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6.8 Summary
The use of inferential statistics is invaluable in analysis and research. Inferential
statistics allows us to infer characteristics for a population from the data obtained
in a sample. We are often forced to collect sample data because the cost and
time required in measuring the characteristics of a population can be prohibitive.
In addition, inferential statistics provides techniques for quantifying the inherent
uncertainty associated with using samples to specify population characteristics. It
does not eliminate the uncertainty due to sampling, but it can provide a quan-
titative measure for the uncertainty we face about our conclusions for the data
analysis.
Throughout Chap. 6 we have focused on analyses that involve a variety of data
types—categorical, ordinal, interval, and rational. Statistical studies usually involve
a rich variety of data types that must be considered simultaneously to answer our
questions or to investigate our beliefs. To this end, statisticians have developed a
highly structured process of analysis known as tests of hypothesis to formally test
the veracity of a researcher’s beliefs about behavior. A hypothesis and its alterna-
tive are posited and then tested by examining data collected in observational or
experimental studies. We then construct a test to determine if we can reject the null
hypothesis based on the results of the analysis.
Much of this chapter focused on the selection of appropriate analyses to per-
form the tests of hypothesis. We began with the chi-squared test of independence
of variables. This is a relatively simple, but useful, test performed on categor-
ical variables. The z-Test and t-Test expanded our view of data from strictly
categorical, to combinations of categorical and interval data types. Depending on
our knowledge of the populations we are investigating, we execute the appro-
priate test of hypothesis, just as we did in the chi-squared. The t-Test was then
extended to consider more complex situations through ANOVA. Analysis of vari-
ance is a powerful family of techniques for focusing on the effect of independent
variables on some response variable. Finally, we discussed how design of experi-
ments helps reduce ambiguity and confusion in ANOVA by focusing our analyses.
A thoughtful design of experiments can provide an investigator with the tools
for sharply focusing a study, so that the potential of confounding effects can be
reduced.
Although application of these statistics appears to be difficult, it is actually very
straight forward. Table 6.16 below provides a summary of the various tests presented
in this chapter and the rules for rejection of the null hypothesis.
In the next chapter we will begin our discussion of Model Building and
Simulation —these models represent analogs of realistic situations and problems that
we face daily. Our focus will be on what-if models. These models will allow us to
incorporate the complex uncertainty related to important business factors, events,
and outcomes. They will form the basis for rigorous experimentation. Rather than
strictly gather empirical data, as we did in this chapter, we will collect data from our
models that we can submit to statistical analysis. Yet, the analyses will be similar to
the analyses we have performed in this chapter.
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