Download presentation

Presentation is loading. Please wait.

Published byXavier Grant Modified over 4 years ago

1
How Much Data Do I Need? Power & Sample Size for Students t test Prof. Tom Willemain 3/2/20141T. R. Willemain

2
Sample Size Calculations Complicated with Students t because the critical value of t is a function of the unknown sample size. R has function power.t.test() to calculate sample size if can assume i.i.d. Normal data with equal variances Complications – Deciding on acceptable Type I (false positive) and Type II (false negative) error rates – Deciding on the size of a shift in mean that would be of interest – Estimating the variances in the two groups – Deciding what to do if variances are unequal – Deciding what to do if data do not have a Normal distribution 3/2/2014T. R. Willemain2

3
3/2/2014T. R. Willemain3 # power.ttest.R # calculate sample size for required power # note: assumes iid Normal data w/equal variances #power.t.test(n = NULL, delta = NULL, sd = 1, sig.level = 0.05, # power = NULL, # type = c("two.sample", "one.sample", "paired"), # alternative = c("two.sided", "one.sided"), # strict = FALSE) # initialize rm(list=ls()) # enter parameters describing your scenario delta0=0.5 # desired difference in means sigma0=1.5 # estimated std dev of data in each group (assumed equal) alpha= 0.05 # type I error probability you can tolerate beta=0.05 # type II error probability you can tolerate #data.type="one.sample" #data.type="paired" data.type="two.sample" #alternative.type="two.sided" alternative.type="one.sided" # compute required sample size n=power.t.test(n = NULL, delta = delta0, sd =sigma0, sig.level = alpha, power = 1-beta,type = data.type, alternative = alternative.type, strict = FALSE) # show results print(n )

4
Output of power.ttest.R 3/2/2014T. R. Willemain4 > print(n) Two-sample t test power calculation n = 195.4794 delta = 0.5 sd = 1.5 sig.level = 0.05 power = 0.95 alternative = one.sided NOTE: n is number in *each* group

5
Dealing with the Complications Deciding on acceptable Type I and Type II error rates – Context sensitive; conventional choices use α and β 0.05 or 0.01 Deciding on the size of a shift in mean – Very context sensitive; 10% improvement? Estimating the variances in the two groups – Either get pilot samples or make guestimates Deciding what to do if variances are unequal – See Monte Carlo code t.power.R on next slide Deciding what to do if data do not have a Normal distribution – See Monte Carlo code; might also use bootstrap if have pilot samples 3/2/2014T. R. Willemain5

6
Output of t.power.R 3/2/2014T. R. Willemain6 Here, could substitute some other distributions Here, plug in different standard deviations

Similar presentations

OK

Statistical hypothesis Statistical hypothesis is a method for testing a claim or hypothesis about a parameter in a papulation The statement H 0 is called.

Statistical hypothesis Statistical hypothesis is a method for testing a claim or hypothesis about a parameter in a papulation The statement H 0 is called.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google