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# Simple Hypothesis Testing

What you will learn in this chapter:

• How to carry out some basic hypothesis tests
• How to carry out the Student’s t-test
• How to conduct the U-test for non-parametric data
• How to carry out paired tests for parametric and non-parametric data
• How to produce correlation and covariance matrices
• How to carry out a range of correlations tests
• How to test for association using chi-squared
• How to carry out goodness of fit tests

Many statistical analyses are concerned with testing hypotheses. In this chapter you look at methods of testing some simple hypotheses using standard and classic tests. You start by comparing differences between two samples. Then you look at the correlation between two samples, and finally look at tests for association and goodness of fit. Other tests are available in R, but the ones illustrated here will form a good foundation and give you an idea of how R works. Should you require a different test, you will be able to work out how to carry it out for yourself.

# Using the Student’s t-test

The Student’s t-test is a method for comparing two samples; looking at the means to determine if the samples are different. This is a parametric test and the data should be normally distributed. You looked at the distribution of data previously in Chapter 5.

Several versions of the t-test exist, and R can handle these using the t.test() command, which has a variety of options (see Table 6-1), and the test can be pressed into service to deal ...

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