the credit card user (quantitative, in years)
 Region of residence (qualitative: categorical)
 Royalty points (quantitative, numerical)
 Total number of chargeback cases (quantitative, numerical)
Task 2
Activity 01
Student
ID
Year
Enrolled
HI00
1
FINA
L
EXA
M
HI001
ASSIG
NMEN
T 01
HI00
1
ASSI
GNM
ENT
02
HI00
2
FINA
L
EXA
M
HI002
ASSIG
NMEN
T 01
HI002
ASSIG
NMEN
T 02
HI003
FINAL
EXAM
HI003
ASSIG
NMEN
T 01
HI003
ASSIG
NMEN
T 02
50 30 20 50 30 20 50 30 20
A 2012 30.00 16.00 12.00 27.00 21.00 14.00 31.00 10.00 12.00
B 2012 38.00 18.00 18.00 25.00 20.00 13.00 32.00 30.00 19.00
C 2012 38.00 18.00 18.00 32.00 10.00 10.00 43.00 30.00 20.00
D 2012 32.00 17.00 17.00 31.00 19.00 13.00 30.00 23.00 15.00
E 2012 35.00 18.00 15.00 29.00 18.00 16.00 27.00 17.00 19.00
F 2012 33.00 18.00 16.00 36.00 22.00 14.00 22.00 10.00 12.00
G 2012 29.00 16.00 13.00 27.00 18.00 12.00 23.00 11.00 12.00
H 2012 35.00 16.00 15.00 25.00 17.00 13.00 39.00 19.00 15.00
I 2012 31.00 16.00 15.00 24.00 21.00 12.00 28.00 11.00 12.00
J 2012 30.00 16.00 12.00 26.00 20.00 12.00 11.00 21.00 14.00
K 2012 37.00 16.00 15.00 26.00 19.00 13.00 28.00 21.00 14.00
L 2012 31.00 16.00 15.00 16.00 20.00 12.00 20.00 22.00 15.00
M 2012 32.00 17.00 17.00 27.00 17.00 11.00 21.00 19.00 15.00
N 2012 33.00 17.00 17.00 26.00 20.00 12.00 8.00 22.00 15.00
O 2012 34.00 18.00 15.00 28.00 20.00 14.00 27.00 18.00 12.00
P 2012 32.00 17.00 17.00 20.00 8.00 7.00 25.00 14.00 12.00
Q 2012 30.00 20.00 17.00 29.00 22.00 14.00 17.00 14.00 15.00
R 2012 34.00 16.00 15.00 27.00 22.00 14.00 16.00 18.00 12.00
S 2012 45.00 18.00 17.00 27.00 20.00 14.00 33.00 10.00 13.00
T 2012 34.00 18.00 15.00 27.00 20.00 14.00 25.00 10.00 10.00
U 2012 36.00 19.00 17.00 29.00 20.00 14.00 42.00 21.00 15.00
V 2012 36.00 17.00 15.00 26.00 18.00 14.00 13.00 10.00 13.00
W 2012 38.00 18.00 17.00 35.00 20.00 12.00 32.00 20.00 13.00
X 2012 41.00 20.00 20.00 32.00 18.00 14.00 24.00 10.00 12.00
Y 2012 43.00 21.00 21.00 22.00 21.00 13.00 30.00 15.00 14.00
Z 2012 37.00 17.00 17.00 23.00 18.00 13.00 18.00 14.00 14.00
AA 2012 40.00 14.00 10.00 39.00 18.00 13.00 16.00 18.00 12.00
Page | 5

HI6007 Group Assignment
AB 2012 38.00 18.00 15.00 26.00 19.00 13.00 25.00 19.00 15.00
AC 2012 29.00 18.00 18.00 MC 17.00 11.00 23.00 10.00 13.00
AD 2012 36.00 17.00 15.00 30.00 20.00 14.00 4.00 10.00 13.00
AE 2013 37.00 18.00 17.00 36.00 21.00 13.00 25.00 10.00 11.00
AF 2013 34.00 16.00 17.00 31.00 18.00 13.00 40.00 18.00 12.00
AG 2013 32.00 17.00 17.00 28.00 20.00 14.00 35.00 15.00 14.00
AH 2013 30.00 8.00 8.00 30.00 19.00 13.00 4.00 19.00 14.00
AI 2013 31.00 17.00 17.00 28.00 20.00 12.00 37.00 19.00 14.00
AJ 2013 34.00 17.00 16.00 29.00 19.00 12.00 25.00 19.00 14.00
AK 2013 36.00 17.00 15.00 24.00 19.00 13.00 20.00 19.00 14.00
AL 2013 30.00 18.00 17.00 28.00 20.00 12.00 39.00 20.00 13.00
AM 2013 37.00 16.00 18.00 24.00 18.00 13.00 26.00 18.00 12.00
AN 2013 31.00 15.00 16.00 24.00 19.00 13.00 24.00 15.00 8.00
AO 2013 37.00 19.00 17.00 28.00 19.00 13.00 40.00 22.00 16.00
AP 2013 38.00 18.00 17.00 35.00 21.00 14.00 25.00 20.00 13.00
AQ 2013 23.00 18.00 14.00 35.00 21.00 14.00 25.00 10.00 10.00
AR 2013 26.00 17.00 13.00 36.00 22.00 14.00 20.00 12.00 14.00
AS 2013 38.00 15.00 15.00 25.00 21.00 11.00 10.00 22.00 18.00
AT 2013 23.00 17.00 14.00 16.00 19.00 13.00 32.00 18.00 13.00
AU 2013 37.00 18.00 17.00 33.00 10.00 13.00 28.00 20.00 15.00
AV 2013 30.00 18.00 17.00 26.00 18.00 13.00 25.00 18.00 13.00
AW 2013 33.00 18.00 16.00 12.00 8.00 7.00 10.00 18.00 13.00
AX 2013 34.00 18.00 16.00 24.00 17.00 14.00 34.00 24.00 16.00
AY 2013 24.00 15.00 10.00 28.00 20.00 13.00 38.00 19.00 13.00
AZ 2013 41.00 20.00 21.00 36.00 18.00 16.00 42.00 18.00 13.00
BA 2013 31.00 18.00 18.00 27.00 10.00 13.00 24.00 20.00 14.00
BB 2013 34.00 18.00 16.00 25.00 20.00 13.00 23.00 20.00 15.00
BC 2013 31.00 17.00 18.00 32.00 21.00 12.00 26.00 20.00 12.00
BD 2013 20.00 10.00 10.00 25.00 18.00 12.00 33.00 19.00 13.00
BE 2013 26.00 19.00 19.00 20.00 10.00 10.00 23.00 22.00 13.00
BF 2013 25.00 18.00 13.00 26.00 17.00 11.00 26.00 19.00 13.00
BG 2013 24.00 18.00 14.00 17.00 18.00 13.00 17.00 18.00 13.00
BH 2013 38.00 22.00 18.00 18.00 10.00 5.00 30.00 20.00 15.00
BI 2013 34.00 20.00 14.00 24.00 4.00 4.00 23.00 20.00 15.00
BJ 2013 MC 22.00 17.00 32.00 18.00 14.00 24.00 20.00 13.00
BK 2013 MC 19.00 17.00 27.00 20.00 14.00 26.00 20.00 12.00
BL 2013 40.00 19.00 17.00 21.00 20.00 14.00 35.00 22.00 13.00
BM 2014 29.00 15.00 14.00 30.00 15.00 14.00 25.00 19.00 13.00
BN 2014 37.00 17.00 17.00 25.00 18.00 14.00 32.00 20.00 12.00
BO 2014 29.00 18.00 15.00 34.00 14.00 12.00 26.00 20.00 12.00
BP 2014 29.00 15.00 13.00 32.00 17.00 11.00 25.00 19.00 14.00
BQ 2014 29.00 16.00 13.00 18.00 18.00 12.00 15.00 19.00 14.00
BR 2014 31.00 18.00 16.00 27.00 18.00 12.00 24.00 19.00 13.00
BS 2014 29.00 17.00 16.00 22.00 18.00 12.00 32.00 19.00 14.00
BT 2014 28.00 16.00 13.00 24.00 20.00 14.00 25.00 19.00 14.00
BU 2014 32.00 18.00 15.00 24.00 20.00 14.00 29.00 22.00 13.00
BV 2014 29.00 17.00 12.00 24.00 20.00 14.00 39.00 18.00 13.00
BW 2014 33.00 16.00 16.00 33.00 13.00 14.00 25.00 18.00 13.00
Page | 6

HI6007 Group Assignment
BX 2014 33.00 18.00 16.00 25.00 12.00 11.00 25.00 19.00 14.00
BY 2014 25.00 16.00 16.00 28.00 14.00 12.00 15.00 19.00 14.00
BZ 2014 29.00 16.00 12.00 28.00 20.00 12.00 26.00 19.00 13.00
CA 2014 40.00 18.00 18.00 19.00 19.00 8.00 16.00 19.00 13.00
CB 2014 23.00 17.00 15.00 26.00 19.00 8.00 18.00 20.00 12.00
CC 2014 36.00 19.00 18.00 28.00 19.00 10.00 30.00 18.00 13.00
CD 2014 30.00 16.00 12.00 23.00 19.00 12.00 15.00 20.00 13.00
CE 2014 36.00 18.00 17.00 25.00 15.00 12.00 37.00 20.00 14.00
CF 2014 24.00 15.00 13.00 20.00 14.00 12.00 24.00 20.00 14.00
CG 2014 30.00 15.00 12.00 31.00 14.00 12.00 26.00 19.00 13.00
CH 2014 29.00 16.00 13.00 18.00 20.00 8.00 22.00 20.00 14.00
CI 2014 35.00 18.00 15.00 26.00 20.00 12.00 32.00 18.00 13.00
CJ 2014 34.00 15.00 16.00 16.00 18.00 14.00 24.00 20.00 14.00
CK 2014 28.00 14.00 14.00 27.00 19.00 12.00 25.00 19.00 14.00
CL 2014 34.00 19.00 15.00 25.00 20.00 13.00 32.00 18.00 13.00
CM 2014 24.00 18.00 14.00 30.00 20.00 13.00 28.00 20.00 15.00
CN 2014 26.00 17.00 14.00 40.00 17.00 13.00 25.00 16.00 13.00
CO 2014 24.00 20.00 13.00 19.00 15.00 14.00 25.00 20.00 13.00
CP 2014 33.00 15.00 17.00 25.00 19.00 13.00 42.00 20.00 12.00
CQ 2014 38.00 18.00 16.00 26.00 18.00 12.00 40.00 15.00 18.00
CR 2014 29.00 16.00 13.00 29.00 13.00 14.00 25.00 20.00 13.00
CS 2014 31.00 18.00 16.00 31.00 18.00 13.00 26.00 20.00 12.00
CT 2014 37.00 21.00 18.00 32.00 17.00 11.00 25.00 22.00 14.00
Activity 02
The variable ‘Student ID’ is a string variable and therefore, histogram and descriptive
summary for this variable cannot be obtained.
Histograms
2012 2013 2014
28
29
30
31
32
33
34
35
Year Enrolled
Year
Frequency
Page | 7

HI6007 Group Assignment
0-6 7-13 14-20 21-27 28-34 35-41 42-48 49 and
over
0
10
20
30
40
50
60
HI001 Final Exam
Marks (out of 50)
Frequency
0-3 4-7 8-11 12-15 16-19 20-23 24-27 28 or
more
0
10
20
30
40
50
60
70
80
HI001 ASSIGNMENT 01
Marks (out of 30)
Frequency
0-2 3-5 6-8 9-11 12-14 15-17 18 and
over
0
10
20
30
40
50
60
HI001 ASSIGNMENT 02
Marks (out of 20)
Frequency
Page | 8

HI6007 Group Assignment
0-6 7-13 14-20 21-27 28-34 35-41 42-48 49 or
more
0
5
10
15
20
25
30
35
40
45
50
HI002 Final Exam
Marks (out of 50)
Frequency
0-3 4-7 8-11 12-15 16-19 20-23 24-27 28 and
over
0
5
10
15
20
25
30
35
40
45
50
HI002 ASSIGNMENT 01
Marks (out of 30)
Frequency
0-2 3-5 6-8 9-11 12-14 15-17 18 or
more
0
10
20
30
40
50
60
70
80
90
HI002 ASSIGNMENT 02
Marks (out of 20)
Frequency
Page | 9

HI6007 Group Assignment
0-6 7-13 14-20 21-27 28-34 35-41 42-48 49 and
over
0
5
10
15
20
25
30
35
40
45
50
HI003 Final Exam
Marks (out of 50)
Frequency
0-3 4-7 8-11 12-15 16-19 20-23 24-27 28 or
more
0
5
10
15
20
25
30
35
40
45
HI003 ASSIGNMENT 01
Marks (out of 30)
Frequency
0-2 3-5 6-8 9-11 12-14 15-17 18 and
over
0
10
20
30
40
50
60
70
80
HI003 ASSIGNMENT 02
Marks (out of 20)
Frequency
Page | 10

HI6007 Group Assignment
Descriptive Statistics
Year
Enrolled
HI001
FINAL
EXAM
HI001
ASSIGNME
NT 01
HI001
ASSIGNME
NT 02
HI002
FINAL
EXAM
Mean 2013.04 31.72 17.21 15.46 26.50
Standard Error 0.08 0.68 0.20 0.23 0.60
Median 2013 32 17 16 27
Mode 2013 29 18 17 27
Standard Deviation 0.81 6.75 1.99 2.31 5.91
Sample Variance 0.66 45.62 3.96 5.34 34.93
Kurtosis -1.475 8.420 5.442 0.762 3.486
Skewness -0.075 -2.062 -1.151 -0.507 -0.908
Range 2 45 14 13 40
Minimum 2012 0 8 8 0
Maximum 2014 45 22 21 40
Sum 197278 3109 1687 1515 2597
Count 98 98 98 98 98
HI002
ASSIGNME
NT 01
HI002
ASSIGNME
NT 02
HI003
FINAL
EXAM
HI003
ASSIGNME
NT 01
HI003
ASSIGNME
NT 02
Mean 17.82 12.42 25.99 18.19 13.54
Standard Error 0.35 0.20 0.84 0.39 0.18
Median 19 13 25 19 13
Mode 20 14 25 20 13
Standard Deviation 3.44 1.99 8.27 3.91 1.76
Sample Variance 11.84 3.96 68.42 15.27 3.10
Kurtosis 3.128 4.999 0.297 1.416 3.590
Skewness -1.755 -1.922 -0.191 -0.457 0.962
Range 18 12 39 20 12
Minimum 4 4 4 10 8
Maximum 22 16 43 30 20
Sum 1746 1217 2547 1783 1327
Count 98 98 98 98 98
Activity 03
Page | 11

HI6007 Group Assignment
a) Correlation summary:
Correlation Analysis
HI001
ASSIGNMENT
02
HI002
FINAL
EXAM
HI002
ASSIGNMENT
01
HI002
ASSIGNMENT
02
HI003
FINAL
EXAM
HI001 ASSIGNMENT 02 1
HI002 FINAL EXAM -0.0374 1
HI002 ASSIGNMENT 01 -0.0969 0.1769 1
HI002 ASSIGNMENT 02 -0.0377 0.3626 0.5490 1
HI003 FINAL EXAM 0.2768 0.1157 0.0155 0.1638 1
b) Discussion summary:
HI001
ASSIGNMEN
T 02
HI002
FINAL
EXAM
HI002
ASSIGNMEN
T 01
HI002
ASSIGNMEN
T 02
HI003
FINAL
EXAM
HI001 ASSIGNMENT
02 -
HI002 FINAL EXAM Negative and
Weak -
HI002 ASSIGNMENT
01
Negative and
Weak
Positive
and
Weak
-
HI002 ASSIGNMENT
02
Negative and
Weak
Positive
and
Weak
Positive and
Strong -
HI003 FINAL EXAM Positive and
Weak
Positive
and
Weak
Positive and
Weak
Positive and
Weak -
Table Index (sub-row wise)
 Positively/negatively correlated
 Weak or strong correlation (Weak < 0.5, Strong > 0.5)
Task 3
Page | 12

HI6007 Group Assignment
1. Descriptive Statistics:
Depression Score of Persons in Good Health
Florida New York North Carolina
Mean 5.55 8 7.05
Standard Error 0.478 0.492 0.634
Median 6 8 7.5
Mode 7 8 8
Standard Deviation 2.139 2.200 2.837
Sample Variance 4.576 4.842 8.050
Kurtosis -1.062 0.626 -0.905
Skewness -0.274 0.626 -0.056
Range 7 9 9
Minimum 2 4 3
Maximum 9 13 12
Sum 111 160 141
Count 20 20 20
Depression Score of Patients with Chronic Health Condition
Florida New York North Carolina
Mean 14.5 15.25 13.95
Standard Error 0.709 0.923 0.659
Median 14.5 14.5 14
Mode 17 14 12
Standard Deviation 3.171 4.128 2.946
Sample Variance 10.053 17.039 8.682
Kurtosis -0.341 -0.030 -0.592
Skewness 0.281 0.525 -0.042
Range 12 15 11
Minimum 9 9 8
Maximum 21 24 19
Sum 290 305 279
Count 20 20 20
Comments
 Florida recorded an average depression score of 5.55 for healthy people while
14.5 for people with chronic health condition.
 New York recorded an average depression score of 8 for healthy people while
15.25 for people with chronic health condition.
 North Carolina recorded an average depression score of 7.05 for healthy
people while 13.95 for people with chronic health condition.
Page | 13

HI6007 Group Assignment
 It is also critical to note that Florida recorded lowest average score for healthy
people while North Carolina recorded lowest score for people with chronic
health condition. New York recorded the highest average depression scores for
both the groups.
 The kurtosis and skewness factors for all three variables indicate that the
variables have an approximately normal distribution (with some measure of
positive/negative skewness).
2. Output summary of Two-way Analysis of Variance performed in MS-Excel:
Anova: Two-Factor With Replication
SUMMARY Florida New York North Carolina Total
Good Health
Count 20 20 20 60
Sum 111 160 141 412
Average 5.55 8 7.05 6.87
Variance 4.58 4.84 8.05 6.66
Chronic Health Conditions
Count 20 20 20 60
Sum 290 305 279 874
Average 14.5 15.25 13.95 14.57
Variance 10.05 17.04 8.68 11.81
Total
Count 40 40 40
Sum 401 465 420
Average 10.025 11.625 10.5
Variance 27.67 24.14 20.36
ANOVA RESULTS
Source of Variation SS df MS F P-value F crit
Sample 1778.7 1 1778.70 200.4466 0.0000 3.9243
Columns 54.02 2 27.01 3.0436 0.0516 3.0759
Interaction 24.05 2 12.02 1.3551 0.2620 3.0759
Within 1011.6 114 8.87
Total 2868.37 119
The null hypotheses are stated as:
H0 :The depression scores are same across different states ( Factor A :Columns)
H0 :The depression scores are same for different groups ( Factor B : Samples)
Page | 14

HI6007 Group Assignment
Also, there is a null hypothesis for the effects due to interaction b/w factors A and B.
H0 :Thereis difference ∈interaction between states∧groups
Conclusions
As read from the output summary above:
 The p-value (groups) = 0.0000<.05=α, therefore, the Factor B null hypothesis
is rejected; concluding that the depression scores are statistically different for
different groups.
 The p-value (states) = 0.0516>.05=α, therefore, the Factor A null hypothesis
cannot be rejected, thus concluding that the depression scores are statistically
not different across different states.
 Also, the p-value (interaction) = 0.2620>.05=α, therefore, concluding that
there are no significant differences in the interaction between states and
groups.
3. Following comments are made relevant to the research study:
 Regression results for ANOVA on depression scores of healthy people across
different states:
Depression Score of Persons in Good Health
Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Florida 20 111 5.55 4.5763
New York 20 160 8 4.8421
North Carolina 20 141 7.05 8.05
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 61.0333 2 30.5167 5.2409 0.0081 3.1588
Within Groups 331.9 57 5.8228
Total 392.9333 59
Conclusion: The results suggest that there is statistically significant difference
in mean depression scores of healthy people across different states.
 Regression results for ANOVA on depression scores of people with chronic
health condition across different states:
Page | 15

HI6007 Group Assignment
Depression Scores of Persons with Chronic Health Condition
Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Florida 20 290 14.5 10.0526
New York 20 305 15.25 17.0395
North Carolina 20 279 13.95 8.6816
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 17.0333 2.0000 8.5167 0.7142 0.4939 3.1588
Within Groups 679.7 57 11.9246
Total 696.7333 59
Conclusion: The results suggest that there is statistically ‘no’ significant
difference in mean depression scores of people with chronic health conditions
across different states.
 Regression results for ANOVA on depression scores of people from both
groups, irrespective of the location:
Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Healthy 60 412 6.8667 6.6599
Chronic Patient 60 874 14.5667 11.8090
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 1778.7 1 1778.7 192.6154 0.0000 3.9215
Within Groups 1089.667 118 9.2345
Total 2868.367 119
Conclusion: The results suggest that there is statistically significant difference
in mean depression scores of people with chronic health conditions and healthy
people.
Page | 16