thesis - Faculty of Information and Communication Technologies ...

Chapter 5. Growth Dynamics
plifying models constructed to understand software. Similar to Succi
et al. [265], we compute the Spearman’s rank correlation coefficient ρ
and applied the t-test to check if the reported coefficient is different from
zero at a significance level of 0.05 for all 10 measures in all systems.
The t-test checks that the reported relationship between the Gini Coefficient
and Age (days since birth) can be considered to be statistically
significant, while the correlation coefficient reports the strength of the
relationship between the Gini Coefficient and Age. The non-parametric
Spearman’s correlation coefficient was selected over Pearson’s correlation
coefficient since as it does not make any assumptions about the
distribution of the underlying data [279], specifically it does not assume
that the data has a gaussian distribution.
5.3.3 Checking Shape of Metric Data Distribution
A consistent finding by other researchers [21, 55, 223, 270, 299] studying
software metric distributions has been that this data is positively
skewed with long-tails. Can we confirm this finding in our own data?
Further, will this shape assumption hold if metric data was observed
over time? We undertook this step in order to provide additional strength
to the current expectation that metric data is highly skewed.
For a population with values x i , i = 1 to n with a mean of µ and a
standard deviation of σ,
MovementSkewness = 1 n
n
(x
∑
i − µ) 3
σ
i=1
3 (5.3.1)
In our analysis, we tested the metric data for each release over the entire
evolution history to ensure that the data did not have a gaussian
distribution by using the Shapiro-Wilk goodness of fit tests for normality
[279] at a significance level of 0.05. The expectation is that the test
will show that the metric data is not normally distributed. Additionally,
to confirm that the distribution can be considered skewed we computed
the descriptive measure of movement skewness (See Equation
105