STAT1008 Lecture Notes - Lecture 16: Unified Atomic Mass Unit, Desipramine, Null Hypothesis
STAT1008 Week 6 Lecture A
● Randomisation Distribution:
○ P values can be calculated by randomisation distributions:
■ Simulate samples, assuming H0 is true
■ Calculate the statistic of interest of each sample
■ Find the p-value as the proportion of simulated statistics as extreme as
the observed statistic
○ E.g. Cocaine Addiction:
■ In a randomised experiment of treating cocaine addiction, 48 people were
randomly assigned to take either Desipramine (a new drug), or Lithium
(an existing drug), and then followed to see who relapses
■ Question of interest: Is Desipramine better than Lithium at treating
Cocaine Addiction
● What are the null and alternative hypotheses? PD, PL: proportion
of cocaine P^D addicts who relapse after taking Desipramine or
Lithium, respectively H0: PD = PL and Ha: PD < PL
● What are the possible conclusions? Reject H0: Desipramine is
better than lithium. Don’t reject H0: We can’t determine from this
data whether Desipramine is better than Lithium
● 1. Randomly assign units to treatment groups
● 2. Conduct Experiment
● 3. Observe relapse counts in each group
● Difference in relapse rate: Pd - Pl
● Repeat the method and getting a difference in relapse rate and
combine them all together to get a randomisation dotplot
● Similar to the bootstrap method.
● Keep doing that until you get a distribution
○ E.g. In a hypothesis test for H0: upside down h = 12 vs Ha: upside down h < 12,
we have a sample with n = 45 and x bar (mean) = 10.2.
■ What do we require about the method to produce randomisation
samples? Upside down h = 12
■ Where will the randomisation distribution be centered? 12
○ For a randomisation distribution, each simulated sample should
■ Be consistent with the null hypothesis
■ Use the data in the observed sample
■ Reflect the way the data were collected
● Randomisation Distribution Centre:
○ A randomisation distribution is centered at the value of the parameter given in the
null hypothesis
○ A randomisation distribution simulates samples assuming the null hypothesis is
true
● Randomised experiments:
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
P values can be calculated by randomisation distributions: Calculate the statistic of interest of each sample. Find the p-value as the proportion of simulated statistics as extreme as the observed statistic. In a randomised experiment of treating cocaine addiction, 48 people were randomly assigned to take either desipramine (a new drug), or lithium (an existing drug), and then followed to see who relapses. Question of interest: is desipramine better than lithium at treating. Lithium, respectively h0: pd = pl and ha: pd < pl. D addicts who relapse after taking desipramine or. Don"t reject h0: we can"t determine from this data whether desipramine is better than lithium. Difference in relapse rate: pd - pl. Repeat the method and getting a difference in relapse rate and combine them all together to get a randomisation dotplot. Keep doing that until you get a distribution.
