Biostatistics Assignment 3: Paired t-test, Independent t-test and LOS Analysis

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Introduction to Biostatistics (Assignment 3)
Introduction to Biostatistics
Assignment 3

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Introduction to Biostatistics (Assignment 3)
Question 1
a) Paired t-test was performed to investigate the effect of Reiki treatment impact on the VAS scores
as follows.
For the VAS scale population, μVA and μVB were taken as the average of visual analogue scale
for pre and post conditions of Reiki treatment. The test was conducted in EXCEL and the output
has been used for hypothesis testing
The hypotheses for the paired t-test were constructed as below.
Null hypothesis: H0: ( μVB−μVA ) =0
Alternate hypothesis: HA: ( μVB−μVA ) ≠0
Level of significance for the test was considered at 5% ( α =0 . 05 ).
The t-statistic was calculated as
t= estimated difference−hypothesized difference
s tan dard error = 1. 95−0
0 . 4 =4 .87
for 19 degrees of freedom.
The p-value was found to be P (|t|> 4 . 87 ) =0 .000 (from EXCEL output)
The p-value implied that at 5% level of significance the null hypothesis could be rejected against
the alternate hypothesis. It could be concluded that the differences in scores were significant (t =
4.87, p < 0.05) at 5% level and average VAS score was better after the Reiki treatment.
The confidence interval for the difference in VAS scores was evaluated as
X d
−
±t∗s tan dard error ( s
√ n )=[1 .11 ,2 .79 ]
(from EXCEL output). With 95% confidence, it was
estimated that the population mean difference would be within the limits of the confidence
interval. But, the hypothesized mean difference of VAS scores was outside the interval. Hence,
decision of rejecting the null hypothesis was justified.

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Introduction to Biostatistics (Assignment 3)
For the Likert scale population, μLA and μLB were taken as the average of visual analogue
scale for pre and post conditions of Reiki treatment. The test was conducted in EXCEL and the
output has been used for hypothesis testing (Sausen et al., 2015)
The hypotheses for the paired t-test were constructed as below.
Null hypothesis: H0: ( μLB−μLA ) =0
Alternate hypothesis: HA: ( μLB−μLA ) ≠0
Level of significance for the test was considered at 5% ( α =0 . 05 ).
The t-statistic was calculated as
t= estimated difference−hypothesized difference
s tan dard error = 1. 18−0
0. 18 =6 .29
for ( n−1 ) =20−1= 19 degrees of freedom, where n was the number of observations.
The p-value was found to be P (|t|> 6 .29 ) =0 . 000(from EXCEL output)
The p-value implied that at 5% level of significance the null hypothesis could be rejected against
the alternate hypothesis. It could be concluded that the differences in scores were significant (t =
6.29, p < 0.05) at 5% level and average Likert score was better after the Reiki treatment.
The confidence interval for the difference in Likert scores was evaluated as
X d
−
±t∗s tan dard error=[0 . 801 ,1 .549 ] (from EXCEL output). With 95% confidence, it was
estimated that the population mean difference would be within the limits of the confidence
interval. But, the hypothesized mean difference of Likert scores was outside the interval. Hence,
decision of rejecting the null hypothesis was justified.

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Introduction to Biostatistics (Assignment 3)
Table 1: Paired t-test Output from EXCEL
Lower Upper
VAS before -
VAS after 1.95 1.79 0.40 1.11 2.79 4.87 19 0.000
Likert before -
Likert after 1.20 0.83 0.19 0.81 1.59 6.44 19 0.000
Paired t-test
Paired Differences
t df Sig. (2-tailed)
Mean Std. Deviation Std. Error Mean 95% Confidence
b) From the outputs of the paired t-test for VAS and Likert scores it was inferred that Reiki
treatment had a positive impact on the volunteers. Considering the VAS scale scores, it was
evident that Reiki treatment was able to reduce pain significantly (t = 4.87, p < 0.05) for the
patients. Similar effect was also noticed from the Likert scale, where significant positive impact
of Reiki treatment (t = 6.29, p < 0.05) was evident at 5% level of significance. Considering the
outputs, it was possible to conclude based on the current sample that Reiki could be a positive
adjuvant to the Opioid therapy.
Question 2
a) Average Cholesterol level for the control group and the treatment group has been provided in
Table 2. Average Cholesterol level for the treatment group was observed to reduce with number
of days. Day 14 Cholesterol levels (M = 221.21, SD = 22.3) was found to be higher than that of
the control group (M = 193.13, SD = 22.3).