Biostatistics Homework Assignment: Statistical Analysis of Data

This biostatistics assignment solution analyzes data related to hand grip strength and hypertension among grandparent carers. It addresses several key questions, including calculating confidence intervals for average grip strength, testing for significant differences, and performing hypothesis tests using t-tests and non-parametric tests like the Wilcoxon test. The assignment also explores the proportion of grandparent carers with hypertension, calculates confidence intervals for the difference in proportions between males and females, and determines the minimum sample size required to detect significant clinical differences. Furthermore, the solution includes the calculation of the standard deviation of hand grip and the impact of confidence interval size on the required sample size. The assignment references relevant statistical methods and provides interpretations of the results, including p-values and confidence intervals, using chi-square tests and calculations for minimum sample sizes.

Introduction to Biostatistics 1
Introduction to Biostatistics
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Introduction to Biostatistics 2
Introduction to Biostatistics
Question 1
a) Average grip
The average grip strength of the grandparent’s carers in Parramatta is 31.60hand grip in
kilograms. With a 95% confidence, the hand grip of the grandparent’s carers of Parramatta will
be between 31.09 and 32.12 kilograms.
b) Significance difference from 33kg
The average hand grip of the grandparent’s carers is statistically different from 33 kilograms
because the value is not included in the 95% confidence interval.
c) Hypothesis test of whether the mean difference in hand grip between males and females
is statistically different from 0.
T test is used to perform one or two sample tests on vectors and that is why it is relevant to test
for differences in means of hand grip between males and female grandparent’s carers. The means
of males and females is 30.75 kilograms and 32.3 kilograms respectively. The difference
between males and females is −1.65 kilograms with a 95% confidence interval of −2.66 ¿−0.64
. The test statistics is −3.22 and it is associated with a p-value of 0.00148, hence the difference is
statistically difference from 0. Logically, female grandparent’s carers have significantly higher
average of hand grip compared with the males.
d) Non-parametric
The non-parametric equivalent test is Mann-Whitney test or Wilcoxon for two-sample test. The
test check whether there is a statistically significant difference in median ranks between male and

Introduction to Biostatistics 3
female hand grip in kilograms. The Wilcoxon test statistics is 5303 with a p-value of 0.004178,
hence the test is significant. Therefore, we conclude that the difference in median ranks between
males and females is statistically different from zero (McHugh, 2012).
Question 2
a) Proportion of grandparent carers with hypertension is greater than 0.25
The count of grandparent carers with hypertension is 78 out of 233, which is approximately 33%.
The chi-square statistic of the test is 8.48 with a p-value of 0.0036. The 95% confidence interval
of the proportion is between 0.275 and 0.4. Therefore, we conclude that the proportion of
grandparent carers is statistically greater than 0.25 (Cumming and Fidler, 2009).
b) 95% confidence interval of the difference between the proportion of males with
hypertension and the proportion of females with hypertension
The proportion of males with hypertension and proportion of females with hypertension is
approximately 0.5 and 0.18 respectively. The difference in proportion is approximately 0.32 with
a 95% confidence interval of 0.19 to 0.44. The confidence interval means that there is 95%
chance that the difference in proportion of male grandparent carers with hypertension and female
grandparent carers with hypertension will be between 0.19 and 0.44.
Question 3
Testing the hypothesis that the non-dominant hand has a significantly lower grip compared with
the dominant hand.

Introduction to Biostatistics 4
Wilcoxon test for an alternative test that the true location shift is less than 0 has a p-value of
0.007. therefore, we conclude that the non-dominant hand has a lower grip strength compared to
the dominant hand.
Question 4
a) The proportion of females with hypertension
The proportion of female grandparent carers with hypertension is approximately 0.18.
b) Minimum sample required to test for a significant clinical difference in hypertension rates
between males and females in a grandparent carer population
power=80 %
alpha=0.05
n= ( Z ∝
2
+Zβ ) 2 [P1 ( 1−P1 ) + P2 ( 1−P2 ) ]
( P1 −P2 )
2
After adding 0.04
n= ( 1.96+ 0.84 )2 [ ( 0.18∗0.82 ) + ( 0.22∗0.78 ) ]
0.0016 = 2.502528
0.0016 =1565
After adding 0.04
n= ( 1.96+ 0.84 )2 [ ( 0.18∗0.82 ) + ( 0.14∗0.86 )]
0.0016 = 2.10112
0.0016 =1314

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The minimum sample to observe clinically significant difference in proportions of males and
females with hypertension in the grandparent carer population will be 1,314 study participants.
c) Standard deviation of grip strength
The standard deviation of hand grip is approximately 3.97 kilograms in the grandparent carer
population.
d) Minimum sample size
Confidence interval = 95 %
Margin error = 1.5 kgs
Standard deviation = 3.97 kgs
n=¿
¿ ( 1.96∗3.97
1.5 ) 2
=27
The minimum sample size required to produce 95% confidence interval with a margin of error or
1.5 kgs and 3.97 kgs of hand grip in grandparent carer population is 27 participants.
e) Disadvantage of using 50% confidence interval and 95% confidence interval
A smaller confidence interval will yield lower minimum sample size required, hence increasing
the potential of biased results (Cumming and Fidler, 2009).
References

Introduction to Biostatistics 6
Cumming, G. and Fidler, F. (2009) ‘Confidence Intervals’, Zeitschrift für Psychologie / Journal
of Psychology, 217(1), pp. 15–26. doi: 10.1027/0044-3409.217.1.15.
McHugh, M. L. (2012) ‘The Chi-square test of independence’, Biochemia Medica, 23(2), pp.
143–149. doi: 10.11613/BM.2013.018.