Statistics Assignment Solutions - Data Analysis, Tests, and Results

This assignment solution covers several key concepts in statistics, including the analysis of basal heart rate distributions, the advantages of nonparametric methods, and the interpretation of statistical significance. It explores the implications of sample size on statistical outcomes, specifically addressing Type I and Type II errors. The solution also delves into specific statistical tests, such as the two-sample independent t-test, and the importance of considering factors like clustering in experimental design. Furthermore, the document explains the calculation and interpretation of confidence intervals, emphasizing their role in providing information about the range of population values and the strength and direction of treatment effects. Finally, the assignment clarifies common misconceptions regarding p-values and the interpretation of statistical results.

Statistics
Student Name:
Instructor Name:
Course Number:
15th June 2019

Q1:
The distribution of basal heart rate is approximately mound shaped and symmetric (apart from a
few large outliers)
Q2:
Nonparametric methods require fewer distributional assumptions (e.g., normality)
Q3:
Type II error due to insufficient sample size
Q4:
Spleen size (continuous)
Q5:
Yes, they suggest a difference in centre and spread. The medians differ by approximately 50 cm3
Q6:
Two sample independent t-test (unequal variances)
Q7:
The excluded people were closely related to both Bajau and Saluan communities which would
have violated the assumption of independent groups
Q8:
Ordinal
Q9:
85 patients per group
Q10:
The power would decrease (from 90%)
Q11:
t= d
SE = 6.45
5.05 =1.277 ≈ 1.3
The test statistic is 1.3 and the associated p-value is notstatistically significant.
Q12:
C . I :d ± ME
ME ¿ zα /2 SE=1.96∗5.05=9.898

d ± ME →6.45 ± 9.898
Lower limit: 6.45−9.898=−3.448≈−3.4
Upper limit: 6.45+9.898=16.348 ≈ 16.3
[-3.4, 16.3]
Q13:
Yes. Multiple outcome testing results in an increase in the overall probability of a Type I error.
Q14:
0.05
n = 0.05
18 =0.003
From the table only two outcomes have p-values that are less than 0.003.
2 (two)
Q15:
Before taking clustering into account around 85 participants would be needed.
For the clustered trial 158 participants would be needed.
Q16:
( ^p1− ^p2 ) ± zα/ 2 √ ^p1 (1− ^p1)
n1
+ ^p2 (1− ^p2)
n2
^p1=0.083 , n1=4502 , ^p2 =0.064 , n2=4512
( ^p1− ^p2 ) ± z α
2 √ ^p1 ( 1− ^p1 )
n1
+ ^p2 ( 1− ^p2 )
n2
→ ( 0.083−0.064 ) ± 1.96 √ 0.083 ( 1−0.083 )
4502 + 0.064 ( 1−0.064 )
4512
0.019 ± 0.010768
Lower bound: 0.019−0.010768=0.008232=0.8232≈ 0.8 %
Upper bound: 0.019+0.010768=0.029768=2.9768 % ≈ 3 %
[0.8%, 3.0%]
Q17:
95% Confidence interval is useful in providing information regarding the range in which the true
population value (proportion) lies with a certain degree of probability, as well as information
regarding the strength and direction of the demonstrated treatment effect. The 95% confidence
interval therefore enables conclusions to be drawn regarding the statistical plausibility and
clinical relevance of the study findings.

Q18:
One of the common misconception about statistical significance (p-value) is that it measures the
probability that the studied hypothesis is true, or the probability that the data were produced by
random chance alone. This misconception that is not true about the statistical significance (p-
value). The p-value however helps a researcher to determine the significance of the results.