1. Statistics: Unlocking the Power of Data Lock 5 STAT 250 Dr. Kari Lock Morgan Synthesis and Review for Exam 2

2. Statistics: Unlocking the Power of Data Lock 5 EXAM 2 In-class on Monday, 11/9 Covers everything we have done in class or lab so far (Chapters 1 – 6 in book, except not 2.6), but with emphasis on Chapters 4 – 6 Bring a non-cell phone calculator Bring two one-sided pages of notes (8 ½ x 11 paper) (or one two-sided page of notes) Review reading and optional review problems posted on WileyPlus (doing lots of problems is the best way to study!)

3. Statistics: Unlocking the Power of Data Lock 5 Exam Topics: Ch 1-3 Chapter 1: Data Collection  Data (cases, variables, etc.)  Sampling  Observational studies and confounding  Randomized experiments Chapter 2: Descriptive Statistics (except not 2.6)  Summary statistics for one or two variable(s)  Graphical displays for one or two variable(s)  Conditional probability Chapter 3: Confidence Intervals  Sampling distributions  Confidence intervals  Margin of error  Standard error and 95% confidence intervals  Bootstrapping  Percentile method for any level of confidence

4. Statistics: Unlocking the Power of Data Lock 5 Exam Topics: Ch 4-6 Chapter 4: Hypothesis Testing  Stating hypotheses  Randomization distribution  p-value  Test conclusions (generic and in context)  Errors  Multiple testing, publication bias, replication of results  Connecting intervals and tests Chapter 5: Normal Distribution  Hypothesis tests using the normal distribution  Confidence intervals using the normal distribution Chapter 6: Inference for Means and Proportions  Central Limit Theorem  Standard error formulas  N(0,1) and t-distribution  Analyzing paired vs unpaired data  Sample size for desired margin of error (proportion only)

5. Statistics: Unlocking the Power of Data Lock 5 Question of the Day Do lizards learn to behaviorally avoid invasive fire ants? Topic, data, and following slides are from Tracy Langkilde, Associate Professor of Biology at Penn State (Langkilde Lab)Langkilde Lab

6. Statistics: Unlocking the Power of Data Lock 5 Red Imported Fire Ant Solenopsis invicta: “World’s worst ant pest” Native to South America, but expansive invasive range, including much of southern US Disperse rapidly Predicted to go global Aggressive Impose novel selective pressures on native species Similar habitats as fence lizards

7. Statistics: Unlocking the Power of Data Lock 5 Fire ants eat lizards

8. Statistics: Unlocking the Power of Data Lock 5 Lizards eat fire ants

9. Statistics: Unlocking the Power of Data Lock 5 Exposure to venom causes immediate and delayed mortality Langkilde and Freidenfelds 2010 Wildlife Res Control Stung Fed Time (weeks) % Survival

10. Statistics: Unlocking the Power of Data Lock 5 Lizards and Fire Ants The study took lizards, exposed them to fire ants, and observed their reactions Lizards were either from an area invaded with fire ants (southern Alabama, invaded for >70 years) or not yet invaded (eastern Arkansas) Researchers recorded the lizards’ time to flee (in seconds) and the number of twitches (number of times lizard did a body twitch within 60 seconds) Langkilde, T. (2009). Invasive fire ants alter behavior and morphology of native lizards, Ecology, 90(1): 208-217.Invasive fire ants alter behavior and morphology of native lizards

11. Statistics: Unlocking the Power of Data Lock 5 Video from Data Collection

12. Statistics: Unlocking the Power of Data Lock 5 Parameter To see if uninvaded lizards take longer to flee than invaded lizards, which parameter would be most appropriate? a) Single mean b) Difference in means c) Single proportion d) Difference in proportions e) Correlation

13. Statistics: Unlocking the Power of Data Lock 5 Hypotheses To see if uninvaded lizards take longer to flee than invaded lizards, state the relevant hypotheses. a) H 0 : μ ui > μ i, H a : μ ui = μ i b) H 0 : μ ui = μ i, H a : μ ui ≥ μ i c) H 0 : μ ui = μ i, H a : μ ui > μ i d) H 0 : μ ui ≥ μ i, H a : μ ui = μ i e) H 0 : μ ui = μ i, H a : μ ui < μ i

14. Statistics: Unlocking the Power of Data Lock 5 Visualization To see if uninvaded lizards take longer to flee than invaded lizards, which type of graph would be most appropriate? a) Bar chart b) Segmented bar chart c) Histogram d) Side-by-side boxplots e) Scatterplot

15. Statistics: Unlocking the Power of Data Lock 5 Standardized Statistic Calculate the relevant standardized statistic.

16. Statistics: Unlocking the Power of Data Lock 5 Distribution Which distribution should you compare this statistic to? a) Standard Normal b) t with 40 df c) t with 39 df d) t with 79 df e) t with 80 df

17. Statistics: Unlocking the Power of Data Lock 5 Significant Are the results statistically significant? a) Yes b) No

18. Statistics: Unlocking the Power of Data Lock 5 Conclusion The appropriate generic conclusion is a) Reject H 0 b) Do not reject H 0 c) Reject H a d) Do not reject H a

19. Statistics: Unlocking the Power of Data Lock 5 Conclusion in Context Write a conclusion in context.

20. Statistics: Unlocking the Power of Data Lock 5 Causal Conclusion? Can we conclude that the presence of invasive fire ants in their habitat causes lizards to adapt their behavior? a) Yes b) No

21. Statistics: Unlocking the Power of Data Lock 5 Number of Twitches Next, we’ll investigate whether number of twitches is higher for invaded lizards than for uninvaded lizards

22. Statistics: Unlocking the Power of Data Lock 5 Randomization Test The p-value is closest to… a) 0.0005 b) 0.001 c) 0.05 d) 0.1 e) 0.4

23. Statistics: Unlocking the Power of Data Lock 5 Conclusion The appropriate conclusions are a) Reject H 0. We have evidence that invaded lizards twitch more than uninvaded lizards. b) Do not reject H 0. We have evidence that invaded lizards twitch more than uninvaded lizards. c) Reject H 0. We do not have evidence that invaded lizards twitch more than uninvaded lizards. d) Do not Reject H 0. We do not have evidence that invaded lizards twitch more than uninvaded lizards.

24. Statistics: Unlocking the Power of Data Lock 5 Error If we did make an error in this test, which type of error would we have made? a) Type I b) Type II c) Either one d) Neither one

25. Statistics: Unlocking the Power of Data Lock 5 Error How could we have reduced the chances of making a Type I error? a) Decrease α b) Increase α c) Increase n d) Decrease n e) Either increase α or increase n

26. Statistics: Unlocking the Power of Data Lock 5 Error How could we have reduced the chances of making a Type II error? a) Decrease α b) Increase α c) Increase n d) Decrease n e) Either increase α or increase n

27. Statistics: Unlocking the Power of Data Lock 5 Number of Twitches and Time to Flee Is there an association between number of twitches and time to flee? Which type of graph would be most relevant? a) Bar chart b) Segmented bar chart c) Histogram d) Side-by-side boxplots e) Scatterplot

28. Statistics: Unlocking the Power of Data Lock 5 Number of Twitches and Time to Flee Is there an association between number of twitches and time to flee? Which statistic would be most relevant? a) Single mean b) Difference in means c) Single proportion d) Difference in proportions e) Correlation

29. Statistics: Unlocking the Power of Data Lock 5 Confidence Interval If we were to create a bootstrap distribution to generate a confidence interval for the correlation between number of twitches and time to flee, where would the distribution be centered? a) 0 b) -0.341 c) ρ

30. Statistics: Unlocking the Power of Data Lock 5 Test If we were to create a randomization distribution to test for an association between number of twitches and time to flee, where would the distribution be centered? a) 0 b) -0.341 c) ρ

31. Statistics: Unlocking the Power of Data Lock 5 Intervals and Tests A 95% confidence interval for the true correlation between number of twitches and time to flee is (-0.50, -0.17). Using α = 0.05, if we were testing for an association between the two variables, we would… a) Reject H 0 b) Not reject H 0 c) Impossible to tell

32. Statistics: Unlocking the Power of Data Lock 5 To Do STUDY FOR EXAM 2! (Monday, 11/9)