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Sir Francis Galton The history of statistics has its roots...

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The history of statistics has its roots in biology Sir Francis Galton Inventor of fingerprints, study of heredity of quantitative traits Regression & correlation Karl Pearson Polymath- Studied genetics Correlation coefficient ! 2 test Standard deviation Sir Ronald Fisher The Genetical Theory of Natural Selection Founder of population genetics Analysis of variance likelihood P-value randomized experiments multiple regression etc., etc., etc.
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Page 1: Sir Francis Galton The history of statistics has its roots ...bole/bio300/overheads/overheads02.pdf · Regression & correlation Karl Pearson Polymath- Studied genetics Correlation

The history of statistics has its roots in biology

Sir Francis Galton

Inventor of fingerprints, study of heredity of quantitative traits

Regression & correlation

Karl Pearson

Polymath-

Studied genetics

Correlation coefficient !2 test Standard deviation

Sir Ronald Fisher

The Genetical Theory of Natural Selection

Founder of population genetics

Analysis of variance likelihood P-value randomized experiments multiple regression etc., etc., etc.

Page 2: Sir Francis Galton The history of statistics has its roots ...bole/bio300/overheads/overheads02.pdf · Regression & correlation Karl Pearson Polymath- Studied genetics Correlation

Displaying Data with Graphics

• Categorical Variables (also known as Class variables, or Nominal variables)"

• Numerical Variables (or Quantitative Variables)"

– Numerical variables are either discrete or continuous.

Types of Data

Categorical variables

•  Sex •  Genotype •  Drug treatment (e.g. aspirin vs. ibuprofen) •  Province •  Survival (i.e., live or die)

Numerical variables

•  Height •  Weight •  Tail length •  Dose (e.g. in micrograms/gram) •  Longevity (i.e., number of years)

Page 3: Sir Francis Galton The history of statistics has its roots ...bole/bio300/overheads/overheads02.pdf · Regression & correlation Karl Pearson Polymath- Studied genetics Correlation

Discrete vs. Continuous

Can be counted

•  Number of limbs •  Number of offspring •  Number of petals

Can be measured

•  Arm length •  Height •  Weight •  Age

Graphing categorical variables

Frequency table showing the 1999. The total number of U.S. children killed or mauled by captive big cats from 1990 to 2006. The total number of children harmed is n = 47.

Year Frequency 1990 2 1991 2 1992 1 1993 2 1994 1 1995 4 1996 1 1997 3 1998 3 1999 4 2000 5 2001 3 2002 3 2003 2 2004 3 2005 5 2006 3

Bar graph

Freq

uenc

y

Year

Page 4: Sir Francis Galton The history of statistics has its roots ...bole/bio300/overheads/overheads02.pdf · Regression & correlation Karl Pearson Polymath- Studied genetics Correlation

0

5

10

15

20

25

tiger cougar leopard lion lynx jungle cat bobcat cheetah liger

Bar graph

Species

Freq

uenc

y Graphing numerical variables

Heights of biostats students (cm)

165 168 163 173 170 163 170 155 152 190 170 168 142 160 154 165 156 177 173 165 165 175 155 166 168 165 180 165

Frequency table

Height Group

Frequency

141-150 1

151-160 6

161-170 15

171-180 5

181-190 1

Page 5: Sir Francis Galton The history of statistics has its roots ...bole/bio300/overheads/overheads02.pdf · Regression & correlation Karl Pearson Polymath- Studied genetics Correlation

Histogram Height histogram with more data

150 160 170 180 190 200 210

0.2

0.4

0.6

0.8

1

Cumulative Frequency

Height (in cm) of Bio300 Students

Cumulative Frequency Distribution

The cumulative frequency of a value is the proportion of individuals equal to or less than that value.

Making a CDF

Page 6: Sir Francis Galton The history of statistics has its roots ...bole/bio300/overheads/overheads02.pdf · Regression & correlation Karl Pearson Polymath- Studied genetics Correlation

Associations between two categorical variables

Association between reproductive effort and avian

malaria Table 2.3A. Contingency table showing incidence of malaria infemale great tits subjected to experimental egg removal.

control group egg removal group row totalmalaria 7 15 22

no malaria 28 15 43

column total 35 30 65

Grouped Bar Graph Mosaic plot

Page 7: Sir Francis Galton The history of statistics has its roots ...bole/bio300/overheads/overheads02.pdf · Regression & correlation Karl Pearson Polymath- Studied genetics Correlation

Associations between categorical and numerical

variables

Multiple histograms

Young, K. V., E. D. Brodie Jr., and E. D. Brodie III. 2004. How the horned lizard got its horns. Science 304:65.

www.netcore.ca/~peleetom

Shrike

Associations between two numerical variables

Scatter plot

Tattersall et al. (2004) Journal of Experimental Biology 207:579-585

Page 8: Sir Francis Galton The history of statistics has its roots ...bole/bio300/overheads/overheads02.pdf · Regression & correlation Karl Pearson Polymath- Studied genetics Correlation

Don’t mislead with graphics Better representation of truth

Summary: Graphical methods for frequency distributions

Type of Data Method

Categorical data Bar graph

Numerical data Histogram Cumulative frequency

distribution

Summary: Associations between variables

Explanatory variable

Response variable

Categorical Numerical

Categorical Contingency table Grouped bar graph

Mosaic plot

Multiple histograms

Cumulative frequency distributions

Numerical Multiple histograms

Cumulative frequency distributions

Scatter plot


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