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226 Part IV: Quality Assurance
Types of defects
200
100
Weighted frequencies
150
100
50
80
60
40
20
Percent
0 0
Types of defects C A B D E
Weighted frequencies 75.0 50.0 45.0 24.0 12.5
Percent 36.3 24.2 21.8 11.6 6.1
Cumulative % 36.3 60.5 82.3 93.9 100.0
Figure 18.13 Pareto chart when weighted frequencies are used.
effective way to investigate for such an association is to prepare a graph by plotting
one variable along the horizontal scale (x-axis) and the second variable along
the vertical scale (y-axis). Each pair of observations (x, y) is then plotted as a point
in the xy-plane. The graph prepared is called a scatter plot. A scatter plot is a very
useful graphical tool because it depicts the nature and strength of associations
between two variables. To illustrate, we consider the following example.
Part IV.A.4
EXAMPLE 18.22
The cholesterol levels and the systolic blood pressures of 30 randomly selected U.S.
males in the age group of 40 to 50 years are given in Table 18.8. Construct a scatter plot
of these data and determine if there is any association between the cholesterol levels
and systolic blood pressures.
Solution:
Figure 18.14 shows the scatter plot of the data in Table 18.8. This scatter plot clearly
indicates that there is a fairly good upward linear trend. Also, if we draw a straight line
through the data points, we can see that the data points are concentrated around the
straight line within a narrow band. The upward trend indicates a positive association
between the two variables whereas the width of the band indicates the strength of the
association, which in this case is very strong. As the association between the two variables
gets stronger and stronger, the band enclosing the plotted points becomes narrower
and narrower. A downward trend indicates a negative relationship between two
variables. A numerical measure of association between two numerical variables is called
the Pearson or simply the correlation coefficient, named after the English statistician
Continued