Social Research Methods: Qualitative and Quantitative Approaches

ANALYSIS OF QUANTITATIVE DATA

or are likely to show effects actually occurring in

the social world.

Statistical significance tells us only what is

likely. It cannot prove anything with absolute cer-

tainty. It states that particular outcomes are more or

less probable. Statistical significance is not the same

as practical, substantive, or theoretical significance.

Results can be statistically significant but theoreti-

cally meaningless or trivial. For example, two vari-

ables can have a statistically significant association

due to coincidence with no logical connection

between them (e.g., length of fingernails and abil-

ity to speak French).

Levels of Significance
We usually express statistical significance in terms
of levels (e.g., a test is statistically significant at a
specific level) rather than giving the specific prob-
ability. The level of statistical significance(usu-
ally .05, .01, or .001) is an easy way of talking about
the likelihood that results are due to chance factors,
that is, that a relationship appears in the sample
when there is none in the population. When we say
that results are significant at the .05 level, we mean
the following:

Results like these are due to chance factors only

5 in 100 times.

There is a 95 percent chance that the sample

results are not due to chance factors alone but

reflect the population accurately.

The odds of such results based on chance alone

are .05, or 5 percent.

One can be 95 percent confident that the results

are due to a real relationship in the population,

not chance factors.

These all say the same thing in different ways. This

may sound a bit like the discussion of sampling dis-

tributions and the central limit theorem in the chap-

ter on sampling. It is no accident! Both are based on

probability theory, which we use to link sample data

to a population. Probability theory lets us predict

what happens in the long run over many events

when a random process is used. In other words, it

allows us to make precise predictions over many sit-

uations in the long run but not for a specific situa-

tion. Because we have just one sample and we want

to infer to the population, probability theory helps

us estimate the odds that our particular sample rep-

resents the population. We cannot know for certain

unless we have the whole population, but probabil-

ity theory lets us state our confidence: how likely it

is that the sample shows one thing while something

else is true in the population.

CHART 2 Summary of Major Types of Descriptive Statistics

TYPE OF TECHNIQUE STATISTICAL TECHNIQUE PURPOSE

Univariate Frequency distribution, Describe one variable.

measures of central tendency,

standard deviation, z-score

Bivariate Correlation, percentage table, Describe a relationship or the association between

chi-square two variables

Multivariate Elaboration paradigm, multiple Describe relationships among several variables,

regression or see how several independent variables have an

effect on a dependent variable.

Level of statistical significance A set of numbers

that researchers use as a simple way to measure the

degree to which a statistical relationship results from

random factors rather than the existence of a true rela-

tionship among variables.