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: 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 puted from a given sample 95 times out of 100. The figure below illustrates the point: Cases or persons minus 2 Standard Errors Standard Error true average value or % -Variable Units or % Plus 2 Standard Errors 95 times out of 100 this area will contain the average value for the percent computed from a given sample. 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. The Pleasure Boating Study, a comprehensive report on recreational salt water boating in Puget Sound and the Strait of Juan de Fuca, provides information on present and future boating patterns in the study area. Basic information on present boating patterns was developed from a questionnaire survey made from a sample of Coast Guard Registered boat owners. The survey, sent to a randomly selected group of 1600 boat owners in the Puget Sound Region, was designed so that its results would be applicable to all boat owners in the Puget Sound Study area. The worth of the questionnaire may be measured, in part, by comparing some of its findings with known information. For this reason several questions were included in the questionnaire to which the answers were already known. The results of these questions and the comparisons with known data are contained in the following text. Verification 1. Boating Season-The boating season by percentage of boat owners using their craft for recreational purposes during different months of the year has been defined in previous Corps of Engineer survey reports for individual small boat projects. The following table gives the results of the present questionnaire survey and other surveys. These data indicate that respondents to the questionnaire use their boats during a particular season in a manner similar to that used by respondents to other surveys. Although some percentages are higher than and some are lower than the questionnaire data, the general month to month trend is the same for all studies. The pleasure boat questionnaire is a composite of several areas such as those mentioned above, and due to its composite nature would not be expected to be identical to any of the other studies. 2. Classification of pleasure boats-Types of pleasure boats in various classifications have been defined in other regional studies as well as nationally. Tabulated below are the questionnaire findings for the Puget Sound study area in comparison with national figures from Boating 1966, A Statistical Report on America's Top Family Sport" by the National Association of Engine and Boat Manufacturers (NAEBM) and The Marketing Department of the Boating Industry Association. Also presented are regional figures from the Recreational Boating Study, Strait of Georgia Area by N. D. Lea and Associates. |