3.82.       

Can dowsers really detect water? The act of search- ing for and finding underground supplies of water with the use of a divining rod is commonly known as ‘‘dowsing.’’ Although widely regarded among sci- entists as a superstition, dowsing remains popular in folklore, and to this day there are individuals who claim to have this skill. A  group  of Ger- man physicists conducted a series of experiments to test the dowsing claim. A source of water was hidden in a random location along a straight line in a Munich barn, then each of 500 self-claimed dowsers was asked to indicate the exact location of the source (measured in decimeters from the beginning of the line). Based on the data collected for three (of the participating 500) dowsers who had particularly impressive results, the German physicists concluded that dowsing ‘‘can be regarded

Source: Enright, J.T. ‘‘Testing dowsing: The failure of the Munich experiments,’’ Skeptical Inquirer, Jan./Feb. 1999, p. 45 (Figure 6a). Used by permission of Skeptical Inquirer.

as empirically proven.’’ All three of these ‘‘best’’ dowsers (numbered 99, 18, and 108) performed the experiment multiple times and the best test series (sequence of trials) for each of these three dowsers was identified. These data are listed in the accompanying table. The conclusion of the German physicists was critically assessed and rebut- ted by Professor  J.T.  Enright  of  the University of California– San Diego (Skeptical Inquirer, Jan- uary/February 1999). Enright applied simple linear regression to conclude the exact opposite of the German physicists.

(a)    Let x = dowser’s guess and y = pipe location for each trial. Graph the data. Do you  detect a trend?

(b)    Fit the straight-line model, E(y) = β0 + β1x, to the data. Interpret the estimated y-intercept of the line.

(c)    Is there evidence that the model is statisti- cally useful for predicting actual pipe loca- tion? Explain.

to this phenomenon as ‘‘the SOB effect.’’) The UFF based its conclusions on a simple linear regres- sion analysis of the data in the next table,   where y = administrator’s raise and x = average rating of administrator.

∗ UFF Faculty Forum, University of South Florida Chapter, Vol. 3, No. 5, May   1991.

Source: aFaculty and A&P Salary Report, University of South Florida, Resource Analysis and Planning, 1990. bAdministrative Compensation Survey, Chronicle of Higher Education, Jan. 1991.

reason was given for removing this data point from the analysis.) Perform the simple   linear

regression analysis using the remaining 14 data points in the table. Is there evidence to sup- port the UFF’s claim of an inverse relationship between raise and rating?

(c)    Based on the results of the regression, part b, the UFF computed estimated raises for selected faculty ratings of administrators. These are shown in the following table. What problems do you perceive with using this table to esti- mate administrators’ raises at the University of South Florida?

(d)   

The ratings of administrators listed in this table were determined by surveying the faculty at the University of South Florida. All faculty are mailed the survey each year, but the response rate is typically low (approximately 10 – 20%). The danger with such a survey is that only dis- gruntled faculty, who are more apt to give a low rating to an administrator, will respond. Many of the faculty also believe that they are under- paid and that the administrators are overpaid. Comment on how such a survey could bias the results shown here.

(e)    Based on your answers to the previous ques- tions, would you support the UFF’s claim?

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