Social Research Methods: Qualitative and Quantitative Approaches

ANALYSIS OF QUANTITATIVE DATA

ideology (see Example Box 4, Example of Multiple
Regression Results).^6 The example suggests that high
income, frequent religious attendance, and a south-
ern residence are positively associated with conser-
vative opinions, whereas having more education is
associated with liberal opinions. The impact of
income is more than twice the size of the impact of
living in a southern region.
Chart 2 summarizes the types and techniques
of descriptive statistics. Next we turn our attention
to inferential statistics.

INFERENTIAL STATISTICS

The Purpose of Inferential Statistics

The statistics discussed so far in this chapter are
descriptive statistics. But we often want to do more
than just describe; we want to test hypotheses, to

find out whether sample results hold true in a pop-

ulation, and decide whether results (e.g., between

the mean scores of two groups) are big enough to

indicate that a relationship truly exists and is not

due to chance alone. Inferential statisticsbuild

on probability theory to test hypotheses formally,

permit inferences from a sample to a population,

and test whether descriptive results are likely to

be due to random factors or to a real relationship.

This section explains the basic ideas of inferential

statistics but does not deal with inferential statis-

tics in any detail. This area is more complex than

descriptive statistics and requires a background

in statistics.

Inferential statistics rely on principles from

probability sampling by which we use a random

process (e.g., a random-number table, random com-

puter process) to select cases from the entire popu-

lation. Inferential statistics are a precise way to talk

about how confident we can be when inferring from

the results in a sample to the population.

You have already encountered inferential sta-

tistics if you have read or heard about “statistical

significance” or results “significant at the 0.05

level.” We use them to conduct various statistical

tests (e.g., a t-test or an F-test). We use statistical

significance in formal hypothesis testing, which is

a precise way to decide whether to accept or to reject

a null hypothesis.^7

Statistical Significance

The term statistically significant resultsmeans that

the results are not likely to be due to chance fac-

tors. Statistical significanceindicates the proba-

bility of finding a relationship in the sample when

there is none in the population. Because probabil-

ity samples involve a random process, it is always

possible that sample results will differ from a pop-

ulation parameter. We want to estimate the odds

that sample results are due to a true population

parameter or to chance factors of random sampling.

With some probability theory from mathematics

and specific statistical tests, we can tell whether the

results (e.g., an association, a difference between

two means, a regression coefficient) are likely to

be produced by random error in random sampling

EXAMPLE BOX 4

Example of Multiple Regression Results

DEPENDENT VARIABLE IS POLITICAL IDEOLOGY
INDEX (HIGH SCORE MEANS VERY LIBERAL)

Standardized
Regression
Independent Variable Coefficients

Region South .19
Age .01
Income .44
Years of education .23
Religious attendance .39
R^2 .38

Statistical significance The likelihood that a finding

or statistical relationship in a sample’s results is due to

random factors rather than to the existence of an actual

relationship in the entire population.

Inferential statistics A branch of applied mathe-

matics based on random sampling that allows

researchers to make precise statements about the level

of confidence they can have that measures in a sample

are the same as a population parameter.