1. Which statistical test is best for my data? or: What do you graph, dear? What do you test, dear?
Refresher on tests that we know
Several examples
Fatal errors
Data for you to analyze

2. Which tests and graphs fit which situations?
Independent variable (X)
Dependent variable (Y)
Graph
Test
Continuous
Scatterplot
Linear regression
Class
Bar graph
t-test, ANOVA
Bar graph, contingency table
Chi-square
Scatterplot, bar chart
(Logistic regression)
David Strayer, Cary Institute
All of these tests assume that the data are independent and normally distributed (more on this later!)

3. Claim 1: Money can’t buy you love, but it can buy you a good ball team
Specifically, claim is that baseball teams with bigger salaries win more games than those will smaller salaries
Data are average (mean) salaries and winning percentages for the 2012 baseball season

4. The data TEAM AVG SALARY winning percentage Arizona Diamondbacks
$ 2,653,029
0.5
Atlanta Braves
$ 2,776,998
0.58
Baltimore Orioles
$ 2,807,896
0.574
Boston Red Sox
$ 5,093,724
0.426
Chicago Cubs
$ 3,392,193
0.377
Chicago White Sox
$ 3,876,780
0.525
Cincinnati Reds
$ 2,935,843
0.599
Cleveland Indians
$ 2,704,493
0.42
Colorado Rockies
$ 2,692,054
0.395
Detroit Tigers
$ 4,562,068
0.543
Houston Astros
$ 2,332,730
0.34
Kansas City Royals
$ 2,030,540
0.444
Los Angeles Angels
$ 5,327,074
0.549
Los Angeles Dodgers
$ 3,171,452
0.531
Miami Marlins
$ 4,373,259
Milwaukee Brewers
$ 3,755,920
0.512
Minnesota Twins
$ 3,484,629
0.407
New York Mets
$ 3,457,554
0.457
New York Yankees
$ 6,186,321
0.586
Oakland Athletics
$ 1,845,750
Philadelphia Phillies
$ 5,817,964
Pittsburgh Pirates
$ 2,187,310
0.488
San Diego Padres
$ 1,973,025
0.469
San Francisco Giants
$ 3,920,689
Seattle Mariners
$ 2,927,789
0.463
St. Louis Cardinals
$ 3,939,316
Tampa Bay Rays
$ 2,291,910
0.556
Texas Rangers
$ 4,635,037
Toronto Blue Jays
$ 2,696,042
0.451
Washington Nationals
$ 2,623,746
0.605
The data

5. How is this claim best evaluated? -graph and statistical analysis

6. How is this claim best evaluated? -graph and statistical analysis
Scatter plot

7. How is this claim best evaluated? -graph and statistical analysis
Scatter plot,
Linear regression

8. Conclusion
Money can’t buy you a winning ball team, either

9. Claim 2: Eels control crayfish populations
Specifically, claim is that crayfish population densities are lower in streams where eels are present
Background: dietary studies show that eels eat a lot of crayfish, and old Swedish stories suggest that eels eliminate crayfish
Data are crayfish densities (count along transects, snorkelling) in local streams with and without eels

10. The data River Site Crayfish (no./m^2) eels Croton Green Chimneys
3.225
PEP
0.119
Delaware
Buckingham
0.25 1
Callicoon
Hankins
0.109
Mongaup
Pond Eddy
0.067
Neversink
Bridgeville
0.233
TNC
Shawangunk
Mount Hope
4.53
Ulsterville
1.1
Webatuck
Levin
0.812
Shope
1.719
Still Point
1.4

11. How is this claim best evaluated? -graph and statistical analysis

12. How is this claim best evaluated? -graph and statistical analysis
Bar graph

13. How is this claim best evaluated? -graph and statistical analysis
Bar graph,
t-test
p = 0.02

14. Conclusion
Looks like streams containing eels have fewer crayfish

15. Claim 3: Human life expectancy varies among continents
Data are mean life expectancy for women in different countries

16. The data Africa Asia Americas Europe algeria 75 bangladesh 70.2
argentina
79.9
austria
83.6
cameroon
53.6
china
75.6
brazil
77.4
belgium
82.8
cote d'ivoire
57.7
india
67.6
canada
85.3
bulgaria
77.1
egypt
75.5
indonesia
71.8
chile
82.4
czech rep 81
kenya
59.2
iran
75.3
columbia
77.7
denmark
87.4
morocco
74.9
japan
87.1
mexico
79.6
estonia 80
nigeria
53.4
malaysia
76.9
peru
finland
83.3
south africa
54.1
pakistan
66.9
usa
81.3
france
84.9
zimbabwe
52.7
philippines
72.6
venezuela
germany 83
singapore
83.7
greece
82.6

17. How is this claim best evaluated? -graph and statistical analysis

18. How is this claim best evaluated? -graph and statistical analysis
Bar graph
Note that y-axis doesn’t start at 0

19. How is this claim best evaluated? -graph and statistical analysis
Bar graph,
1-way ANOVA,
p =

20. Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
Africa 9
556.1
Asia 10
747.7
74.77
Americas
718.2
79.8
7.7875
Europe
825.7
82.57
ANOVA
Source of Variation SS df MS F
P-value
F crit
Between Groups
2351.6 3
1.42E-07
Within Groups 34
Total 37

21. Conclusion Life expectancy of women appears to differ among continents
(The ANOVA doesn’t tell us which continents are different; further tests would be necessary to test claims about specific continents)

22. Claim 4: predators with experience eat more invasive prey
Specific claim is that sunfish from bodies of water that were invaded a long time ago will eat more zebra mussels than sunfish from recently invaded waters or waters without zebra mussels
Data are from an aquarium experiment using sunfishes from rivers invaded 20 years ago, a lake that was invaded 9 years ago, and streams without zebra mussels
Each aquarium contained 15 zebra mussels; the number of mussels eaten in 3 days was recorded

23. The data old invasions recent invasions uninvaded 15 5 2 14 1 12 8 311 6

24. How is this claim best evaluated? -graph and statistical analysis

25. How is this claim best evaluated? -graph and statistical analysis
Bar graph

26. How is this claim best evaluated? -graph and statistical analysis
Bar graph,
p =

27. Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
old invasions 12
160
recent invasions 6 64
uninvaded 9 13
ANOVA
Source of Variation SS df MS F
P-value
F crit
Between Groups 2
8.67E-08
Within Groups 24
Total 26

28. Conclusion
Fish living in places that have had zebra mussels for a long time eat more zebra mussels

29. Claim 5: Zebra mussels reduce phytoplankton biomass in the Hudson
Data are growing-season (May-Sept) means for zebra mussel population filtration rate and phytoplankton biomass in the freshwater tidal Hudson River

30. The data
year
ZMFR
chl a
1987
0.00
17.45
1988
28.95
1989
17.25
1990
17.52
1991
0.03
25.48
1992
0.36
12.18
1993
7.10
5.04
1994
3.96
4.91
1995
4.44
5.34
1996
2.60
3.74
1997
6.50
6.89
1998
5.06
7.50
1999
2.79
6.56
2000
3.59
4.40
2001
3.02
11.47
2002
5.70
5.44
2003
2.34
4.81
2004
3.16
4.64
2005
1.51
8.84
2006
0.06
5.90
2007
4.09
4.10
2008
0.26
4.96
2009
4.08
6.71

31. How is this claim best evaluated? -graph and statistical analysis

32. How is this claim best evaluated? -graph and statistical analysis
scatterplot

33. How is this claim best evaluated? -graph and statistical analysis
Scatterplot,
linear regression,
… but clearly not linear

34. How is this claim best evaluated? -graph and statistical analysis
Non-linear regression (available in many statistical packages)
Not really fair to choose a non-linear model after looking at the data, so think about whether your claim suggests a linear model or a non-linear one before analyzing the data

35. Conclusion
Yes, it looks like zebra mussel feeding reduces phytoplankton population in the Hudson
The relationship is nonlinear

36. What to do if both variables are class variables?
Status
birds + mammals
FW fish
FW shellfish
FW insects
extinct (GX, GH)
1.65
2.13
6.56
1.34
Critically imperiled (G1)
3.71
11.39
20.85
2.2
Imperiled (G2)
4.89
10.89
15.6
9.09
Vulnerable (G3)
7.95
13.14
17.24
19.98
Secure (G4, G5)
81.57
62.33
39.73
67.4

37. What to do if the predictor variable is continuous but the response variable is a class variable?
Baby mussels
present
Baby mussels
absent

38. Common fatal errors: non-independence

39. Common fatal errors: undue influence of a single point

40. Claims for you to test
Large, mobile predators (i.e., crabs) reduce zebra mussel populations in the Hudson
Cell phone ownership increases with income among countries
Levels of dissolved oxygen affect behavior of baby mussels