Case study using one way ANOVA

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CASE STUDY 1 GROUP 1 Name: Nadzirah Hanis P75182 Ashok Sivaji P77800 Dwi Budiningsari P75375 Hamzah Wali P74918 Ooi Theng Choon P75129 Haruna Emmanuel P73270 Marwan Jalambo P75376 Suresh Mani P77104

Transcript of Case study using one way ANOVA

CASE STUDY 1

GROUP 1

Name: Nadzirah Hanis P75182

Ashok Sivaji P77800

Dwi Budiningsari P75375

Hamzah Wali P74918

Ooi Theng Choon P75129

Haruna Emmanuel P73270

Marwan Jalambo P75376

Suresh Mani P77104

INTRODUCTION

Hypertension called a silent Killer (WHO 2013).

Associated with cardiovascular disease thataccounts for approximately 17 million deaths a year(WHO, 2008).

Complications account for 9.4 million deathsworldwide every year (Lim et al., 2012).

Prevalence rate among population aged 18 yearsand above was 32.2% in Malaysia (Kaplan, 2011;Syer et al. 2010).

(NHMS) III in 2006, number of people affected with

hypertension has increased from 33% to 41% from 1996-

2006 (Mohammad et al., 2008).

risk factors include race, sex, consumption of food

containing too much salt and fat (WHO, 2013).

Hypertension prevalence among Malaysians in urban

regions were (17%Malay, 11.1%Chines and 10.6% Indian)

(Sutha et al. 2011).

RESEARCH QUESTION

Is there any significant difference in systolic blood

pressure among different races in Malaysia?

RESEARCH HYPOTHESIS

Null hypothesis: There are no significant differences

between systolic blood pressure among races in

Malaysia.

Alternative hypothesis: At least one group of race

have differences in systolic blood pressure in

Malaysia.

STATISTIC HYPOTHESIS

Ho= μMalay= μChinese= μIndian

Ha = μMalay ≠μChinese≠ μIndian

or μMalay ≠ μChinese

or μChinese ≠ μIndian

or μMalay ≠ μIndian

CHOICE OF TEST

We use one way ANOVA( F test) because:

We wish to compare the difference in systolic blood

pressure of more than two race groups ( Malay,

Chinese and Indian)

ASSUMPTION OF TEST

1) Population is normal

Tests of Normality

RaceNew

Kolmogorov-Smirnova Shapiro-Wilk

Statistic df Sig. Statistic df Sig.

Systolic Malay .063 50 .200* .984 50 .741

Chinese .118 30 .200* .942 30 .104

Indian .194 16 .110 .883 16 .044

*. This is a lower bound of the true significance.

a. Lilliefors Significance Correction

• We look at Shapiro-Wilk since the sample size is

less than 100.

•Malay: p=0.741

•Chinese: p=0.104

•Indian: p=0.044

*α=0.05

For Indian we can double check for normality by using

Skewness. Value of std error (0.564) at Skewness times 2 and

within ± 1.96. So we can assume that data is normal.

2. Homogeneity of variances

Null hypothesis: The assumed variance between

Malay, Chinese and Indian are equal

Ho : σMalay = σChinese = σIndian

Alternative hypothesis: The assumed variance

between Malay, Chinese and Indian are not equal.

Ha : σMalay ≠σChinese≠ σIndian

or σMalay ≠ σChinese

or σChinese ≠ σIndian

or σMalay ≠ σIndian

From the Levene test for equality of variance, the p value

is 0.469.

The alpha value, α=0.05.

Since p-value is bigger 0.05, thus the equal variances are

assumed.

Ho : σMalay = σChinese = σIndian is accepted

Test of Homogeneity of Variances

Systolic

Levene Statistic df1 df2 Sig..764 2 93 .469

3. Sample is randomly selected and independent

between samples.

4.The dependent variables should be continuous data.

Thus, the assumption for one way ANOVA was met so

we can proceed with ANOVA analysis.

g) Descriptive analysis

Systolic

N Mean

Std.

Deviation Std. Error

95% Confidence Interval for

Mean

Minimum MaximumLower Bound Upper Bound

Malay50 128.0400 16.30069 2.30527 123.4074 132.6726 94.00 162.00

Chinese30 136.6667 16.40507 2.99514 130.5409 142.7924 108.00 185.00

Indian16 136.7500 14.07835 3.51959 129.2482 144.2518 117.00 170.00

Total96 132.1875 16.41329 1.67517 128.8619 135.5131 94.00 185.00

INFERENTIAL ANALYSIS (F)

ANOVA

Systolic

Sum of

Squares df Mean Square F Sig.

Between Groups 1795.038 2 897.519 3.507 .034

Within Groups23797.587 93 255.888

Total25592.625 95

•F(2, 93)= 3.507, p=0.034

•Data is significant because p< 0.05.

•Thus the null hypothesis is rejected. There is a statistically

significance difference between the systolic blood pressure of at

least two of the race groups.

•Post- hoc analysis is needed.

Since the sample size are very different between

Malay, Chinese and Indian so process with

Hochberg’s GT2.

Multiple Comparisons

Dependent Variable: Systolic

(I)

RaceNew

(J)

RaceNew

Mean

Difference

(I-J) Std. Error Sig.

95% Confidence Interval

Lower Bound Upper Bound

Hochberg Malay Chinese -8.62667 3.69423 .063 -17.6033 .3499

Indian -8.71000 4.59464 .171 -19.8745 2.4545

Chinese Malay 8.62667 3.69423 .063 -.3499 17.6033

Indian -.08333 4.95203 1.000 -12.1163 11.9496

Indian Malay 8.71000 4.59464 .171 -2.4545 19.8745

Chinese .08333 4.95203 1.000 -11.9496 12.1163

However, the significant value by using Hochberg is >

0.05 for all group of races. As alternative we can use t-

test between

1. Malay and Chinese

2. Malay and Indian

3. Chinese and Indian

MALAY AND CHINESEIndependent Samples Test

Levene's Test for Equality of

Variances t-test for Equality of Means

F Sig. T DfSig. (2-tailed)

Mean Differen

ce

Std. Error

Difference

95% Confidence Interval of the

Difference

Lower UpperSystolic Equal

variances assumed

.234 .630-

2.28678 .025 -8.62667 3.77346

-16.1390

6

-1.11428

Equal variances not assumed

-2.282

60.889 .026 -8.62667 3.77957-

16.18466

-1.06868

• p = 0.025

• α = 0.05

• Since p<0.05, so there is a significance difference

in systolic blood pressure between Malay and

Chinese.

MALAY AND INDIAN

Independent Samples TestLevene's Test for

Equality of Variances t-test for Equality of Means

F Sig. t dfSig. (2-tailed)

Mean Differenc

e

Std. Error

Difference

95% Confidence Interval of the

DifferenceLower Upper

Systolic Equal variances assumed

1.658 .202-

1.91864 .060 -8.71000 4.54047 -17.78063 .36063

Equal variances

not assumed

-2.070

28.997 .047 -8.71000 4.20735 -17.31503 -.10497

• p = 0.06

• α = 0.05

• Since p>0.05, so there is no significance difference

in systolic blood pressure between Malay and

Indian.

CHINESE AND INDIAN

Independent Samples TestLevene's Test for

Equality of Variances t-test for Equality of Means

F Sig. t dfSig. (2-tailed)

Mean Differenc

e

Std. Error Differenc

e

95% Confidence Interval of the

DifferenceLower Upper

Systolic Equal variances assumed

.541 .466 -.017 44 .986 -.08333 4.84501 -9.84780 9.68113

Equal variances not assumed

-.018 35.077 .986 -.08333 4.62151 -9.46477 9.29810

• p = 0.986

• α = 0.05

• Since p>0.05, so there is no significance difference

in systolic blood pressure between Chinese and

Indian.

CONCLUSION

The ANOVA assumptions of normality abd homogeneityof variance were not violated. The ANOVA wasstatistically significant, indicating that there is asignificance difference in the systolic blood pressureamong different race group, F (2,93)= 3.507, p= 0.034.

However, post-hoc analysis with Hochberg’s GT2showed that there is no significant difference betweenthe systolic blood pressure in any pairs of race group.Alternatively, independent T-test showed that there is asignificant different in systolic blood pressure betweenMalay and Chinese (p=0.025), but not between Malayand Indian (p=0.06), nor between Chinese and Indian(p=0.986). So we reject null hypotesis.

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Lim SS, Vos T, Flaxman AD, Danaei G, et al A comparative risk assessment of burden of

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