Statistics

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:

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 

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;

Experiment 2

Methodology

A similar experiment again just like the previous one, involved the taking of samples from deceased individual’s lungs. However, contrary to the previous experiment, each individual was categorized as either a control subject (group 1), or an asthma subject (group 2). However, each subject had samples taken from only one lobe then 3 samples per lobe were taken at different levels (small, medium, large). The main purpose of this particular experiment was to do a comparison of the two groupings (control vs asthma) along with the level to see if they had an impact on the response measurement the perimeter of the airway basement membrane (pbm). This experiment is a split plot design in a completely randomized structure (Tsangari & Akritas, 2004).  Just like experiment 1, ANOVA test though in this case a split plot design was used. 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 model for this split plot design is:

Results

Boxplot

First a boxplot was constructed to help visualize the means in the two groups (control subject and asthma subject). Looking at the two plots, little differences can be seen in terms of the averages for the groups. It can also be seen that none of the two groups presents outliers in their datasets.

Figure 2: Boxplot for the pbm versus groups

ANOVA Results

We performed ANOVA test for the split plot design in a completely randomized structure (no blocking) and results are presented in table 2 below;

As can be seen, the results of the ANOVA clearly shows 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 patient type nor the interaction between group and patient type (Wilcox, 2005).

Contrasts between the two experiments

Nested design takes into account the levels of the variables, and does not take the experiment units. Split-plot on the other hand breaks up the experimental units, and does not take into account the levels of the variables (Wright, 2006). Split-plot designs are suitable for situations where one of the factors can only be varied on a “large” scale this is not possible for the nested design.

Conclusion

The aim of this study was to analyze two datasets where the first experiment sought to compare three groupings with respect to the response measurement the perimeter of the airway basement membrane (peri-inter) using nested design approach. The second experiment sought to compare the two groupings (control vs asthma) along with the level to see if they had an impact on the response measurement the perimeter of the airway basement membrane (peri-inter) though in this case using a split plot design in a completely randomized structure (no blocking). Lobe, level, replication and patients were used in the mixed-model analysis so as to correct for any likely confounders and also to assess the effect of asthma on Pbm. Results of both experiments showed that there are significant differences in the groupings with respect to the response measurement the perimeter of the airway basement membrane (pbm). The current study indicated that the length (perimeter) of the basement membrane, which is observed on airways, is not statistically significantly different in large airways among the subjects without asthma and those with asthma.  Based on the results, the length of the Pbm can therefore be used as a reliable marker of airway size in comparing the dimensions of large airways from the different asthma cases irrespective of lung size.

References

Algina, J. & Olejnik, S., 2003. Conducting power analyses for ANOVA and ANCOVA in between-subjects designs. Evaluation & the Health Professions, 26(3), pp. 288-314..

Cardinal, R. N. & Aitken, M. F., 2006. ANOVA for the behavioural sciences researcher.

Tsangari, H. & Akritas, M. G., 2004. Nonparametric ANCOVA with two and three covariates. Journal of Multivariate Analysis, 88(2), pp. 298-319.

Wilcox, R. R., 2005. An approach to ANCOVA that allows multiple covariates, nonlinearity, and heteroscedasticity. Educational and Psychological Measurement, 65(3), pp. 442-450.

Wright, D. B., 2006. Comparing groups in a before-after design: When t test and ANCOVA produce different results. British Journal of Educational Psychology, 76(5), pp. 663-675.