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Evaluating Claims through Graphs and Statistical Analysis

This article provides a refresher on statistical tests and graphs, with several examples and analysis of common errors. It explores different situations where tests and graphs are appropriate for evaluating claims using relevant data. The language of the text is English.

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Evaluating Claims through Graphs and Statistical Analysis

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  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? 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

  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

  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

  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 = 0.0000001

  20. 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)

  21. 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

  22. The data

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

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

  25. How is this claim best evaluated?-graph and statistical analysis Bar graph, p = 0.00000009

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

  27. 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

  28. The data

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

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

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

  32. 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

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

  34. What to do if both variables are class variables?

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

  36. Common fatal errors: non-independence

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

  38. 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

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