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
Sullivan – Fundamentals of Statistics – 2nd Edition – Chapter 7 Section 4 – Slide 7 of 11
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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