Departures from Normality Departures from Normality Many - - PowerPoint PPT Presentation

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Departures from Normality Departures from Normality Many - - PowerPoint PPT Presentation

Dec 15, 2023 161 likes •523 views

Departures from Normality Departures from Normality Many statistical test depend on our population being normally distributed. Departures from Normality Many statistical test depend on our population being normally distributed.

slide-1
SLIDE 1

Departures from Normality

slide-2
SLIDE 2

Departures from Normality

  • Many statistical test depend on our population being

normally distributed.

slide-3
SLIDE 3

Departures from Normality

  • Many statistical test depend on our population being

normally distributed.

slide-4
SLIDE 4

Departures from Normality

  • Many statistical test depend on our population being

normally distributed.

  • How do we test if our population is normally

distributed?

slide-5
SLIDE 5

Departures from Normality

  • Many statistical test depend on our population being

normally distributed.

  • How do we test if our population is normally

distributed?

  • compare mean and median
slide-6
SLIDE 6

Departures from Normality

  • Many statistical test depend on our population being

normally distributed.

  • How do we test if our population is normally

distributed?

  • compare mean and median
  • graphically
slide-7
SLIDE 7

Departures from Normality

  • Many statistical test depend on our population being

normally distributed.

  • How do we test if our population is normally

distributed?

  • compare mean and median
  • graphically
  • goodness of fit (Shapiro-Wilk Hypothesis test)
slide-8
SLIDE 8

Departures from Normality

  • Many statistical test depend on our population being

normally distributed.

  • How do we test if our population is normally

distributed?

  • compare mean and median
  • graphically
  • goodness of fit (Shapiro-Wilk Hypothesis test)
  • using symmetry and kurtosis hypothesis testing
slide-9
SLIDE 9

Departures from Normality

  • Many statistical test depend on our population being

normally distributed.

  • How do we test if our population is normally

distributed?

  • compare mean and median
  • graphically
  • goodness of fit (Shapiro-Wilk Hypothesis test)
  • using symmetry and kurtosis hypothesis testing
slide-10
SLIDE 10

Departures from Normality

  • Many statistical test depend on our population being

normally distributed.

  • How do we test if our population is normally

distributed?

  • compare mean and median
  • graphically
  • goodness of fit (Shapiro-Wilk Hypothesis test)
  • using symmetry and kurtosis hypothesis testing
  • What do we do if our data are not normally distributed,

but are Abby Normal?

slide-11
SLIDE 11

Departures from Normality

  • Many statistical test depend on our population being

normally distributed.

  • How do we test if our population is normally

distributed?

  • compare mean and median
  • graphically
  • goodness of fit (Shapiro-Wilk Hypothesis test)
  • using symmetry and kurtosis hypothesis testing
  • What do we do if our data are not normally distributed,

but are Abby Normal?

slide-12
SLIDE 12

Departures from Normality

  • Many statistical test depend on our population being

normally distributed.

  • How do we test if our population is normally

distributed?

  • compare mean and median
  • graphically
  • goodness of fit (Shapiro-Wilk Hypothesis test)
  • using symmetry and kurtosis hypothesis testing
  • What do we do if our data are not normally distributed,

but are Abby Normal?

  • Transformations
slide-13
SLIDE 13

Departures from Normality

  • Many statistical test depend on our population being

normally distributed.

  • How do we test if our population is normally

distributed?

  • compare mean and median
  • graphically
  • goodness of fit (Shapiro-Wilk Hypothesis test)
  • using symmetry and kurtosis hypothesis testing
  • What do we do if our data are not normally distributed,

but are Abby Normal?

  • Transformations
  • Non-parametric tests (coming later)
slide-14
SLIDE 14

Non-Normal Data

50 100 Count 1 2 3 4 5 6 7 8 Tail Length (cm)

Skewed Right (Positively)

20 40 60 80 100 Count 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Toe Length (cm)

Skewed Left (Negatively) Skewness

slide-15
SLIDE 15

Non-Normal Data

50 100 Count 1 2 3 4 5 6 7 8 Tail Length (cm)

Skewed Right (Positively)

20 40 60 80 100 Count 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Toe Length (cm)

Skewed Left (Negatively) Skewness Platykurtic (flaty) Leptokurtic

  • 3
  • 2
  • 1

1 2 3

  • 2.33

10 20 30 40 50 60 70 80 90

Kurtosis

slide-16
SLIDE 16

Graphical Assessments of Normality

Histograms Normal Probability Plot

  • r

Cumulative Density Function

slide-17
SLIDE 17

Graphical Tests of Normality

Normal Quantile Plot/Normal Probability Plot Normal- Black dots follow red line(straight) Negatively skewed black dots concave up compared to red line

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SLIDE 18

Graphical Tests of Normality

Normal- Black dots follow red line Positively skewed black dots concave down compared to red line

  • 3.09
  • 2.33
  • 1.64
  • 1.28
  • 0.67

0.0 0.67 1.28 1.64 2.33 3.09 0.5 0.8 0.2 0.05 0.01 0.95 0.99 0.001 1e-4

Normal Quantile Plot

1 2 3 4 5 6 7 8

Normal Quantile Plot/Normal Probability Plot

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SLIDE 19

Graphical Tests of Normality

Platykurtic-black dots form backwards S Leptokurtic black dots form an S Normal Quantile Plot/Normal Probability Plot

  • 2.33
  • 1.64
  • 1.28
  • 0.67

0.0 0.67 1.28 1.64 2.33 0.5 0.8 0.9 0.2 0.1 0.05 0.02 0.95 0.98

Normal Quantile Plot

10 20 30 40 50 60 70 80 90

  • 2.33
  • 1.64
  • 1.28
  • 0.67

0.0 0.67 1.28 1.64 2.33 0.5 0.8 0.9 0.2 0.1 0.05 0.02 0.95 0.98

Normal Quantile Plot

  • 3
  • 2
  • 1

1 2 3

slide-20
SLIDE 20

Graphical Tests of Normality

Cumulative Density Function (CDF) Normal- symmetric tails Skewed

  • ne tail longer than the other
slide-21
SLIDE 21

Statistical Tests of Normality

Overlay a normal distribution with the same mean and variance

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SLIDE 22

Statistical Tests of Normality

Overlay a normal distribution with the same mean and variance

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SLIDE 23

Statistical Tests of Normality

Overlay a normal distribution with the same mean and variance

Perform Goodness-of-Fit Test

slide-24
SLIDE 24

Statistical Tests of Normality

Overlay a normal distribution with the same mean and variance

Perform Goodness-of-Fit Test

slide-25
SLIDE 25

Skewness and Kurtosis

Choose “Customize Summary Statistics”

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SLIDE 26

Skewness and Kurtosis

Choose “Customize Summary Statistics”

Many/most software will subtract 3 from the kurtosis value.

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SLIDE 27

Skewness and Kurtosis

Choose “Customize Summary Statistics”

But, is this -3 or not? Many/most software will subtract 3 from the kurtosis value.

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SLIDE 28

Skewness and Kurtosis

OK, now that we know that, we need to do a hypothesis test.

Choose “Customize Summary Statistics”

slide-29
SLIDE 29

Skewness and Kurtosis

Choose “Customize Summary Statistics”

Hypothesis Tests

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SLIDE 30

Skewness and Kurtosis

Choose “Customize Summary Statistics”

slide-31
SLIDE 31

Skewness and Kurtosis

Choose “Customize Summary Statistics”

slide-32
SLIDE 32

Now What?

slide-33
SLIDE 33

Now What?

slide-34
SLIDE 34

Now What?

slide-35
SLIDE 35

Transform the Data

Thanks to Andy Rhyne