University:
McMaster University
Course:
STATS 1LL3 | Introduction to Probability and Statistics
Academic year:

2023
Views:

417

Pages:

3
Author:

Sabrina S.

Video 21: Hypothesis testing using measurement Drug trial testing alertress. Participants must record how many times they can roll a die in 1 min. Given the drug Then 30 min later record how many times they can roll a die in 1 min. Your friend thinks they are going to analyse the mean before the drug and compare to mean number of rolls after use of drug. Surely what actually matters is the difference between each individual participants before-score (B) and after-score (A) B-A test statistic 2- paired two sample for means p-value t-distribution absolute value of test statistic and degrees of freedom (n-1) 4 two-sample assuming equal variances Summary of hypothesis test Comparing means of twe dependent samples Step 1 define the null hypothesis Ho Ho NB NA οι μαμα το difference Step 2 define the alternative hypothesis H1 (now a one-sided a (im above example we want drug to have an effect and therefore mean ofter drug should be greater than it was before) Step 3 significance level (a) Step 4 Calculate rejection region d = X- XA can be tested with a 1-sample t-test degrees of freedom 0-1 where in refers to the number of pairs of data 0.05 Rejeck Ho if test statistic t 34 appropriate critical value-1.691 Step 5 calculate test statistic test stat do -149-0 1.788/135 = -4.91- ہو Step b conclusion test statistic is more extreme thon critical value -491-1691 reject Ho fulls in rejection region. the drug is effective in improving motor functioning Modified approach (What is the probability of gotting a test statistic as small as -491? t-table df 34 look a find probability closest to 4.91 جا p-value is less than 0.0005 If Ho is true we would have observed a difference of this hature only 5 times in 10 000 (very very unlikely) on this basis we have strong evidence to reject Ho and again conclude the medication is effective it our alternative was a two-sided we would double our p-value pvalue is < 0.001 You will always have the same number of observations in your two groups Critical point → We need paired tests because our paired data are not independent of each other A paired test is most appropriate with repeated measures example 10 A pg 206 We convert our two sets of measurements into a single measurement of the differences between the two sets We then use the 1- sample t-test