A clear description of the meaning of margin of error (sampling error)

When researchers gather data for statistical analysis, there is always some slippage, by which I mean that the results would likely vary within a calculable range if the researchers duplicated the study. Statisticians refer to that variability of results as margin of error or sampling error. Here is a good description of that flux from a recent survey. “The margin of sampling error at the 95% level of confidence is ±4.6 for total lawyers (N=455) and ±9.8 for total students (N=100). This means that if we were to replicate the study, we would expect to get the same results (within 4.6 percentage points for lawyers and 9.8 percentage points for students) 95 times out of 100.” Thus, for example, if 30 percent of the lawyers said they were underpaid, only five percent of the time if a similar survey were conducted over and over would the result be lower than 25.4 percent or higher than 34.6 percent.

All statistical survey findings should explain their margin of error so that those who use the findings can determine their degree of reliability. Smaller samples for the most part have larger margins of error (See my post of Dec. 9, 2005: margin of error and sample size; Aug. 29, 2006: margin of error and subgroups; Aug. 30, 2006; sampling error; April 22, 2007: sampling error; Oct. 31, 2007: formula for margin of error and benchmarks; Feb. 7, 2008: margin of error of a group, yl√n = 4xl√16 = x; and Jan. 11, 2011: synthetic indices and margins of error.).

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