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Robin Lock St. Lawrence University USCOTS 2013 - Opening Session.

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1 Robin Lock St. Lawrence University USCOTS 2013 - Opening Session

2 A Historical Comparison Traditional: p-value in the year 10 BC* vs. Modern: p-value today *BC = Before Cobb

3 Example: Beer and Mosquitoes Does consuming beer attract mosquitoes? Experiment*: Volunteer were randomly assigned to drink a liter of either beer or water Mosquitoes were caught in traps as they approached the volunteers. H 0 : μ B =μ W H 0 : μ B >μ W *Lefvre, T., et. al., “Beer Consumption Increases Human Attractiveness to Malaria Mosquitoes, ” PLoS ONE, 2010; 5(3): e9546. nmeanstd. dev. Beer2523.604.1 Water1819.223.7

4 Traditional p-value 1. Pick a formula 2. Plug & Chug 3. Pick a reference distribution Where is my t-table?

5 0.0005 < p-value < 0.001 d.f. t=3.68

6 Oops! I forgot to check conditions... Sample sizes are both less than 30, is the t-distribution even appropriate? What if the data are heavily skewed?...and, by the way, how does this method connect to the definition of a p-value?

7 The p-value is the proportion of samples, when H 0 is true, that would give results as (or more) extreme as the original sample.

8 “when H 0 is true”  It doesn’t matter whether the subject drank beer or water Create randomization samples (under H 0 ) by randomly re-assigning the beer/water labels to the 43 mosquito counts.

9 Put the 43 mosquito counts on cards. Shuffle and deal cards into two piles (25 beer and 18 water). Compute the difference in means. Repeat MANY times.

10 StatKey www.lock5stat.com/statkey

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15 “as extreme as the original sample”

16 Background Required Random shuffle Compute sample means Dotplot Find a proportion by counting

17 What about other parameters or different hypotheses? What about checking conditions? What about confidence intervals? What was that address for StatKey?

18 www.lock5stat.com/statkey

19 p-value = proportion of samples, when H 0 is true, that are as (or more) extreme as the original sample.

20 p-value

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