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

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Presentation transcript:

Robin Lock St. Lawrence University USCOTS Opening Session

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

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. Beer Water

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

< p-value < d.f. t=3.68

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?

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.

“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.

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.

StatKey

“as extreme as the original sample”

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

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

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

p-value