Lecture 6 Notes

0 05 00 05 10 theoretical quantiles sta102bme102 colin

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Unformatted text preview: n Rundel) Lec 6 February 5, 2013 5 / 23 Sta102/BME102 (Colin Rundel) Evaluating nearly normalness Lec 6 February 5, 2013 6 / 23 Evaluating nearly normalness Normal probability plot and skewness Fat tails Normal Q−Q Plot Sample Quantiles 0.15 q Sta102/BME102 (Colin Rundel) Lec 6 February 5, 2013 7 / 23 0.05 0 Long/Fat Tails - A curve which starts below the normal line, bends to follow it, and ends above it indicates long tails. That is, you are seeing more variance than you would expect in a normal distribution, i.e. wider than expected. q q q qq −5 0.00 Short/Skinny Tails - An S shaped-curve indicates shorter than normal tails, i.e. narrower than expected. q qq q q qq qq qq qq q q q q q q qq qq q qq qq qq qq qq q qq qqq qqq qqq qqq qq q q q qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qqq qq qq qq qq qq qq qq qq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq q q q q qq qq qq qq qqq qqq qqq qqq qqq qqq qq qq qq qq qq qq qq qq qq qq qq qq qq qqq qqq qqq qqq qq qqq qq qq qq qqq qq qq qqq qq qq qq qq qqq qq q qq qqq 0.10 Left Skew - If the plotted points bend down and to the right of the normal line that indicates a long tail to the left. 5 10 0.25 0.30 q 0.20 Right Skew - If the plotted points appear to bend up and to the left of the normal line that indicates a long tail to the right. −5 0 5 10 q −3 −2 −1 0 1 2 3 Theoretical Quantiles Best to think about what is happening with the most extreme values here the biggest values are bigger than we would expect and the smallest values are smaller than we would expect (for a normal). Sta102/BME102 (Colin Rundel) Lec 6 February 5, 2013 8 / 23 Evaluating nearly normalness Evaluating nearly normalness Skinny tails Right Skew −2 −1 0 1 −3 −2 −1 0 1 2 10 q 0.5 q qq q 0.4 8 q q q 3 6 2 4 0.2 0.3 Sample Quantiles q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq qq qq q q q q q q qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq qqq q q q q qqq qqq qqqq qqqq qqqq qqqqq qqqqq qqqqq qqqqq qqqqq q qqq qqq qqqq qqqqqqqq qqqqqq qq q qqqqqqqqqq q q qq qqqqqqqqq 0 0 2 4 6 8 10 q −3 −2 −1 Theoretical Quantiles Lec 6 0 1 2 3 Theoretical Quantiles Here the biggest values are smaller than we would expect and the smallest values are bigger than we would expect. Sta102/BME102 (Colin Rundel) q q q 0.1 0.0 −0.5 q 2 Normal Q−Q Plot qq q q qq q qq qq qq qq qq q q qq qq q q...
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