STA640
EXPERIMENTAL DESIGN AND ANALYSIS OF VARIANCE
PROJECT 1 - COMPLETELY RANDOMIZED DESIGN (CRD)
PERSONALITY AND HEALTH
PREPARED FOR:
DR. NOR AZURA MD GHANI
PREPARED BY:
GROUP: CS241 5A
1) NOR SYAHIDA BINTI MUSA (2016359443)
2) NURHANINA BINTI NAZAMID (2016314927)
3) NURSYAHIRAH AMIRAH BINTI ZAHARIN (2016586333)
4) SITI KHATIJAH BINTI ZAKARIYA (2016352109)
DATE OF SUBMISSION: 3rd APRIL 2018
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TABLE OF CONTENTS
Table of Contents 1
List of Tables and Figures 3
1 Introduction
1.1 Introduction 4
1.2 Data Description 5
1.3 Problem Statement 5
1.4 Objectives 5
2 Literature Review
2.1 Personality and Health 6
2.2 Relationship between Personality and Health 6
3 Methodology
3.1 Completely Randomized Design (CRD) 7
3.2 Statistical Model 7
3.3 Assumption Testing 8
3.4 Experimental Design 9
4 Data Analysis
4.1 Model Adequacy Checking 10
4.1.1 Checking for Outliers 10
4.1.2 Normality 11
4.1.3 Constant Variance 12
4.1.4 Independence 13
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4.2 Analysis Of Variance (ANOVA) 14
4.3 Post Hoc Test 16
4.3.1 Tukey Test 17
4.3.2 Fisher LSD Test 19
4.4 Homogeneous Subsets 21
5 Conclusion 22
References 23
Appendix 24
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LIST OF TABLES
Table 1 - Shapiro-Wilk Test of Normality 11
Table 2 - Levene Test for Equality of Variances 12
Table 3 - Analysis Of Variance (ANOVA) 14
Table 4 - Multiple Comparison 16
Table 5 – Homogeneous Subsets 21
LIST OF FIGURES
Figure 1 - Boxplot of Health Scores 10
Figure 2 - Histogram of Health Scores 11
Figure 3 - Normal P-P Plot of Health Scores 11
Figure 4 – Plot of Residuals versus Predicted Value 12
Figure 5 - Plot of Residuals versus Time 13
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CHAPTER 1: INTRODUCTION
1.1 Introduction
Personality traits have been emerged in the recent years as one of the predictors of
important health outcomes (Hampson & Friedman, 2008). Associations between personality and
health have been hold across decades as childhood personality traits will predict the self-rated
health during the middle age (Hampson, Goldberg, Vogt, & Dubanoski, 2007). Personality is
define as a collection of mental characteristics that consistently exists within individuals and
influences their behaviors and thoughts.
In order to evaluate the research conducted, it is important to understand the relationship
between personality and health. In a study of health and illness by Bury (2005), health is an
incredible riddle and hard to define but simple to spot. However, health approval is the expression
for a very wide range of performances that improve good health and well-being and put a stop to
ill (Simnett, 1995). Betz and Thomas (1979) have reported a distinct connection between
personality and health. They identified three personality types who differ in their susceptibility to
serious and stress-related illnesses such as heart attack, high blood pressure and others.
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1.2 Data Description
This study involved the use of data about distinct connection between personality and
health under three different personality types. Basically, the three different personality types are
listed as the independent variables (X) and the general health scores for each of these three groups
is listed as the dependent variable (Y). This study involved thirty observations with ten replications
for each treatments.
The three different personality types mentioned in the study are alphas, betas and gammas.
The first one is alphas which the people are cautious and steady. The second personality type is
betas which the people are carefree and outgoing. Meanwhile, the third personality type is gammas,
who tend toward extremes of behavior such as being overly cautious or very careless. The data
representing the general health scores for each of these three groups where a low score indicates
poorer health is attached at the appendix.
The data was extracted from http://people.virginia.edu/~ent3c/psyc771/final96.html
1.3 Problem Statement
Personality refers to individual differences in characteristic patterns of thinking, feeling
and acting. Personality traits are said to affect numerous health outcomes but there are little studies
that used personality traits to predict the health outcomes. Hence, this study is carried out to
investigate whether the types of personalities truly affect the health outcomes.
1.4 Objectives
1. To identify whether there is a significance difference between the types of personalities.
2. To determine which pairs of personalities that differ.
3. To identify the best type of personality.
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CHAPTER 2: LITERATURE REVIEW
2.1 Personality and Health
According to Moghadam, Malekian and Karamshahi (2015), personality is a mental
characteristics that consistently exists within individuals and it influences behaviors and thoughts.
The study also mentions that one of the unique personality characteristics is self-control. This type
of personality varies from one person to another, where those belongs to this group of personality
tend to express their reactions and behaviors depending on the person that they communicate.
Another study by Young & Beaujean (2011) also stated that personality of people can be expressed
in different reactions and behaviors depends on whom they communicate.
Kewly & RR Jr. in their study proves that personality may be a reliable predictor of health
behavior patterns. In addition, personality factors have been found to be related to various health
outcomes (Deary et al., 2010).
2.2 Relationship between Personality and Health
According to a dissertation by Sirois (2015), people with high agreeableness and low
neuroticism tend to continue health promoting behaviors, which is a key for disease management.
This is because they incline to view their future health positively. The study also indicates that
positive expectations for the future can be motivated by the current health behaviors.
Many personality problems contribute to the level of health problem (Sinaj, 2015). The
study reflects that person who show stable humor qualities tend to have depression and more likely
to develop a low quality of life. Hence, they are more risked to have health problem. Sinaj (2015)
in his study also concludes that there is a strong connection between personality traits and health
behaviors. In his study, the result shows that there exists positive association between compliance
and healthy behaviors health.
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CHAPTER 3: METHODOLOGY
3.1 Completely Randomized Design
A completely randomized design (CRD) is a design where the treatments are assigned to
the experimental units completely at random. Each experimental unit has the same chance of
receiving any one of the treatment. Hence, CRD is appropriate when the experimental units are
homogeneous. CRD is used in this study to analyze the data since the data has one factor with
three levels. The levels are the three personality types which are (i) alphas, who are cautious and
steady; (ii) betas, who are carefree and outgoing; and (iii) gammas, who tend toward extremes of
behavior.
3.2 Statistical Model
The statistical model for the Completely Randomized Design is
𝑦𝑖𝑗 = 𝜇 + 𝜏𝑖 + 𝜀𝑖𝑗 { 𝑖 = 1, 2, 3 𝑎𝑛𝑑 𝑗 = 1, 2, … , 10
where:
𝑦𝑖𝑗 is the ijth observation
𝜇 is the overall mean of the ith factor level
𝜏𝑖 is the ith treatment effect
𝜀𝑖𝑗 is a random error
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3.3 Assumption Testing
Before proceed to further analysis, the assumption must be fulfilled to make sure that the data does
not violate any of the assumptions. If one of the assumptions is violated, the conclusion made
based on the analysis is not valid to be used. The assumptions for Completely Randomized Design
are:
1. The model errors are assumed to be normally and independently distributed random
variables with mean zero and variance.
2. The variance is assumed to be constant for all levels of the factors.
3. The observations are mutually independent.
4. ∑𝛼𝑖=1 𝜏𝑖 = 0
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3.4 Experimental Design
Below are the list of all components involved in this experiment.
Experimental Unit : People
Number of Replication : 10 replications
Number of Observation : 30 observations
Experimental Design : Completely Randomized Design
Type of Experiment : Fixed Factor Experiment
Factor : Three personality types
Treatments : Three different personality types which are Alphas, Betas
and Gammas
Response Variable : The general health scores for each of the personality types
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CHAPTER 4: DATA ANALYSIS
4.1 Model Adequacy Checking
Certain assumptions need to be formerly satisfied in order to proceed with the test for difference
in the treatment means.
4.1.1 Checking for Outliers
Boxplot is used to check for the existence of outliers.
Figure 1 – Boxplot of Health Scores
Figure 1 shows that there might be two potential outliers exist in the data. However, since the
outliers are not considered to be as extreme outliers as well as did not affect the analysis, therefore
the outliers are not being removed from the data.
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4.1.2 Normality
Figure 2 – Histogram of Health Scores Figure 3 – Normal P-P Plot of Health Scores
Figure 2 shows a histogram with a slight bell-shaped curve. Meanwhile, Figure 3 shows a P-P plot
where the points lie approximately along the straight line. These figures indicate that the residuals
might be assumed to be normally distributed. In order to confirm for the normality assumption,
therefore Shapiro-Wilk Test is conducted.
Table 1 – Shapiro-Wilk Test of Normality
Tests of Normality
Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
HealthScores .124 30 .200* .954 30 .218
a. Lilliefors Significance Correction
*. This is a lower bound of the true significance.
The null hypothesis for this test is that the distribution of the residuals is normal, while the
alternative hypothesis is that the distribution of the residuals is not normal. Since the significance
value (0.218) is greater than the alpha (0.05), therefore there is no enough evidence to reject the
null hypothesis. This indicates that the distribution of the residuals is normal.
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4.1.3 Constant Variance
Figure 4 – Plot of Residuals versus Predicted Value
Figure 4 shows that there is no pattern in the distribution of the plots. Therefore, by analyzing the
pattern of the plot, it can be concluded that the residuals have a constant variance. The homogeneity
of variance can also be checked by using Levene’s Test.
Table 2 – Levene Test for Equality of Variances
Test of Homogeneity of Variances
HealthScores
Levene Statistic df1 df2 Sig.
.661 2 27 .524
The null hypothesis for this test is that the variance is equal across groups, while the alternative
hypothesis is that the variance is unequal across groups. Since the significance value (0.524) is
greater than the alpha (0.05), therefore there is no enough evidence to reject the null hypothesis.
This indicates that the variance is equal across groups.
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4.1.4 Independence
Figure 5 – Plot of Residuals versus Time
Figure 5 shows that the distribution of the error term has no pattern over time. Therefore, it can be
concluded that the residual is independent and has no potential problem with dependency.
Since all of the assumptions for the error terms, which are normality, constant variance and
independence are not violated, therefore the test for difference in the treatment means can be
developed.
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4.2 Analysis Of Variance (ANOVA)
The objective of the ANOVA is to identify whether there is a significance difference between the
types of personalities.
Table 3 – Analysis Of Variance (ANOVA)
HealthScores
Source of Sum of Mean
Variation Squares df Square F Sig.
Personalities 564.200 2 282.100 4.501 .021
Error 1692.100 27 62.670
Total 2256.300 29
(43+⋯+36)2 (1281)2
SSTotal = (432 + ⋯ + 362 ) − = 56 955 − = 2256.300
30 30
1 (43+⋯+36)2
SSPersonalities = 10 (4422 + 4712 + 3682 ) − = 564.200
30
SSError = 2256.300 − 564.200 = 1692.100
564.200
MSPersonalities = = 282.100
2
1692.100
MSError = = 62.670
27
282.100
F= = 4.501
62.670
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1. Hypothesis
H0: μi = 0, i = 1, 2, 3 (There is no significance difference between the types of personalities)
H1: μi ≠ 0; for at least one i (There is a significance difference between the types of
personalities)
2. α = 0.05
3. P-value = 0.021
4. Decision rule
Reject H0 if p-value ≤ α
Since p-value ≤ α, therefore reject H0.
5. Conclusion
There is a significance difference between the types of personalities.
Since the ANOVA is significant, thus proceed to multiple comparison test to determine which
pairs of personalities differ by using Tukey Test and Fisher LSD Test.
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4.3 Post Hoc Tests
The objective of the post hoc tests is to determine which pairs of personalities differ.
Table 4 – Multiple Comparison
Dependent Variable:HealthScores
Mean Std.
(I) Groups (J) Groups Difference (I-J) Error Sig.
Tukey HSD Alphas Betas -2.900 3.540 .695
Gammas 7.400 3.540 .111
Betas Alphas 2.900 3.540 .695
Gammas 10.300* 3.540 .019
Gammas Alphas -7.400 3.540 .111
Betas -10.300* 3.540 .019
LSD Alphas Betas -2.900 3.540 .420
Gammas 7.400* 3.540 .046
Betas Alphas 2.900 3.540 .420
Gammas 10.300* 3.540 .007
Gammas Alphas -7.400* 3.540 .046
Betas -10.300* 3.540 .007
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4.3.1 Tukey Test
1. Hypothesis
H0: μi = μj (Mean personality i is not differ from mean personality j)
H1: μi ≠ μj (Mean personality i is differ from mean personality j)
2. α = 0.05
3. Critical value
62.670
𝑇∝ = 𝑞0.05 (3,27)√
10
62.670
𝑇∝ = 3.505√
10
𝑇∝ = 8.7744
4.
μi = μj P-value Decision Mean Decision Rule Conclusion
Rule difference, ( Reject H0 if
( Reject H0 if │ȳi-ȳj│ │ȳi-ȳj│≥ Tα )
p-value ≤ α )
μAlphas = 0.695 ˃α 2.9 ˂ Tα (8.7744) Failed to μAlphas =
μBetas reject H0 μBetas
μAlphas = 0.111 ˃α 7.4 ˂ Tα (8.7744) Failed to μAlphas =
μGammas reject H0 μGammas
μBetas = 0.019 ˂α 10.3 ˃ Tα (8.7744) Reject H0 μBetas ≠
μGammas μGammas
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5. Conclusion
Hence, there are difference in the general health score for the Betas personality and the Gammas
personality. Meanwhile, there are no difference in the general health score for the Alphas
personality and the Betas personality as well as for the Alphas personality and the Gammas
personality.
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4.3.2 Fisher LSD Test
1. Hypothesis
H0: μi = μj (Mean personality i is not differ from mean personality j)
H1: μi ≠ μj (Mean personality i is differ from mean personality j)
2. α = 0.05
3. Critical value
2(62.670)
𝐿𝑆𝐷 = 𝑡0.025,27 √
10
2(62.670)
𝐿𝑆𝐷 = 2.052√
10
𝐿𝑆𝐷 = 7.2648
4.
μi = μj P-value Decision Rule Mean Decision Rule Conclusion
( Reject H0 if difference, ( Reject H0 if
p-value ≤ α ) │ȳi-ȳj│ │ȳi-ȳj│≥ LSD )
μAlphas = 0.420 ˃α 2.9 ˂ LSD (7.2648) Failed to μAlphas =
μBetas reject H0 μBetas
μAlphas = 0.046 ˂α 7.4 ˃ LSD (7.2648) Reject H0 μAlphas ≠
μGammas μGammas
μBetas = 0.007 ˂α 10.3 ˃ LSD (7.2648) Reject H0 μBetas ≠
μGammas μGammas
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5. Conclusion
Hence, there are difference in the general health score for the Betas personality and the Gammas
personality as well as for the Alphas personality and the Gammas personality. Meanwhile, there
are no difference in the general health score for the Alphas personality and the Betas personality.
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4.4 Homogeneous Subsets
The objective of the homogeneous subsets is to identify the best type of personality.
Table 5 – Homogeneous Subsets
HealthScores
Subset for alpha =
0.05
Groups N 1 2
Tukey HSDa Gammas 10 36.80
Alphas 10 44.20 44.20
Betas 10 47.10
Sig. .111 .695
Means for groups in homogeneous subsets are displayed.
Based on the Table 6, the mean of Alphas personality does not differ from the mean of Gammas
and Betas personality. On the other hand, the mean of Betas personality differs from the mean of
Gammas personality since the mean score is in a different subset. To conclude, Betas personality,
the one who are carefree and outgoing has the best personality as it has the highest mean health
score since higher health score indicates a better health.
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CHAPTER 5: CONCLUSION
Completely Randomized Design (CRD) is used in this study to analyze the data since the data has
one factor with three levels. The levels are the three personality types which are (i) alphas, who
are cautious and steady; (ii) betas, who are carefree and outgoing; and (iii) gammas, who tend
toward extremes of behavior such as being overly cautious or very careless. All of the assumptions
for the model adequacy checking are fulfilled. Next, ANOVA is used to test if there is a
significance difference between the types of personalities. The result shows that there is a
significance difference between the types of personalities. Future test are done to identify which
pair of personalities are differ by using Tukey Test and Fisher LSD Test. Tukey Test shows that
the general health score of Betas personality is differ from Gammas personality. On the other hand,
the Fisher LSD Test show that Gammas personality differs from both of Alphas and Betas
personality. To conclude, Betas personality, the one who are carefree and outgoing has the best
personality as it has the highest mean health score since higher health score indicates a better
health.
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REFERENCES
Bury, M. (2005). Health and illness. Cambridge. Polity.
Deary, I. J., Weiss, A., & Batty, G. D. (2010). Intelligence and personality as predictors of illness
and death: How researchers in differential psychology and chronic disease epidemiology
are collaborating to understand and address health inequalities. Psychological science in
the public interest, 11(2), 53-79.
Hampson, S. E., & Friedman, H. S. (2008). Personality and health: A lifespan perspective.
Hampson, S. E., Goldberg, L. R., Vogt, T. M., & Dubanoski, J. P. (2007). Mechanisms by which
childhood personality traits influence adult health status: educational attainment and
healthy behaviors. Health psychology, 26(1), 121.
Kewly, B., & RR Jr. Associations between major domains of personality and health behavior.
Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/7965560.
Mousavi Moghadam, S. R., Malekian, S., & Karamshahi, M. (2016). Investigating the relationship
between personality characteristics, self-control, and general health among the students of
public and clinical psychology in Islamic Azad University of Ilam. Journal of Basic
Research in Medical Sciences, 3(2), 20-25.
Simenett I. (1995). Managing health promotion: developing health organisations and
communities. New York. John Wiley & sons.
Sinaj, D. S. E. (2015). Associations between the five-factor model of personality and health
behaviors among adult in Albania. European Journal of Psychological Research Vol, 2(3).
Sirois, F. M. (2015). Who Looks Forward to Better Health? Personality Factors and Future Self-
Rated Health in the Context of Chronic Illness. International journal of behavioral
medicine, 22(5), 569-579.
Young, J. K., & Beaujean, A. A. (2011). Measuring personality in wave I of the national
longitudinal study of adolescent health. Frontiers in psychology, 2, 158.
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APPENDIX
Alphas Betas Gammas
43 41 36
44 52 29
41 40 38
56 57 36
49 36 45
42 48 42
52 51 25
53 55 40
41 52 41
21 39 36
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