Making Science Make Sense

Bayer Facts of Science Education Survey

Sampling Tolerances

In interpreting survey results, it should be borne in mind that all sample surveys are subject to sampling error, that is, the extent to which the results may differ from what would be obtained if the whole population had been interviewed. The size of such sampling errors depends largely on the number of interviews.

The following tables may be used in estimating the sampling error of any percentage in this report. The computed allowances have taken into account the effect of the sample design upon sampling error. They may be interpreted as indicating the range (plus or minus the figure shown) within which the results of repeated samplings in the same time period could be expected to vary, 95 percent of the time, assuming the same sampling procedures, the same interviewers, and the same questionnaire.

The first table shows how much allowance should be made for the sampling error of a percentage:

* THE CHANCES ARE 95 IN 100 THAT THE SAMPLING ERROR IS NOT LARGER THAN THE FIGURE SHOWN.

The table would be used in the following manner: Let us say a reported percentage is 33 for a group which includes 1000 respondents. Then we go to row "percentages near 30" in the table and go across to the column headed "1000". The number at this point is 3, which means that the 33 percent obtained in the sample is subject to a sampling error of plus or minus 3 points. Another way of saying it is that very probably (95 chances of 100) the true figure would be somewhere between 30 and 36, with the most likely figure the 33 obtained.

In comparing survey results in two samples, such as, for example, men and women, the question arises as to how large a difference between them must be before one can be reasonably sure that it reflects a real difference. In the tables below, the number of points which must be allowed for in such comparisons is indicated.

Two tables are provided. One is for percentages near 20 or 80; the other for percentages near 50. For percentages in between, the error to be allowed for is between those shown in the two tables.