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"A Margin of Error of."This phrase took flight during the last federal election campaign, which was steered on the basis of survey polls conducted in wholesale lots across the country. It is popular again while Ontario's PC politicians jockey during their present leadership campaign. (The Alliance Party seems to have better than marginal errors.) Great quantities of polling figures are being published, and the end sentence invariably reads something like "This has a Margin of Error of 4 percentage points 19 times out 20."
A Margin of Error of 4 percent I understand; that means the figure quoted would be considered correct, even if it varied either way by 4 percent. (Why wasn't I allowed that kind of leeway when my examinations were marked in school?) It is the "19 times out of 20 " that has me stymied. What of or where is the missing "1 time out of 20 "? Surely the supposedly mathematically precise statisticians aren't going to let a "1 time out of 20" wander around unbeknown. I am worried about the consequences from that loose digit hovering about.
There is another concern; the ready acceptance of a Margin of Error. Is nothing accurate? Must we accept such indecisiveness in an answer? Have the pollsters caught the evasiveness of the politicians they are measuring?
Consider swooping across Toronto on Highway 401 in a dozen lanes of traffic, cars in front, trucks behind, buses to the left and an idiot talking on a cell phone while driving on the right. I would estimate that the margin of error in that situation is about 3 feet plus or minus a hiccup. Now, where is the "1 time out of 20"? How can I spot him or her? Of the 20 vehicles swooping around me, which is he or she? See the basis of my concern about that loose 20th being unaccounted for?
Some Margins of Error are so accurately calculated that they seem not to exist. Surfing one evening, I came across the statistic that the average Canadian marriage lasts for 12 years. There are some marriages which last longer, some which seem to last longer, and some are shorter. Average I can understand; add all the years up, divide by the number of marriages, and there is the average - not a real brain teaser calculation. In this particular report, there was no mention of plus or minus a percentage or of the 19 times out of 20. Is there no Margin of Error in marriage? Hardly, or we wouldn't have the excessive divorce rate we have. There is hope of achieving the 19 times out of 20 in some marriages: I know of several individuals who are well on the way.
These are only 2 examples of the importance of mathematical accuracy. One 'Margin of Error', while tearing through the big city, can be destructive if it kicks in at the wrong time in the wrong place, a situation that explains many of the accidents and homicides in the greater Toronto area. On the other hand, the 'Margin of Error' during the courting process is creative; some of us owe our very existence to a miscalculation of it many years ago.
I wish these heavy thinkers would get together and standardize their product. No trouble with the real basics; 2 and 2 are 4, either by adding or multiplying, but from then on it gets confusing. They talk of the whole being more than the sum of its parts; squares and hypotenuses being related; results being partially accurate only 19 times out of 20; and in addition having a 'Margin of Error' to play with. No wonder our kids complain about the wonderful world of mathematics.
