Page 212 - Statistics for Dummies

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Following are the general steps for estimating a parameter with a confidence
interval. Details on Steps 1 and 4–6 are included throughout the remainder of
this chapter. Steps 2 and 3 involve sampling and data collection, which are
detailed in Chapter 16 (sampling and survey data collection) and Chapter 17
(data collection from experiments).
1. Choose your confidence level and your sample size.
2. Select a random sample of individuals from the population.
Part IV: Guesstimating and Hypothesizing with Confidence
3. Collect reliable and relevant data from the individuals in the sample.
4. Summarize the data into a statistic, such as a mean or proportion.
5. Calculate the margin of error.
6. Take the statistic plus or minus the margin of error to get your final
estimate of the parameter.
This step calculates the confidence interval for that parameter.
Interpreting Results with Confidence

Suppose you, a research biologist, are trying to catch a fish using a hand
net, and the size of your net represents the margin of error of a confidence
interval. Now say your confidence level is 95%. What does this really mean?
It means that if you scoop this particular net into the water over and over
again, you’ll catch a fish 95% of the time. Catching a fish here means your
confidence interval was correct and contains the true parameter (in this case
the parameter is represented by the fish itself).

But does this mean that on any given try you have a 95% chance of catching
a fish after the fact? No. Is this confusing? It certainly is. Here’s the scoop
(no pun intended): On a single try, say you close your eyes before you scoop
your net into the water. At this point, your chances of catching a fish are 95%.
But then go ahead and scoop your net through the water with your eyes still
closed. After that’s done, however, you open your eyes and see one of only
two possible outcomes; you either caught a fish or you didn’t; probability
isn’t involved anymore.

Likewise, after data have been collected, and the confidence interval has been
calculated, you either captured the true population parameter or you didn’t.
So you’re not saying you’re 95% confident that the parameter is in your par-
ticular interval. What you are 95% confident about is the process by which
random samples are selected and confidence intervals are created. (That is,
95% of the time in the long run, you’ll catch a fish.)

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