departures from normality
TRANSCRIPT
![Page 1: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/1.jpg)
Departures from Normality
![Page 2: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/2.jpg)
Departures from Normality
• Many statistical test depend on our population being normally distributed.
![Page 3: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/3.jpg)
Departures from Normality
• Many statistical test depend on our population being normally distributed.
![Page 4: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/4.jpg)
Departures from Normality
• Many statistical test depend on our population being normally distributed.
• How do we test if our population is normally distributed?
![Page 5: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/5.jpg)
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
![Page 6: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/6.jpg)
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
![Page 7: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/7.jpg)
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)
![Page 8: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/8.jpg)
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
![Page 9: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/9.jpg)
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
![Page 10: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/10.jpg)
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?
![Page 11: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/11.jpg)
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?
![Page 12: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/12.jpg)
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
![Page 13: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/13.jpg)
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)
![Page 14: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/14.jpg)
Non-Normal Data
0
50
100
Cou
nt
0 1 2 3 4 5 6 7 8Tail Length (cm)
Skewed Right (Positively)
0
20
40
60
80
100
Cou
nt
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7Toe Length (cm)
Skewed Left (Negatively)
Skewness
![Page 15: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/15.jpg)
Non-Normal Data
0
50
100
Cou
nt
0 1 2 3 4 5 6 7 8Tail Length (cm)
Skewed Right (Positively)
0
20
40
60
80
100
Cou
nt
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7Toe Length (cm)
Skewed Left (Negatively)
Skewness
Platykurtic(flaty)
Leptokurtic
Nor
mal
Qua
ntile
Plo
t
-3 -2 -1 0 1 2 3
-2.33
-1.64-1.28
-0.67
0.0
0.67
1.281.64
2.33
0.5
0.8
0.9
0.2
0.10.050.02
0.950.98
Nor
mal
Qua
ntile
Plo
t
0 10 20 30 40 50 60 70 80 90Kurtosis
![Page 16: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/16.jpg)
Graphical Assessments of Normality
Histograms
Normal Probability Plot or
Cumulative Density Function
![Page 17: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/17.jpg)
Graphical Tests of NormalityNormal Quantile Plot/Normal Probability Plot
Normal- Black dots follow red line(straight)
Negatively skewedblack dots concave up compared
to red line
![Page 18: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/18.jpg)
Graphical Tests of Normality
Normal- Black dots follow red line
Positively skewedblack dots concave down
compared to red line
-3.09
-2.33
-1.64-1.28-0.67
0.00.671.281.64
2.33
3.09
0.5
0.8
0.2
0.05
0.01
0.95
0.99
0.0011e-4
Nor
mal
Qua
ntile
Plo
t
0 1 2 3 4 5 6 7 8
Normal Quantile Plot/Normal Probability Plot
![Page 19: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/19.jpg)
Graphical Tests of Normality
Platykurtic-black dots form backwards S
Leptokurticblack dots form an S
Normal Quantile Plot/Normal Probability Plot
-2.33
-1.64-1.28
-0.67
0.0
0.67
1.281.64
2.33
0.5
0.8
0.9
0.2
0.10.050.02
0.950.98
Nor
mal
Qua
ntile
Plo
t
0 10 20 30 40 50 60 70 80 90
-2.33
-1.64-1.28
-0.67
0.0
0.67
1.281.64
2.33
0.5
0.8
0.9
0.2
0.10.050.02
0.950.98
Nor
mal
Qua
ntile
Plo
t
-3 -2 -1 0 1 2 3
![Page 20: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/20.jpg)
Graphical Tests of NormalityCumulative Density Function (CDF)
Normal- symmetric tails
Skewedone tail longer than the other
![Page 21: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/21.jpg)
Statistical Tests of NormalityOverlay a normal
distribution with the same mean and
variance
![Page 22: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/22.jpg)
Statistical Tests of NormalityOverlay a normal
distribution with the same mean and
variance
![Page 23: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/23.jpg)
Statistical Tests of NormalityOverlay a normal
distribution with the same mean and
variance
Perform Goodness-of-Fit Test
![Page 24: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/24.jpg)
Statistical Tests of NormalityOverlay a normal
distribution with the same mean and
variance
Perform Goodness-of-Fit Test
![Page 25: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/25.jpg)
Skewness and Kurtosis
Choose “Customize Summary Statistics”
![Page 26: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/26.jpg)
Skewness and Kurtosis
Choose “Customize Summary Statistics”
Many/most software will subtract 3 from the
kurtosis value.
![Page 27: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/27.jpg)
Skewness and Kurtosis
Choose “Customize Summary Statistics”
But, is this -3 or not?
Many/most software will subtract 3 from the
kurtosis value.
![Page 28: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/28.jpg)
Skewness and Kurtosis
OK, now that we know that, we need to do a hypothesis test.
Choose “Customize Summary Statistics”
![Page 29: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/29.jpg)
Skewness and Kurtosis
Choose “Customize Summary Statistics”
Hypothesis Tests
![Page 30: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/30.jpg)
Skewness and Kurtosis
Choose “Customize Summary Statistics”
![Page 31: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/31.jpg)
Skewness and Kurtosis
Choose “Customize Summary Statistics”
![Page 32: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/32.jpg)
Now What?
![Page 33: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/33.jpg)
Now What?
![Page 34: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/34.jpg)
Now What?
![Page 35: Departures from Normality](https://reader030.vdocuments.site/reader030/viewer/2022021804/620d55993c871e7bf14a1aca/html5/thumbnails/35.jpg)
Transform the Data
Thanks to Andy Rhyne