An analysis of variance model is recommended for data which display a peaked trend. This type of data is particularly common in psychological studies of stimulus generalization. The model consists of quadradic polynomial segments which are constrained to meet in a peak at a predetermined value of the quantitative independent variable. A variety of hypotheses are suggested and the testing of these hypotheses is illustrated with some data contrived to be consistent with results from a published article.
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References
1.
Bogartz, R. S.A least squares method for fitting intercepting line segments to a set of data points. Psychological Bulletin, 1968, 70, 749-755.
2.
Bogartz, R. S.Least squares methods for locating function and disturbance regions. Psychological Bulletin, 1971, 75, 294-296.
3.
Bookstein, F. L.On a form of piecewise linear regression. The American Statistician, 1975 , 29, 116-117.
4.
Dixon, W. J. (Ed.) Biomedical computer programs, X-series supplement. U.C.L.A.: University of California Press, 1970.
5.
Draper, N. R. and Smith, H.Applied regression analysis. New York : John Wiley and Sons, 1966.
6.
Francis, I.A comparison of several analysis of variance programs. Journal of the A merican Statistical Association, 1973, 68, 860-865.
7.
Hudson, D. J.Fitting segmented curves whose join points have to be estimated. Journal of the American Statistical Association, 1966, 61, 1097-1129.
8.
Kimble, G. A.Hilgard and Marquis' conditioning and learning. New York: Appleton-Century-Crofts , 1961.
9.
Kirk, R. E.Experimental design: Procedures for the behavioral sciences. Monterey, Calif.: Brooks/Cole, 1968.
10.
Quandt, R. E.The estimation of the parameters of a linear regression system obeying two separate regimes. Journal of the American Statistical Association, 1958, 53, 873-880.
11.
Robinson, D. E.Estimates for the points of intersection of two polynomial regressions. Journal of the American Statistical Association, 1964, 59, 214-224.
12.
Searle, S. R.Linear models. New York: Wiley, 1971.
13.
Thomas, D. R. and DeCapito, A.Role of stimulus labeling in stimulus generalization . Journal of Experimental Psychology, 1966 , 71, 913-915.
14.
Timm, N. H.Multivariate analysis with applications in education and psychology. Monterey, California: Brooks/Cole, 1975.
15.
Winer, B. J.Statistical principles in experimental design. (2nd ed.) New York: McGraw-Hill, 1971.
