Transcript 7.4

Chapter 7
Section 4
Assessing
Normality
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 7 Section 4 – Slide 1 of 11
Chapter 7 – Section 4
● Learning objectives
1

Draw normal probability plots to assess normality
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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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 7 Section 4 – Slide 3 of 11
Chapter 7 – Section 4
● The main method used to assess whether
sample data is approximately normal is the
normal probability plot
● This plot graphs the observed data, ranked in
ascending order, against the “expected” Z-score
of that rank
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 7 Section 4 – Slide 4 of 11
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)
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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
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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
● 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
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Chapter 7 – Section 4
● The two plots below are for the data in Table 6
 One using MINITAB (from the text)
 One using StatCrunch (the axes are switched)
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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
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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
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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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 7 Section 4 – Slide 11 of 11
Example: Chapter 7 – Section 4
● Would this be approximately normal?
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Example: Chapter 7 – Section 4
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Example: Chapter 7 – Section 4
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