Inferential Statistics
Prerequisites
None
Learning Objectives
 Distinguish between a sample and a population
 Define inferential statistics
 Describe the various types of sampling and the implications of using each
With inferential statistics, we generally take
a sample, or a small subset of a larger set of data, and we use
this sample to draw inferences about the population as a whole.
As you might be able to imagine, it is very easy
for a sample to be biased. Thus, there are strategies that researchers
adopt in an attempt to eliminate or decrease the bias in their
sample. One of these strategies is the use of simple
random sampling. Simple random sampling occurs when every
member of the population has an equal chance of being selected
into the sample. In addition, the selection of one member is independent
from the selection of another member.
Sometimes, however, it is simply not possible or
feasible to take a simple random sampling. For instance, consider
the fact that both Dallas and Houston are vying to be hosts of
the 2012 Olympics. And consider that you are hired to assess whether
Texans, as a whole, would prefer the Olympics to be in Dallas
or Houston. Because you have already learned the difficulty of
getting every single Texan's opinion, you know you must get a
sample and you want to use a simple random sampling. However,
even this may be very difficult. Consider, for instance, how will
you get a hold of those individuals who don’t vote, who don’t
have a phone, and show address has changed? What do you do with
those individuals in the sample how happened to move from Texas
to California? What do you do about the fact that since the beginning
of the study, an additional 4,212 people moved to the state of
Texas? As you can see, it is sometimes very difficult to develop
a truly random procedure.
Recall that the definition of a random sample is
a sample in which every member of the population has an equal
chance of being selected. This means that the sampling procedure
rather than the results of the sampling procedure define what
it means for a sample to be random. Random samples, especially
if the sample size is small, are not necessarily representative
of the entire population. Inferential statistics use mathematical
models that take sample size into account when generalizing
from a sample to a population.
Random Assignment
In experimental research, populations are often
hypothetical. For example, in an experiment comparing the effectiveness
of a new antidepressant drug with a placebo,
there is no actual population of individuals taking the drug.
In this case, a specified population of people with some degree
of depression is defined and a random sample is taken from this
population. The sample is then randomly divided into two groups;
one group is assigned to the treatment condition (drug) and the
other group is assigned to the control condition (placebo). This
random division of the sample into two groups is called random
assignment.
