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Chapter 7 Section 4

Chapter 7 Section 4. Assessing Normality. 1. Chapter 7 – Section 4. Learning objectives Draw normal probability plots to assess normality. Chapter 7 – Section 4.

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Chapter 7 Section 4

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  1. Chapter 7Section 4 Assessing Normality

  2. 1 Chapter 7 – Section 4 • Learning objectives • Draw normal probability plots to assess normality

  3. Chapter 7 – Section 4 • Many real world variables have bell shaped histograms, so we would say that they should or could have normal probability distributions • We need methods to assess whether this is a good assumption or not

  4. Chapter 7 – Section 4 • The main method used to assess whether sample data is approximately normal is the normalprobabilityplot • This plot graphs the observed data, ranked in ascending order, against the “expected” Z-score of that rank

  5. Chapter 7 – Section 4 • The chart compares • The lowest observed value with where it is expected to be (according to the normal) • The second lowest observed value with where it is expected to be (according to the normal) • Etc. • The highest observed value with where it is expected to be (according to the normal)

  6. Chapter 7 – Section 4 • The expected lowest value, the expected second lowest value, etc. are not easy to derive • Technology should be used to construct these graphs • If the sample data was taken from a normal random variable, then this plot should be approximately linear

  7. Chapter 7 – Section 4 • Excel • The PHStat add-in to Excel includes this plot • It is also an option under the Regression package, but the axes are linear percents (unlike MINITAB and StatCrunch) … that can be changed manually • Excel • The PHStat add-in to Excel includes this plot • It is also an option under the Regression package, but the axes are linear percents (unlike MINITAB and StatCrunch) … that can be changed manually • StatCrunch • The option Graph – QQ Plot in StatCrunch creates normal probability plots (also called QQ plots) • The StatCrunch axes are switched compared to the MINITAB axes

  8. Chapter 7 – Section 4 • The two plots below are for the data in Table 6 • One using MINITAB (from the text) • The two plots below are for the data in Table 6 • One using MINITAB (from the text) • One using StatCrunch (the axes are switched)

  9. Chapter 7 – Section 4 • Both of these show that this particular data set is far from having a normal distribution • It is actually considerably skewed right

  10. Chapter 7 – Section 4 • The plot below is from Excel’s Data Analysis – Regression package, with the horizontal axes modified to be normal quantiles instead of linear percents

  11. Summary: Chapter 7 – Section 4 • We can assess whether sample data is approximately normal by using the normal probability plot • If the data is approximately normal, then the normal probability plot (a.k.a. the QQ plot) should be approximately normal also

  12. Example: Chapter 7 – Section 4 • Would this be approximately normal?

  13. Example: Chapter 7 – Section 4

  14. Example: Chapter 7 – Section 4

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