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handout_1_3_normal_quantile

handout_1_3_normal_quantile - Normal Quantile Plots Normal...

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Normal Quantile Plots Normal quantile plots are used to determine whether or not data distributions are normal. Constructing a normal quantile plot 1. Arrange the observed data values from smallest to largest. Record what percentile of the data each value occupies. Suppose, for example, that the 10 th percentile test score is 60. 2. Do normal distribution calculations to find the z -scores at these same percentiles. For example, z = -1.282 is the 10% point of the standard normal distribution. z -score -1.282 -0.842 -0.524 -0.253 0 0.253 0.524 0.842 1.282 percentile 10% 20% 30% 40% 50% 60% 70% 80% 90% 3. The variable of interest we call x . Plot each data point x (on y axis) against the corresponding z (on x axis). For example, the 10 th percentile test score (60) is plotted against the 10 th percentile z -score (- 1.282). This is done for all of the observations in the data set. • If the data distribution is close to normal , the plotted points will lie close to some straight line. •If the data distribution is close to standard normal , the plotted points will lie close to the 45- degree line.
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