According to a well known statistical theorem, the Central Limit theorem, if we were to draw another sample from this same population, and then another and then another until we had drawn a very large number of such samples, and if, from each of those samples, we computed an average value in which we were interested, those average values would distribute themselves around the true average value of the population in a normal, bell-shaped distribution. The measure of the variability of that distribution is called Standard Error and is computed for two different cases by the formulas below. For the first case, which we call an attribute, the formula is: Since we do not know we compute it for the sample and use that value in our computations. The result, again, is an estimate. Because not every respondent will provide a usable response to every question for one reason or another, the value of n will usually be different for each question, leading to a different standard error for each question. Where appropriate, the computer tabulations contain the standard error, which will permit the Corps to make a statement such as the following: "95 times out of 100 the true population statis- Such a statement is possible, because according to the laws of probability, the true value plus or minus the Standard Error will contain the value computed from a given sample, 2 times out of 3, and plus or minus two times the Standard Error will contain the value com The key to knowing whether or not these reliability statements can also reasonably be expected to pertain to the entire population of boat owners lies in knowing something about the 30% non-respondents. At my suggestion, Corps personnel drew a random sample of one-hundred from the non-respondents to each questionnaire and made several attempts to contact each by telephone. The exact results of these efforts are in your hands. Generally speaking, according to the initial analysis, there seems to be no consistent bias among the non-respondents, and if the inferences are drawn according to the instructions which I set forth in my last meeting with the persons in charge of the surveys, the Corps can be quite confident that they will provide a valid basis for making economic analyses of boating for the intended purposes. Obviously, these inferences must be tempered with judgment, because the surveys have discovered what the boating population says it will do, not what it actually does, and we know from experience that what people say they will do is oftentimes different from what they actually do. However, given the kinds of questions which people were asked in these surveys, the subject matter of the surveys, and the care with which the surveys were constructed, considerable reliance on the results seems justified. All-in-all these surveys provide, in my judgment, a sound basis for making decisions with regard to boating in Puget Sound. The very high response rate makes them useful as base-line studies for comparison purposes in future years. They are well-defined, carefully performed, and should prove to be of great benefit to the Corps. |