Page 50 - Intermediate Statistics for Dummies

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Chapter 1: Beyond Number Crunching: The Art and Science of Data Analysis
Now does this association you found in the data set for this sample of 450
people carry over to the entire population? In order to answer this question,
you need to conduct a hypothesis test. And not just any hypothesis test — a
Chi-square test for independence. You’re testing to see whether the two quali-
tative variables, political affiliation and views on the president, are related or
not. If they are related, the variables are deemed not independent; if they are
unrelated, the variables are independent.
A Chi-square test basically does the following: It figures out the number of
values that you expect to see in each cell of the table if the variables are inde-
pendent (these values are brilliantly called the expected cell counts). The Chi-
square test then compares these expected cell counts to what you actually
saw in the data (called the observed cell counts) and compares them to each
other in a Chi-square statistic (see Chapter 14).
If the Chi-square test statistic is large, you’re likely to find an association
between the two variables, because the total differences are large between
the observed and expected cell counts. In other words, the variables are not 29
independent, and you can look at the observed cell counts to discuss the
relationship you see. If the Chi-square test statistic is small, then you can’t
conclude you’ve found a relationship, and the two variables are independent.
In the case of political affiliation and views on the president, the Chi-square
test statistic is huge, and you conclude a relationship is there somewhere.
You can say that in the population, Republicans tend to support the presi-
dent, Democrats tend to oppose the president, and the Independents are
split down the middle. (You can find the details of how to find the expected
counts and conduct the Chi-square test in Chapter 14.)
You can also use the Chi-square test to see whether your theory about what
percent of each group falls into a certain category is true or not. For example,
can you guess what percentage of M&Ms fall into each color category? More
on these Chi-square variations, as well as the M&Ms question, in Chapter 15.
Nonparametrics
Nonparametrics is an entire area of statistics that provides analysis tech-
niques to use when the conditions for the more traditional and commonly
used methods aren’t met. For example, in order to use a t-test, the data needs
to be collected from a population that has a normal distribution (that is, it
has to have a bell-shaped curve). In order to do a hypothesis test for two
means, the data from each group must be from its own normal population. In
fact, most all of the commonly used data-analysis procedures have condi-
tions that must be met in order to use them.