Page 34 - Statistics for Dummies

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Part I: Vital Statistics about Statistics
But no one can give you a single-number result and claim it’s an accurate esti-
mate of the entire population unless he collected data on every single member
of the population. For example, you may hear that 60 percent of the American
people support the president’s approach to healthcare, but you know they
didn’t ask you, so how could they have asked everybody? And since they didn’t
ask everybody, you know that a one-number answer isn’t going to cut it.
What’s really happening is that data is collected on a sample from the popula-
tion (for example, the Gallup Organization calls 2,500 people at random), the
results from that sample are analyzed, and conclusions are made regarding the
entire population (for example, all Americans) based on those sample results.
The bottom line is, sample results vary from sample to sample, and this
amount of variability needs to be reported (but it often isn’t). The statis-
tic used to measure and report the level of precision in someone’s sample
results is called the margin of error. In this context, the word error doesn’t
mean a mistake was made; it just means that because you didn’t sample the
entire population, a gap will exist between your results and the actual value
you are trying to estimate for the population.
For example, someone finds that 60% of the 1,200 people surveyed support
the president’s approach to healthcare and reports the results with a margin
of error of plus or minus 2%. This final result, in which you present your find-
ings as a range of likely values between 58% and 62%, is called a confidence
interval.
Everyone is exposed to results including a margin of error and confidence
intervals, and with today’s data explosion, many people are also using them
in the workplace. Be sure you know what factors affect margin of error (like
sample size) and what the makings of a good confidence interval are and how
to spot them. You should also be able to find your own confidence intervals
when you need to.
In Chapter 12, you find out everything you need to know about the margin
of error: All the components of it, what it does and doesn’t measure, and
how to calculate it for a number of situations. Chapter 13 takes you step by
step through the formulas, calculations, and interpretations of confidence
intervals for a population mean, population proportion, and the difference
between two means and proportions.
Hypothesis tests
One main staple of research studies is called hypothesis testing. A hypothesis
test is a technique for using data to validate or invalidate a claim about a

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