Page 198 - Statistics for Dummies
P. 198

182
                                         Part IV: Guesstimating and Hypothesizing with Confidence
                                                    how the sample of selected individuals felt about the issue; they don’t reflect
                                                    how the entire population may have felt, had they all been asked. The margin
                                                    of error helps you estimate how close you are to the truth about the popula-
                                                    tion based on your sample data.
                                                   Results based on a sample won’t be exactly the same as what you would’ve
                                                    found for the entire population, because when you take a sample, you don’t
                                                    get information from everyone in the population. However, if the study is done
                                                    right (see Chapters 16 and 17 for more about designing good studies), the
                                                    results from the sample should be close to and representative of the actual
                                                    values for the entire population, with a high level of confidence.
                                                    The MOE doesn’t mean someone made a mistake; all it means is that you
                                                    didn’t get to sample everybody in the population, so you expect your sample
                                                    results to vary from that population by a certain amount. In other words, you
                                                    acknowledge that your results will change with subsequent samples and are
                                                    only accurate to within a certain range — which can be calculated using the
                                                    margin of error.
                                                    Consider one example of the type of survey conducted by some of the lead-
                                                    ing polling organizations, such as the Gallup Organization. Suppose its latest
                                                    poll sampled 1,000 people from the United States, and the results show that
                                                    520 people (52%) think the president is doing a good job, compared to 48%
                                                    who don’t think so. Suppose Gallup reports that this survey had a margin of
                                                    error of plus or minus 3%. Now, you know that the majority (more than 50%)
                                                    of the people in this sample approve of the president, but can you say that
                                                    the majority of all Americans approve of the president? In this case, you can’t.
                                                    Why not?
                                                    You need to include the margin of error (in this case, 3%) in your results.
                                                    If 52% of those sampled approve of the president, you can expect that the
                                                    percent of the population of all Americans who approve of the president will
                                                    be 52%, plus or minus 3%. Therefore, between 49% and 55% of all Americans
                                                    approve of the president. That’s as close as you can get with your sample of
                                                    1,000. But notice that 49%, the lower end of this range, represents a minor-
                                                    ity, because it’s less than 50%. So you really can’t say that a majority of the
                                                    American people support the president, based on this sample. You can only
                                                    say you’re confident that between 49% and 55% of all Americans support the
                                                    president, which may or may not be a majority.
                                                    Think about the sample size for a moment. Isn’t it interesting that a sample
                                                    of only 1,000 Americans out of a population of well over 310,000,000 can lead
                                                    you to be within plus or minus only 3% on your survey results? That’s incred-
                                                    ible! That means for large populations you only need to sample a tiny portion
                                                    of the total to get close to the true value (assuming, as always, that you have
                                                    good data). Statistics is indeed a powerful tool for finding out how people feel
                                                    about issues, which is probably why so many people conduct surveys and
                                                    why you’re so often bothered to respond to them as well.




                                                                                                                           3/25/11   8:15 PM
                             19_9780470911082-ch12.indd   182                                                              3/25/11   8:15 PM
                             19_9780470911082-ch12.indd   182
   193   194   195   196   197   198   199   200   201   202   203