STAT3012 Lecture Notes - Lecture 20: Test Statistic, Null Hypothesis, Weight Function
23 Jun 2018
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Lecture 20 – Assessing normality
New concepts
✷Pearson’s chi-squared test
✷Goodness of fit tests based on the empirical distribution function
✷Kolmogorov-Smirnov test, Cramer-von Mises test, Anderson-Darling test
✷R-package nortest
✷Shapiro-Wilk test, Shapiro-Francia test
✷Monte-Carlo p-values
Applied Linear Models: Lecture 20 1
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find more resources at oneclass.com
New topic – Assessing normality
✷So far we only ever assessed the normality assumption by inspection of Q-Q
plots.
✷When is it clear that the normality assumption is wrong?
✷Can you think of any normality tests?
Applied Linear Models: Lecture 20 2
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find more resources at oneclass.com
Theory – Data and testing problem
Given a data set x= (x1, x2, . . . , xn)we want to test if there is evidence against
assuming that the data is a sample from a N(µ, σ2)population.
Example – Six pseudo-random samples of size n= 64
set.seed(1)
n<- 64
e.1 <- rnorm(n, 0,1)
e.2 <- rnorm(n, 0,1)
e.3 <- rnorm(n, 0,1)
e.4 <- rexp(n) -1
e.5 <- 4*runif(n, 0,1)-2
e.6 <- rchisq(n, 1)-1
Applied Linear Models: Lecture 20 3
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find more resources at oneclass.com
Document Summary
Goodness of t tests based on the empirical distribution function. Kolmogorov-smirnov test, cramer-von mises test, anderson-darling test. So far we only ever assessed the normality assumption by inspection of q-q plots. Given a data set x = (x1, x2, . , xn) we want to test if there is evidence against assuming that the data is a sample from a n ( , 2) population. N(0,1) s1 s e l i t n a u. 1 s e l i t n a u. Chisq(1) 1 s e l i t n a u. 2 s e l i t n a u. First calculate the sample mean, x, and the sample variance, s2. Form a grouped frequency table summary of the data with say at most g =( n/5 n 50. To check the normal claim work out the expected frequencies (ei) for each category by tting n (x, s2).
