Social Research Methods: Qualitative and Quantitative Approaches

ANALYSIS OF QUANTITATIVE DATA

nominal variable categories; then calculate the
mean for the cases in each variable category from
the raw data. Table 3 shows the mean age of people
in each of the attitude categories. The results sug-
gest that the mean age of those who disagree is
much higher than for those who agree or have no
opinion.

Measures of Association

A measure of associationis a single number that
expresses the strength, and often the direction, of a
relationship. It condenses information about a bivari-
ate relationship into a single number. There are many
measures of association. The correct one to use
depends on the level of measurement of the data and
specific research purposes. Many measures are

identified by letters of the Greek alphabet. Lambda,

gamma, tau, chi (squared), and rho are commonly

used measures. The emphasis here is on interpret-

ing the measures, not on their calculation. To under-

stand each measure, you will need to complete at

least one statistics course. Some measures of asso-

ciation, such as gamma, are for data measured at the

ordinal level (see Expansion Box 2, Gamma). Other

measures, such as the correlation coefficient,

assume data measured at the ratio-level (see Expan-

sion Box 3, Correlation).

Most of the elementary measures discussed

here follow a proportionate reduction in error

logic. The logic asks how much does knowledge

of one variable reduce the errors that are made

when guessing the values of the other variable.

Independencemeans that knowledge of one vari-

able does not reduce the chance of errors on the

other variable. Measures of association equal zero

if the variables are independent.

If there is a strong association or relationship

between the independent and dependent variable,

we make few errors in predicting a dependent vari-

able based on knowledge of the independent vari-

able, or the proportion of errors reduced is large. A

large number of correct guesses suggests that the

measure of association is a nonzero number if an

association exists between the variables. Table 4

describes five commonly used bivariate measures

of association. Notice that most range from –1 to

1, with negative numbers indicating a negative

relationship and positive numbers a positive rela-

tionship. A measure of 1.0 means a 100 percent

reduction in errors, or perfect prediction.

TABLE 3 Attitude about Changing the

Drinking Age by Mean Age of Respondent

DRINKING AGE

ATTITUDE MEAN AGE (N)

Agree 26.2 (37)

No opinion 44.5 (25)

Disagree 61.9 (39)

Missing cases  8

Proportionate reduction in error A logic in many

statistics that measures the strength of association

between two variables. A strong association reduces

most errors in predicting the dependent variable using

information from the independent variable.

TABLE 2A Age by Schooling

YEARS OF SCHOOLING

AGE 0–11 12 13–14 16+ TOTAL

Under 30 5% 25 30 40 100
30–45 15 25 40 20 100
46–60 35 45 12 8 100
61 + 4 5 3 5 15 5 10 0

TABLE 2B Age by Schooling

YEARS OF SCHOOLING

AGE 0–11 12 13–14 16+ TOTAL

61 + 4 5 % 3 5 15 5 10 0
46–60 35 45 12 8 100
30–45 15 25 40 20 100
Under 30 5 25 30 40 100