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Part I: Data Analysis and Model-Building Basics
You use a hypothesis test in situations where you have a certain model in
mind, and you want to see whether that model fits your data. Your model may
be one that just revolves around the population mean (testing whether that
mean is equal to ten, for example). Your model may be testing the slope of a
regression line (whether or not it’s zero, for example, with zero meaning you
find no relationship between x and y). You may be trying to use several differ-
ent variables to predict the marketability of a product, and you believe a model
using customer age, price, and shelf location can help predict it, so you need to
run one or more hypothesis tests to see whether that model works. (This
process is called multiple regression; more info on this in Chapter 5.)
A hypothesis test is made up of two hypotheses:
The null hypothesis (Ho): Ho symbolizes the current situation — the
one that everyone assumed was true until you got involved.
The alternative hypothesis (Ha): Ha represents the alternative model
that you want to consider. It stands for the researcher’s hypothesis, and
the burden of proof lies on the researcher to prove it.
Ho is the model that’s on trial. If you get enough evidence against it, you con-
clude Ha, which is the model you’re claiming is the right one. If you don’t get
enough evidence against Ho, then you can’t say that your model (Ha) is the
right one.
Gathering your evidence
into a test statistic
A test statistic is the statistic from your sample, standardized so you can look
it up on a table, basically. While each hypothesis test is a little different, the
main thought is the same. For whatever model you’re trying to test, you
come up with a statistic that you use to test that model. Take that statistic,
standardize it (take the statistic minus its expected value from Ho and divide
all that by the standard error). Then look up your test statistic on a table to
see where it stands. That table may be the t-table (Table A-1 in the Appendix),
it may be the Chi-square table (Table A-3 in the Appendix), or it may be a dif-
ferent table. The type of test you need to you use on your data dictates which
table you use.
In the case of testing a hypothesis for a population mean, µ, you use the sample
mean, x, as your statistic. To standardize it, you take x and convert it to a
x - µ 0
value of t by using the formula t n 1 = , where µ 0 is the value in Ho. This
- s
n
value is your test statistic. You compare your test statistic to the t-distribution
(check out Table A-1 in the Appendix).