Understanding Statistics in the Behavioral Sciences ... - NelsonBrain

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10 C H A P T E R 1 Statistics and Scientifi c Method
but usually it is far too costly, so a sample is taken. Note that not just any sample
will do. The sample should be a random sample. Random sampling is discussed in
Chapter 8. For now, it is suffi cient to know that random sampling allows the laws of
probability, also discussed in Chapter 8, to apply to the data and at the same time
helps achieve a sample that is representative of the population. Thus, the results
obtained from the sample should also apply to the population. Once the data are
collected, they are statistically analyzed and the appropriate conclusions about the
population are drawn.
DESCRIPTIVE AND INFERENTIAL STATISTICS
definitions
Statistical analysis, of course, is the main theme of this textbook. It has been divided
into two areas: (1) descriptive statistics and (2) inferential statistics. Both involve analyzing
data. If an analysis is done for the purpose of describing or characterizing the
data, then we are in the area of descriptive statistics. To illustrate, suppose your biology
professor has just recorded the scores from an exam he has recently given you. He hands
back the tests and now wants to describe the scores. He might decide to calculate the
average of the distribution to describe its central tendency. Perhaps he will also determine
its range to characterize its variability. He might also plot the scores on a graph
to show the shape of the distribution. Since all of these procedures are for the purpose
of describing or characterizing the data already collected, they fall within the realm of
descriptive statistics.
Inferential statistics, on the other hand, is not concerned with just describing the
obtained data. Rather, it embraces techniques that allow one to use obtained sample
data to make inferences or draw conclusions about populations. This is the more complicated
part of statistical analysis. It involves probability and various inference tests,
such as Student’s t test and the analysis of variance.
To illustrate the difference between descriptive and inferential statistics, suppose
we were interested in determining the average IQ of the entire freshman class at your
university. It would be too costly and time-consuming to measure the IQ of every
student in the population, so we would take a random sample of, say, 200 students and
give each an IQ test. We would then have 200 sample IQ scores, which we want to use
to determine the average IQ in the population. Although we can’t determine the exact
value of the population average, we can estimate it using the sample data in conjunction
with an inference test called Student’s t test. The results would allow us to make a statement
such as, “We are 95% confi dent that the interval of 115–120 contains the mean IQ
of the population.” Here, we are not just describing the obtained scores, as was the case
with the biology exam. Rather, we are using the sample scores to infer to a population
value. We are therefore in the domain of inferential statistics. Descriptive and inferential
statistics can be defi ned as follows:
■ Descriptive statistics is concerned with techniques that are used to describe or
characterize the obtained data.
■ Inferential statistics involves techniques that use the obtained sample data to
infer to populations.
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