ABSTRACT
Normal Distribution .............................................................................................35 Role in the General Linear Model ..................................................................35 Distributions Growing Up ..............................................................................36 Skewed Distributions.......................................................................................37 GrotesqueAberrations ..................................................................................... 37
Power Law Distributions .....................................................................................40 Fractal Dimensions ...........................................................................................40 Other Similar Distributions ............................................................................42 Interpretation of Dimensions..........................................................................42 Numerical Example .........................................................................................44 Central Limit Theorem ....................................................................................45
Exponential Distributions .................................................................................... 47 Numerical Example .........................................................................................48 Implications for ANOVA Designs ..................................................................48 Complex Exponential Distributions ..............................................................48 Location and Scale ............................................................................................ 49
Structure of Behavioral Measurements ..............................................................50 Error Components ............................................................................................51 Durbin-Watson Statistic ..................................................................................52 BDS Statistic ......................................................................................................54
Linear and Nonlinear Determinism ...................................................................55 Distinguishing Linear and Nonlinear Model Components .......................55 Comparing Linear and Nonlinear Models ...................................................56 Global versus Local Dynamics .......................................................................58
Sample Size ............................................................................................................ 61 Restriction of Topological Range ...................................................................61 Myth of the Million Data Points .....................................................................63
Computational Filtering Techniques ..................................................................63 z-Filtering ...........................................................................................................64 MovingAverages and Medians......................................................................65 Use of Prediction Models ................................................................................65 Singular Value Decomposition ....................................................................... 67
References ............................................................................................................... 69
Biologistsinthenineteenthcenturydiscoveredmanyexamplesofnormally (Gaussian)distributedvariables.Theyaskedmathematicianswhetherthere wassomelawofmathematicsthatexplainedtheprevalenceofnormaldistributions.Themathematiciansrepliedthattheyknewofnosuchlaw,and thatanyexplanationwouldhavetobealawofbiology(Zeeman,1977).One mightquestionwhethernormaldistributionsactuallyexistinrealdata,or whethertheyaresimplyapproximationsthatallowthestatisticalmathematics to become more tractable.
