MAT 2377 Lecture 11: Lecture 11 - Normal Probality Plot.pdf
9 May 2014
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Quantile-quantile plot (qq-plot) and the normal probability plot. Goal : to verify the underlying assumption of normality, we want to compare the distribution of the sample to a normal distribution. Normal population : suppose that the population is normal, i. e. x . X " where z n (0, 1). Hence, there is a linear association between a normal variable and a standard normal random variable. If our sample is randomly selected from a normal population, then we should be able to observer this linear association. Consider a random sample of size n : x1, x2, . We will obtain the order statistics (i. e. order the values in an ascending order) : y1 y2 . We will compare the order statistics (called sample quantiles) to quantiles from a standard normal distribution n (0, 1). We rst need to compute the percentile rank of the ith order statistic.
