Report Project 1.docx

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 1|Page

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 2|Page

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. 6|Page

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. 7|Page

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

HealthScores

Shapiro-Wilk

Statistic

df

Sig.

Statistic

df

Sig.

.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. 12 | P a g e

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 Variation

Sum of Squares

df

Mean Square

F

Sig.

Personalities

564.200

2

282.100

4.501

.021

Error

1692.100

27

62.670

Total

2256.300

29

SSTotal = (432 + ⋯ + 362 ) −

(43+⋯+36)2 30

1

= 56 955 −

SSPersonalities = 10 (4422 + 4712 + 3682 ) − SSError = 2256.300 − 564.200 MSPersonalities = MSError = F=

282.100 62.670

564.200

1692.100 27

2

(43+⋯+36)2 30

(1281)2 30

= 2256.300

= 564.200

= 1692.100

= 282.100

= 62.670

= 4.501

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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

Tukey HSD

(I) Groups

Mean (J) Groups Difference (I-J)

Std. Error

Sig.

Alphas

Betas

-2.900

3.540

.695

Gammas

7.400

3.540

.111

Alphas

2.900

3.540

.695

Gammas

10.300*

3.540

.019

Alphas

-7.400

3.540

.111

Betas

-10.300*

3.540

.019

Betas

-2.900

3.540

.420

Gammas

7.400*

3.540

.046

Alphas

2.900

3.540

.420

Gammas

10.300*

3.540

.007

Alphas

-7.400*

3.540

.046

Betas

-10.300*

3.540

.007

Betas

Gammas

LSD

Alphas

Betas

Gammas

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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

μAlphas = μBetas μAlphas = μGammas μBetas = μGammas

Mean difference, │ȳi-ȳj│

0.695

Decision Rule ( Reject H0 if p-value ≤ α ) ˃α

Decision Rule ( Reject H0 if │ȳi-ȳj│≥ Tα )

2.9

˂ Tα (8.7744)

0.111

˃α

7.4

˂ Tα (8.7744)

0.019

˂α

10.3

˃ Tα (8.7744)

Failed to reject H0 Failed to reject H0 Reject H0

Conclusion

μAlphas = μBetas μAlphas = μGammas μBetas ≠ 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

μAlphas = μBetas μAlphas = μGammas μBetas = μGammas

0.420

Decision Rule ( Reject H0 if p-value ≤ α ) ˃α

Mean difference, │ȳi-ȳj│ 2.9

0.046

˂α

7.4

Decision Rule ( Reject H0 if │ȳi-ȳj│≥ LSD ) ˂ LSD (7.2648) Failed to reject H0 ˃ LSD (7.2648) Reject H0

0.007

˂α

10.3

˃ LSD (7.2648)

Reject H0

Conclusion μAlphas = μBetas μAlphas ≠ μGammas μBetas ≠ 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 Tukey HSDa Gammas

N

1

2

10

36.80

Alphas

10

44.20

Betas

10

Sig.

44.20 47.10

.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 SelfRated 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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