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Further Information
Primer of Statistical Tools
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Margin of Error and Confidence Intervals are descriptions of a range of scores that statistically define the probable limits of an aggregated measure. When survey data are reported we frequently hear that the results are accurate at a ± 3% margin of error. A confidence interval is another way of expressing these results, but the important issue is that most measures are not a specific point but a range within which we are certain the results fall. Thus, when one says that two measures a significantly different, one is saying that the two ranges of possible results do not overlap. Since a confidence interval is a direct application of the margin of error, let's begin with it. Calculation of a Margin of Error begins with the standard deviation (SD) and count of the number of data points (N) being used. Using these figures the standard error (SE) is calculated by dividing the standard deviation (SD) by the square root of the number of data points being used. SE = SD / Ö N To find the margin of error the standard error is multiplied by the z-score for the probability of error we are willing to accept. That sounds complicated, and there is some more information about it further down this page. However, it turns out to be fairly easy to implement since there are only a few probabilities which are widely used. The probability of error is the chance that we may be mistaken in concluding a significant difference when there is none. So back to our survey example. If in a survey 45% of respondents say they will vote for Smith and 39% say they will vote for Jones and the margin of error is ± 3%, then we predict that somewhere between 42% and 48% of the voting population will vote for Smith and between 36% and 43% will vote for Jones. Since the two ranges overlap from 42% to 43%, the two numbers (45% and 39%) are not statistically significant in their difference. What is not mentioned is the level of probability of error. In most public survey that probability is 95%, or 5 chances out of 100 that we will make a mistake or error is we conclude that the numbers are different when they occur outside the margin of error. The following table summarizes the most commonly used probabilities of error.
Based on these numbers if we want to be more confident in predicting that one candidate is ahead of the other in a survey, then we would use the 99% confidence interval and apply a 4% margin of error to our results. If we were willing to accept that we might be wrong 10% of the time we would apply the 90% probability of error with ± 2.3%. In this case the lower limit for Smith is 42.7% (45% - 2.3% ) and the upper limit for Jones is 41.3% (39% + 2.3%). In this case the two results are significantly different because we are willing to accept a higher probability of making an error. |
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