Psychology 202a Advanced Psychological Statistics September 15, 2015 The plan for today • • • • Descriptive statistic for kurtosis. Linear transformations (cont.). Models. Conditional distributions. Numerical assessment of kurtosis • fourth moment: x M 3(n 1) n(n 1) 4 (n 1)( n 2)( n 3) s (n 2)( n 3) 4 • bad idea except in very large data sets 2 Changes in mean and sd under linear transformation • • • • • • Linear transformation: Y = a + bX New mean = a + b(old mean) New sd = b(old sd) Special case: the Z score Income example Nonlinear transformations Models • What is a model? • Example: estimating lumber yield • Why are models useful? – Models allow us to clarify what interests us. – Confining our attention to those interests helps us see structure. – But danger lurks in those details that we ignore.