Stat 301 Statistics 1 Day 4 Binomial distribution

Stat 301 – Statistics 1 Day 4: Binomial distribution

Last Time – Statistical Significance n To refute the “they just got lucky” argument, we analyzed how often they would get such a result (e. g. , 14 helper choices) if the babies were choosing equally between the two toys q “Null model” Our coin flip results (16 tosses each) indicated that 14 heads was a bit unusual Strong evidence to rule out the “fluke” explanation n

Last Time – p-value n The p-value is the probability that a random process alone (under the null model – by chance alone) would produce data at least as extreme as the actual study. q Small p-values are evidence against the random chance alone explanation = statistically significant n q “Test of significance” The smaller the p-value, the stronger the evidence against the null model

Quiz 3 n n (a) If you were to toss a coin to simulate the null model of "no bias, " how many times would you toss the coin for one trial? (b)

Announcements n Any HW questions? q n Submit hard copy (to me or under my office door) or electronic copy (in Poly. Learn) by noon tomorrow Remaining Office Hours this week q Tonight 8 -9 chat room in Poly. Learn n q n Ping me if not “in progress” Tomorrow around before 9: 30, maybe after 1: 30 (Reminder of job talks this week) q Today 4 -5 pm, Tomorrow 11 -12)

Binomial random process (p. 27) n n Two outcomes Independent trials n Constant probability of success Fixed number of trials n n n Heads or Tails Outcome of one toss doesn’t impact next Assuming 0. 5 for each toss n = 16

Binomial random process (p. 27) n n Two outcomes Independent trials n Constant probability of success Fixed number of trials n n n Helper or hinderer Babies were tested individually Assuming 0. 5 for each infant (null model) n = 16

Binomial random process (p. 27) n Two outcomes n n Independent trials n n Constant probability of success Fixed number of trials n n n Define success and failure No pattern, nothing influencing next result Not changing over time Not “keep going until you are a winner”

An exact p-value? n So if assuming the babies’ outcomes can be reasonably modeled as a binomial process, can find P(X > 14) using the binomial probability distribution

An exact p-value? n n n Open the One Proportion Inference applet Specify. 5 and n = 16 Check the Exact Binomial box q n n You can also check the Hide coins box Put 14 in the As Extreme As box and press Count How does the result compare?

An exact p-value?

An exact p-value? n n R? JMP?

Repeat the calculations in JMP n Open the JMP Journal file q Click the link from the Data files and applets page and it should launch JMP n n May have to download and then open Click the area to the left of Probability Distributions Click Distribution Calculator See Technology instructions (p. 29) q Make sure you get 14 or more

Investigation 1. 2 n Skipping for now…

Investigation 1. 3 (p. 32)

Investigation 1. 3

Investigation 1. 3 (p. 32) n n n (a)-(d) (e)-(j) (m)-(n)

To Do n n By Friday: Submit HW 1 By Monday: q Optional Practice Problem 1. 3 n q HW 2 will be posted this weekend n q q q Fixed online solutions? Which location? More binomial practice will be posted this weekend Review/Replicate the technology instructions Quiz 4 in Canvas