The Media’s Error on the Margin of Error of Polls

               The media usually reports polls in a number of erroneous or misleading ways.  One of the most common regards the margin of error.  I shall examine the other errors and misleading expressions in future posts.

               The margin of error is the statistical degree of deviation, usually based upon at least a 95% degree of confidence.  The margin is determined by the sample size, as is the degree of confidence.  The larger the sample size, the lower the margin of error and the higher the degree of confidence.

               The margin of error refers to each figure of results in a poll, not the difference between the two figures, as the media erroneously reports it.  Thus, the results may represent a statistical tie, even though the difference between two results in a poll may be greater than the margin of error for the total sample.

               For example, if Candidate A’s result is that he is favored by 49% of those polled and Candidate B by 44% and the margin of error is plus or minus 3%, then their race is within the margin of error.  Candidate A’s result is plus or minus 3% of 49% (i.e. 46%-52%) while Candidate B is plus or minus 3% of 44% (41-47%).  Because the ranges for Candidates A and B overlap (i.e. Candidate A’s lowest possible low is lower than Candidate B’s highest possible high), their race is a dead heat.  The media would therefore be wrong to report the result of such a poll as “outside the margin of error.”

               Note: A poll of polls using the same type of polling sample should produce a margin of error and a degree of confidence commensurate with the total number polled.  For example, the results of a poll of 300 registered voters and a margin of error of plus or minus 5% should not be averaged with a poll of 1,000 likely voters and a margin of error of plus or minus 3%.  Not only are the polling samples different, but even if they were the same, a new margin of error and degree of confidence should be calculated based upon the combined results and then the combined total could be reported instead of averaging the results of the two polls as if they are of equal weight, margin of error and degree of confidence.  In other words, averages of the results of polls are inaccurate because they do not take into account these factors.  Instead, the results using similar polling samples should be combined and weighted as if they were one poll.