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
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.
REFERENCES
Causes of Death 2008 [online database]. Geneva, World Health Organization
(http ://www.who.int/healthinfo/global_burden_disease/cod_2008_sources_methods.pdf.)
Lim SS, Vos T, Flaxman AD, Danaei G, et al A comparative risk assessment of burden of
disease and injury attributable to 67 risk factors and risk factor clusters in 21 regions, 1990-
2010 : a systematic analysis for the Global Burden of Disease Study 2010. Lancet. 2012; 380
(9859): 2224-60
Kaplan, Norman M., Victor, Ronald G. and Flynn, Joseph T. Kaplan 2010. Clinical
Hypertension, 10th Edition, China: Lippinkott Williams & Wilkins, 2010.
Mohammad et al., 2008. The Third National Health and Morbidity Survey (NHMS III) 2006:
nutritional status of adults aged 18years old and above. Malaysia Journal of Nutrition, 14 (2).
pp. 1-87. ISSN 1394-035X, 2008.
World Health Organization. 2013. A global brief on Hypertension, silent killer, global public
health crisis. World Health Day. Geneva, World Health Organization, 2011.
Sutha Rajakumar, Lim Li Ann, Preeti Kaur Gill, Goon Wan Xin, Anandarajagopal
Kalasalingam (2012). A comparative study of hypertension, diabetes mellitus and obesity
among Malaysians in urban regions - A cross sectional study Int. J. Res. Pharm. Sci., 3(1), 38-
44.
Syer Ree Tee, Xin Yun Teoh, Wan Abdul Rahman Wan Mohd Aiman, Ahmad Aiful, Calvin Siu
Yee Har, Abdul Rashid Khan, Zi Fu Tan. The Prevalence of Hypertension and Its Associated
Risk Factors in Two Rural Communities in Penang, Malaysia. 2010. IeJSME 2010: 4(2): 27-
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