Comparison of Two Experiments on Perimeter of Airway Basement Membrane (PBM)

Statistics
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Institution:
24th May 2018
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Experiment 1
Statistical methods
This experiment involved the taking of samples from deceased individual’s lungs. Each
individual was categorized as either a control subject (group 1), a fatal asthma subject (group 2),
or a none-fatal asthma subject (group 3). Each subject had samples taken from two lobes and the
4 random samples per lobe were taken. The main purpose of this particular experiment was to do
a comparison of the three groupings with respect to the response measurement the perimeter of
the airway basement membrane (pbm). This experiment is a nested design (Cardinal & Aitken,
2006).
In order to test the differences in the means of the three groups, analysis of variance (ANOVA)
test was performed. ANOVA refers to a statistical technique that investigates the potential
differences in a scale-level dependent variable by a nominal-level variable having 2 or more
categories (Algina & Olejnik, 2003). This test is able to tell whether a group of three independent
factors are significantly the different or not at a given level of significance. For this study, a 5%
level of significance was applied in testing the differences in the means of the three groups.
The additive model for this design is:
yij=μ+α i + β ( i ) j+ εijk
Where:
μ is the constant; overall mean
α i is a constant for ith treatment group; deviation from mean of i
βi j is a random effect due to the ith group nested witin the jth experimental unit
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ε ijk is the random deviation associated with each observation
Results
Box plot
First a boxplot was constructed to help visualize the means in the three different groups. Looking
at the three plots, little differences can be seen in terms of the averages for the groups. It can also
be seen that group 1 (control subject) and group 3 (Non-fatal asthma subject) have visible
outliers.
Figure 1: Boxplot for the pbm versus groups
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ANOVA Results
We performed ANOVA test for the nested design and results showed that there is evidence of
significant differences in the three groupings with respect to the response measurement the
perimeter of the airway basement membrane (pbm). However, there is no evidence of
differences in the mean pbm based on the interaction between group and patient type nor the
interaction between group and Lobe. This is based on the fact that the computed p-value for the
interaction tests was found to be greater than the 5% level of significance. Results are presented
in table 1 below;
But there was significant statistical evidence that the interaction
between group and replicates yielded evidence of significant
differences in the pbm.
The other results are presented in table 2 below;
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> nested_aov1 <-
lm(pbm ~ group +
group/patient,
data=dat1)
> anova(nested_aov1)
Analysis of Variance
Table
Response: pbm
Df Sum Sq
Mean Sq F value Pr(>F)
group 1 72.32
72.322 11.2763
0.0008479 ***
group:patient 1 11.11
11.113 1.7327
0.1887031
Residuals 477 3059.32
6.414
---
Signif. codes: 0 ‘***’
0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’
0.1 ‘ ’ 1
Table 1 ANOVA results for the Nested design