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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.