400 likes | 422 Views
Explore different statistical tests and graphs for data analysis including case studies and common errors. Learn how to evaluate claims using graphs and statistical methods for various scenarios.
E N D
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
Which tests and graphs fit which situations? All of these tests assume that the data are independent and normally distributed (more on this later!)
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
How is this claim best evaluated?-graph and statistical analysis
How is this claim best evaluated?-graph and statistical analysis Scatter plot
How is this claim best evaluated?-graph and statistical analysis Scatter plot, Linear regression
Conclusion • Money can’t buy you a winning ball team, either
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
How is this claim best evaluated?-graph and statistical analysis
How is this claim best evaluated?-graph and statistical analysis Bar graph
How is this claim best evaluated?-graph and statistical analysis Bar graph, t-test p = 0.02
Conclusion • Looks like streams containing eels have fewer crayfish
Claim 3: Human life expectancy varies among continents • Data are mean life expectancy for women in different countries
How is this claim best evaluated?-graph and statistical analysis
How is this claim best evaluated?-graph and statistical analysis Bar graph Note that y-axis doesn’t start at 0
How is this claim best evaluated?-graph and statistical analysis Bar graph, 1-way ANOVA, p = 0.0000001
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)
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
How is this claim best evaluated?-graph and statistical analysis
How is this claim best evaluated?-graph and statistical analysis Bar graph
How is this claim best evaluated?-graph and statistical analysis Bar graph, p = 0.00000009
Conclusion • Fish living in places that have had zebra mussels for a long time eat more zebra mussels
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
How is this claim best evaluated?-graph and statistical analysis
How is this claim best evaluated?-graph and statistical analysis scatterplot
How is this claim best evaluated?-graph and statistical analysis Scatterplot, linear regression, … but clearly not linear
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
Conclusion • Yes, it looks like zebra mussel feeding reduces phytoplankton population in the Hudson • The relationship is nonlinear
What to do if the predictor variable is continuous but the response variable is a class variable? Baby mussels present Baby mussels absent
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