Chapter 16
Inferential Statistics
(REMINDER: as you read the lectures, it’s a good idea to also look at the concept map
for each
chapter. The concept maps help to give you the big picture and see how the
concepts are related. Here is the link to all of the concept maps; just select the one for this
chapter:
http://www.southalabama.edu/coe/bset/johnson/dr_johnson/2conceptmaps.htm
)
This is probably the most challenging chapter in your book. However, you can
understand it. It just takes attention and effort. After you carefully study the material, it
will become clear to you. I will also be available to answer any questions you have.
Please start this chapter by taking a look (again) at the divisions in the field of statistics
that were shown in Figure 15.1 (p. 434) and also shown in the previous lecture.
•
This shows the "big picture."
•
As you can see, inferential statistics is divided into estimation and hypothesis
testing, and estimation is further divided into point and interval estimation.
Inferential statistics
is defined as the branch of statistics that is used to make inferences
about the characteristics of a
populations based on sample data.
•
The goal is to go beyond the data at hand and make inferences about population
parameters.
•
In order to use inferential statistics, it is assumed that either random selection or
random assignment was carried out (i.e., some form of randomization must is
assumed).
Looking at Table 16.1 (p.464 and shown below) you can see that statisticians use Greek
letters to symbolize population parameters
(i.e., numerical characteristics of populations,
such as means and correlations) and English letters to symbolize sample statistics
(i.e.,
numerical characteristics of samples, such as means and correlations).
For example, we use the Greek letter mu (i.e., μ) to symbolize the population mean
and
the Roman/English letter X with a bar over it,
X
(called X bar), to symbolize the sample
mean
.
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View Full DocumentSampling Distributions
One of the most important concepts in inferential statistics is that of the sampling
distribution. That's because the use of a sampling distributions is what allows us to make
"probability" statements in inferential statistics.
•
A sampling distribution
is defined as "The theoretical probability distribution of
the values of a statistic that results when all possible random samples of a
particular size are drawn from a population." (For simplicity you can view the
idea of "all possible samples" as taking a million random samples. That is, just
view it as taking a whole lot of samples!)
•
A one specific type of sampling distribution is called the sampling distribution of
the mean
. If you wanted to generate this distribution through the laborious process
of doing it by hand (which you would NOT need to do in practice),
you would
randomly select a sample, calculate the mean, randomly select another sample,
calculate the mean, and continue this process until you have calculated the means
for all possible samples. This process will give you a lot of means, and you can
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 Spring '11
 Staff
 Statistics, Null hypothesis, Statistical hypothesis testing, researcher, Statistical significance

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