Page 31 - Statistics II for Dummies

Chapter 1: Beyond Number Crunching: The Art and Science of Data Analysis 15

Hypothesis test

A hypothesis test is a statistical procedure that you use to test an existing
claim about the population, using your data. The claim is noted by Ho (the
null hypothesis). If your data support the claim, you fail to reject Ho. If your
data don’t support the claim, you reject Ho and conclude an alternative
hypothesis, Ha. The reason most people conduct a hypothesis test is not to
merely show that their data support an existing claim, but rather to show
that the existing claim is false, in favor of the alternative hypothesis.

The Pew Research Center studied the percentage of people who turn to ESPN
for their sports news. Its statistics, based on a survey of about 1,000 people,
found that in 2000, 23 percent of people said they go to ESPN; in 2004, only 20
percent reported going to ESPN. The question is this: Does this 3 percent reduc-
tion in viewers from 2000 to 2004 represent a significant trend that ESPN
should worry about?
To test these differences formally, you can set up a hypothesis test. You
set up your null hypothesis as the result you have to believe without your
study, Ho = No difference exists between 2000 and 2004 data for ESPN viewer-
ship. Your alternative hypothesis (Ha) is that a difference is there. To run a
hypothesis test, you look at the difference between your statistic from your
data and the claim that has been already made about the population (in Ho),
and you measure how far apart they are in units of standard deviations.
With respect to the example, using the techniques from Chapter 3, the
hypothesis test shows that 23 percent and 20 percent aren’t far enough apart
in terms of standard deviations to dispute the claim (Ho). You can’t say the
percentage of viewers of ESPN in the entire population changed from 2000 to
2004.

As with any statistical analysis, your conclusions can be wrong just by chance,
because your results are based on sample data, and sample results vary. In
Chapter 3 I discuss the types of errors that can be made in conclusions from a
hypothesis test.

Analysis of variance (ANOVA)

ANOVA is the acronym for analysis of variance. You use ANOVA in situations
where you want to compare the means of more than two populations. For
example, you want to compare the lifetimes of four brands of tires in number
of miles. You take a random sample of 50 tires from each group, for a total of
200 tires, and set up an experiment to compare the lifetime of each tire, and
record it. You have four means and four standard deviations now, one for
each data set.

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