Analysis

1
Analysis Evaluation of Data

• The collected data should be
• Reliable
• none or very little error is committed in the
  gathering and tabulation of data
• Accurate
• maintain the desired degree of precision
• Valid
• the data is applicable to the issue and attribute
  of interest

2
Sample Consideration

• We have collected error data on Requirements
  Inspection, Design Inspection and Unit Testing
  and want to analyze them for quality attribute
• Potential Reliability problem?
• Did we collect and count the data correctly in
  all three cases
• Potential Accuracy problem ?
• Did we use the same level of precision (e.g. same
  level of severity breakdown)
• Potential Validity problem ?
• Is number of defect a valid quality attribute
• Do these data reflect a measure of the extent of
  defects committed (extent number, severity,
  complexity of fix, etc. ?)

3
Some Common Analysis Methods of Data

1. Distribution of Data
2. Centrality and Dispersion
3. Moving Averages
4. Data Correlation
5. Normalization of Data

4
1. Distribution of Data

• We often look at a scatter diagram of the raw
  data and pick out the outliers
• We count the frequency of occurrences and get a
  distribution to get a view of the shape of the
  distribution and the range of distribution.
• severity 1 7 defects
• severity 2 24 defects
• severity 3 26 defects
• severity 4 88 defects
• severity 5 92 defects

• Range is from 7 defects to 92 defects
• Shape is not that important in this case,
• the skew is towards the less severe defects

5
Common Distributions of Data

• There are some recognizable distributions

Normal
Linear













Logarithmic
Exponential
Negative Exponential
6
2. Centrality and Dispersion

• Use centrality to compare two sets of data
  distribution
• mean
• median

median value
mean value
median value
median value
mean value
Mean value
7
Variance Standard Deviation

• A measure of dispersion from the central value
  (see below)
• we measured number of defects (xi) from n similar
  sized functional areas
• the mean or central value is calculated Xmean
  ?(xi) / n
• the variance ? ( (Xi Xmean )2 ) / n
• Std Dev. SQRT (variance)
• For Normal Distribution, 1 Std captures about 68
  of the sample.
• Given a new function of similar size, we can
  measure the number of defects found and compare
  against the mean of the earlier group and the 1
  std deviation.

8
Control Chart

1 Std Dev.




Mean 5.3


1 Std Dev.

9
3. Moving Average - a Smoothing Technique
Jump smoothed
Jump smoothed
Special jump
10
4. Correlation

• Only addresses whether there is a relationship
• Does not address cause and effect
• Example
• size of the module may correlate to number of
  defects
• but size of the module may or may not be the
  cause

11
Linear Relationship
Y
Linear equation of the form Y a bX where
- b is the slope and - a is the y
intercept









X
12
Least Square Linear Regression

• A method of estimating the linear relationship of
  Y variables with the X variables in the following
  form by minimizing the distance of Y coordinates
  from the linear line to get Y abX.
• We can estimate the parameters a, b as follows
• b ?(XY) - (1/n)(?X)(?Y)/ ?(X2) -
  (1/n)(?X)2
• this b estimate gives the same value as the one
  shown in the book
• a Yave - (bXave)
• where X is each of the X observation and Xave is
  the average of Xs

13
Least Square Linear Regression - Example

• (size,defects) (150,2) (230,3)(500,4)(730,7)
  (1000,9)
• Xs 150, 230, 500, 730, 1000 ?(Xs) 2610
• X2 22,500 52,900 250,000 532,900 1,000,000
  and
  ?(X2) 1,858,300
• Ys 2, 3, 4, 7, 9 ?(Y) 25
• XY 300, 690, 2000, 5110, 9000 ?(XY) 17,100
• b 17100-(1/5)(2610)(25)/1858300
  -(1/5)((2610)2)
• 4050/495880 .0081
• a 25/5 - (.0081)(2610/5) 5 - 4.23 .77
• Least Square Regression line is Y .77 .0081
  X

Lets plug in x 150 and see what we get. .0081
(150) .77 1.22 .77 1.99 (close!) More
accurate for interpolation than extrapolation.
14
5. Normalization

• Pure data gives 1-dimensional comparison
• program A 52 person days to complete
• program B 33 person days to complete
• program C 64 person days to complete
• 64 gt 52 gt 33 what else can we say ? (suspect
  different sizes of programs)
• Normalization gives an equalizing factor in terms
  of another attribute.
• 52 person days 5000 loc or 96.1 loc /
  person day
• 33 person days 3000 loc or 90.9 loc /
  person day
• 64 person days 6000 loc or 93.7 loc /
  person day