Statistics

Two potential sources of error occur in statistical estimation—two reasons a statistic might misrepresent a parameter. Random error occurs as a result of sampling variability. The ten sample means in the preceding section differed from the true population mean because of random error. Some were below the true value; some above it. Similarly, the mean of the distribution of ten sample means was slightly lower than the true population mean. If ten more samples of 100 subscribers were drawn, the mean of that distribution—that is, the mean of those means—might be higher than the population mean.

Systematic error or bias refers to the tendency to consistently underestimate or overestimate a true value. Suppose that your list of magazine subscribers was obtained through a database of information about air travelers. The samples that you would draw from such a list would likely overestimate the population mean of all subscribers' income because lower‐income subscribers are less likely to travel by air and many of them would be unavailable to be selected for the samples. This example would be one of bias.

In Figure 1, both of the dot plots on the right illustrate systematic error (bias). The results from the samples for these two situations do not have a center close to the true population value. Both of the dot plots on the left have centers close to the true population value.

Figure 1.Random (sampling) error and systematic error (bias) distort the estimation of population parameters from sample statistics.