Social Research Methods: Qualitative and Quantitative Approaches

ANALYSIS OF QUANTITATIVE DATA

curvilinear relationshipmeans that the center of a
maze of cases would form a U curve, right side up
or upside down, or an S curve.
2.Direction.Linear relationships can have a
positive or negative direction. The plot of a positive
relationship looks like a diagonal line from the
lower left to the upper right. Higher values on Xtend
to go with higher values on Y,and vice versa. The
income and life expectancy example described a
positive linear relationship. A negative relationship
looks like a line from the upper left to the lower
right. It means that higher values on one variable go
with lower values on the other. For example, people
with more education are less likely to have been
arrested. If we look at a scattergram of data on a
group of males that plots years of schooling (Xaxis)
by number of arrests (Yaxis), we see that most cases

(or men) with many arrests are in the lower right

because most of them completed fewer years of

school. Most cases with few arrests are in the upper

left because most have had more schooling. The

imaginary line for the relationship can have a shal-

low or a steep slope. More advanced statistics pro-

vide precise numerical measures of the line’s slope.

3. Precision.Bivariate relationships differ in
   their degree of precision. Precisionis the amount of
   spread in the points on the graph. A high level of
   precision occurs when the points hug the line that
   summarizes the relationship. A low level occurs
   when the points are widely spread around the line.
   We can “eyeball” a highly precise relationship or
   use advanced statistics to measure the precision of
   a relationship in a way that is analogous to the stan-
   dard deviation for univariate statistics.

Bivariate Tables

We use the bivariate contingency tablein many sit-

uations. It presents the same information as a scat-

tergram in a more condensed form. One advantage

of it over the scattergram is that the data can be

FIGURE 5 Example of a Scattergram: Years of Education by Number of Natural
Children for 33 Women

8.00 10.00 12.00 14.00 16.00 18.00 20.00 22.00

Number of Natural Children

Years of Formal Education

6.00

5.00

4.00

3.00

2.00

1.00

0.00

Curvilinear relationship An association between

two variables so that as the values of one variable

increase, the values of the second show a changing pat-

tern, for example, first decrease, then increase, and

finally decrease; not a linear relationship.