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Chapter 10: Using Significance Tests
Chapter 10
Using Significance Tests
In This Chapter
Understanding estimation statistics
Using the Student t-distribution test functions
Analyzing probabilities and results with the Chi Square functions
When you have data from a population, you can draw a sample and run
your statistical analysis on the sample. You can also run the analysis
on the population itself. Is the mean of the sample data the same as the mean
of the whole population? You can calculate the mean of both the sample and
the population and then know precisely how well the sample represents the
population. Are the two means exact? Off a little bit? How much different?
The problem with this though is that getting the data of the entire population
in the first place isn’t always feasible. On average, how many miles per gallon
does a Toyota Camry get after five years on the road? You cannot answer
this question to an exact degree because it’s impossible to test every Camry
out there.
So instead we infer the answer. Testing a handful, or sample, of Camrys is
certainly possible. Then the mean gas mileage of the sample is used to
represent the mean gas mileage of all five-year-old Camrys. The mean of the
sample group will not necessarily match the mean of the population, but it is
the best value that can be attained.
This type of statistical work is known as estimation, or inferential statistics. In
this chapter, I show you the functions that work with the Student t-distribution,
useful for gaining insight into the unknown population properties. This is the
method of choice when using a small sample, say 30 data points or less.
The tests presented in this chapter deal with probabilities. If the result of a
test — a t-test, for example — falls within a certain probability range, then
the result is said to be significant. Outside that range, the result is considered
nonsignificant. A common rule of thumb is to consider probabilities less than
5 percent, or 0.05, to be significant, but exceptions to this rule exist.
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