Statistics in Psychology A-11are differences between the two groups that have nothing to do with the manipulations
of the experimenter). When researchers want to know if the differences they find in the
data that come from studies like the Cheryan experiment are large enough to be caused
by the experimental manipulation and not just by the chance differences that exist within
and between groups, they have to use a kind of statistical technique that can take those
chance variations into account. These kinds of statistical analysis use inferential statistics.
Inferential statistical analysis also allows researchers to determine how much con-
fidence they should have in the results of a particular experiment. As you might remem-
ber, results from other kinds of studies that look for relationships—observations, surveys,
and case studies—are often analyzed with descriptive statistics, especially correlations.
But experiments look for causes of relationships, and researchers want to have some evi-
dence that the results of their experiments really mean what they think they mean.
There are many different kinds of inferential statistical methods. The method that
is used depends on the design of the experiment, such as the number of independent
and dependent variables or the number of experimental groups. All inferential statis-
tics have one thing in common—they look for differences in group measurements that
are statistically significant. Statistical significance is a way to test differences to see how
likely those differences are to be real and not just caused by the random variations in
behavior that exist in everything animals and people do.
For example, in a classic study investigating the effects of intrinsic versus extrin-
sic motivation on children’s creativity, Dr. Teresa Amabile’s 1982 study showed that the
collages of the children who were promised prizes (an extrinsic reward) were judged to
be less creative than those of the children who created collages just for fun. to
Learning Objective 9.1. But was that difference between the creativity scores of the
two groups a real difference, or was it merely due to chance variations in the children’s
artistic creations? Dr. Amabile used an inferential test on her results that told her that
the difference was too big to be just chance variations, which means her results were
significant—they were most likely to be real differences. How likely? Tests of signifi-
cance give researchers the probability that the results of their experiment were caused
by chance and not by their experimental manipulation. For example, in one test called
a t-test, the scores of the children’s artwork would have been placed into a formula that
would result in a single number (t) that evaluates the probability that the difference
between the two group means is due to pure chance or luck. That number would be
compared to a value that exists in a table of possible t values, which tells researchers the
probability that the result is due to chance or luck. If the number obtained by the calcu-
lation is bigger than the value in the table, there will be a probability associated with that
number in the table. The probability, symbolized by the letter p, will tell researchers the
probability that the difference was due to chance. In Dr. Amabile’s case, the probability
was p < 0.05, which means the probability that the results were due to chance alone
was less than 5 out of 100. Another way of stating the same result is that Dr. Amabile
could be 95 percent certain that her results were real and not due to chance. Dr. Amabile
would, thus, report that the study found a significant difference, which means a differ-
ence thought not to be due to chance.
There are several statistical techniques to test if groups are different from each
other. Here are some common ones you might encounter if you read journal articles.- t-test—determines if two means are different from each other.
- F-test or analysis of variance—determines if three or more means are different from
each other. Can also evaluate more than one independent variable at a time. - chi-square—compares frequencies of proportions between groups to see if they are
different. For example, the proportion of women hired at a company is too low and
might indicate discrimination. Chi is pronounced like the beginning of the word
kite. Don’t say “chee.” It will be ugly.
statistically significant
referring to differences in data sets
that are larger than chance variation
would predict.t-test
type of inferential statistical analysis
typically used when two means
are compared to see if they are
significantly different.significant difference
a difference between groups
of numerical data that is considered
large enough to be due to factors other
than chance variation.Z01_CICC7961_05_SE_APPA.indd 11 9/2/16 11:57 PM