Stat 301 Day 8 Twosided pvalues plausible values
Stat 301 – Day 8 Two-sided p-values, plausible values
Last Time – Two-sided p-value n n Two-sided alternative hypothesis: If don’t have a prior suspicion (does the parameter “differ” from) or want both large and small values to count as evidence against the null hypothesis (probability is “too large or too small”), specify “not equal to” for the alternative Two-sided p-value: Probability of your result or more extreme in either direction
Two-sided p-values n n Approach 1: As extreme on the other side of the mean of the distribution Approach 2: Values that have a probability smaller than the probability at the observed value (“method of small p-values”) q q q n Makes more sense for skewed distributions Used by applet and R Equivalent with symmetric distributions Other approaches to come…
Quiz 7 n n n Is p, the probability of leaning right = 0. 5? Is p, the probability of leaning right = 0. 74? So then what is it?
Plausible values n n n We think p is somewhere between (. 557, . 726) Based on two-sided p-value > 0. 05 Called a “ 95% confidence interval” q n I’m 95% confident that between 55. 7% and 72. 6% of kissing couples lean right How would we find a 99% confidence interval?
99% confidence 0. 529 . 748
Changing confidence level n n n 95% confidence: (. 557. , 726) 99% confidence: (. 529, . 748) Similar center q n Longer q n Roughly sample proportion =. 645 To be more confident the parameter is inside the interval, need a wider interval Technology detour p. 49
Technology (p. 49) n R: q n iscambinomtest(80, 124, conf. level =. 95) JMP: q q Open JMP using the ISCAM Journal file (on data files and applets page) Confidence Interval for One Proportion n Summary Stats (80, 124) Binomial Enter
PP 1. 6 (p. 51)
Summary n n Two-sided p-values: Might not have a particular direction in mind Confidence interval: Might not even have an exact number in mind to compare to q q What are the plausible values? Estimate the size of the parameter
Investigation 1. 7
To Do n Finish HW 2 q q n n n Upload separate files in Canvas or problems start on new pages if hard copy Remember to integrate your output with your discussion Finish Inv 1. 7 (a)-(r) Quiz 8 (under Assignments) Tuesday is a Monday schedule (meet in the lab) q Mini-project proposal…
Project 1 Proposal
- Slides: 13