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Lecture 8
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Carleton University
Psychology
PSYC 2002
Steven Carroll
Winter
Description
Lecture 8: corrections
What we know
 N
 n
 µ
 M

 ❑ M
Hypothesis testing
 Your knowledge of all of that stuff will let you do some real science!
 Here are the steps that you will follow:
1. State your hypotheses, and define your population parameters
2. Define your critical region
3. Run your test
4. Compare your sample statistic to your population parameter
5. State your conclusion
State your hypotheses, and define your population parameters
 Suppose you believed that you had developed the cure for disease X. You’ve decided to run an
experiment wherein you give a sample of people you drug and see whether they get better more
quickly than the known average 7 day recovery time in the population ( = 3)
• State your hypothesis
The null hypothesis
 H 0 : there will be no difference between the two groups
 The limitations of inferential statistics requires that we do things a little bit assbackwards
when it comes to hypothesis testing
 We directly test the “null hypothesis”
 We NEVER directly test the “alternative hypothesis”
The null hypothesis
 Why?
 You’ll have to take a symbolic logic course for the answer
 Suffice it to say that, logically, it is a lot simpler to falsify a universal assumption than to
prove a universal assumption
The null hypothesis  If we believe that untreated people in the population get better in, on average, 7 days then
we test the hypothesis:
H 0 : µwithtreatmen= 7
The alternative hypothesis
 We also state the alternative hypothesis, even though we don’t test it:
H 1 : µwithtreatmen≠ 7
Definitions
H 0
 The null hypothesis ( ) states that in the general population there is no relationship
between the independent variable and the dependent variable
• What are the IV and DV in our cure example?
 The alternative hypothesis ( H 1 ) states that in the general population there is a
relationship between the independent variable and the dependent variable
Define your critical region
 What are we hoping to do is “reject the null hypothesis”
 In other words, we are hoping that the difference between the two groups is so large that
we can’t support the hypothesis that there is no difference between the groups
 How different does different have to be?
 That depends on your willingness to make a type I error
• What is a type I error?
= p (type I error)
 The Greek letter is your probability of committing a type I error
 You choose this pvalue and then use the ztable to find the associated zscore
 Suppose we were not willing to accept more than a 5% chance of making a type I error
• What is ?
.05
• What is the associated zscore?
+ /  1.96
Why?
= p (type I error)
 You state:
 With = .05 twotailed, zcritica= + /  1.96
Critical region  So, for this example, when we do our ztest we need to observe a zscore more extreme than +/
1.96 in order to reject the null hypothesis.
 If we don’t observe a value this extreme then we “fail to reject the null hypothesis”.
• You NEVER accept the null hypothesis.
• You NEVER reject the alternative hypothesis.
• You NEVER accept the alternative hypothesis
Run your test
 I give my drug to a sample of 10 people
 Average recovery time for the untreated population = 7 days
 Standard deviation for the population = 3 days
 Observed mean for treatment group = 5 days
 What is our observed zscore?
M−µ 10−7
Z = ❑ = 3
M 10
3
= = 3.16
.95
Compare your sample statistic to your population parameter
 Is zobserved more extreme than zcritical?
 If so, state: “zobserved is more extreme than zcritical”
 If not, state: “zobserved is less extreme than zcritical”
State your conclusion
H 0 H 0
 Either “reject ” or “fail to reject ”
 What is our conclusion?
Factors that influence a hypothesis test
1. The size of the treatment effect:
• If M is much more extreme than µ, you are more likely to observe a significant result
• Why (mathematically speaking)?
2. The size of the variability between the scores
• If is extremely large, you are less likely to observe a significant result
• Why (mathematically speaking)?
3. The size of your sample
• If n is extremely large, you are more likely to observe a significant result
• Why (mathematically speaking)?
• Keep this one in mind! It is a very very evil way to cheat using statistics
• We’ll come back to this one
Assumptions  Based on what we’ve talked about in previous lectures, what assumptions must
we make in order to accept the conclusions of a ztest?
 Ones you should’ve known:
• Random sampling
When does this get violated? When is it OK anyways?
• A normal sampling distribution
When can you be assured of a normal sampling distribution?
 Ones you might not have known:
• Independent observations
There can be no predictable relationship between your observations
Ex: what if you test depression and all of your subjects are from the same
family
Or what if you test half of your subjects at 6:30am and the other half at
3pm?
• Constant
The value of the variance in the population cannot be changed as a result
of treatment
If = 10 in the population, but drops to = 2 afterwards, what formula is
rendered invalid?
We’re assuming that the only thing treatment does is add or subtract a
constant to the scores!
CHANGES IN CHANGE THE KURTOSIS OF THE DISTRIBUTION!
Another kind of null hypothesis
 What if I knew that there was no way that my treatment could make the patients
any worse?
H 0
 How would that change my
H µ
• 0 : withtreatm≤ 7
 How would that change my H 1
• H 0 : µwithtreatm> 7
 How would that change my
• It doesn’t! What does it change?
• zcritic= +1.65
An example
 I believe that people who don’t watch the stats video lectures until the night
before the exam will do worse on the test
 I administer a questionnaire to my students and ask “Did you put off watching all
of the videos until the night before the exam?”
• I identify 18 procrastinators. The average mark for this group was 70%. • The rest of the class obtained an average mark of 75%, with a standard
deviation of 15%.
• Test my hypothesis, maintaining a Type I Error rate of .03.
Step 1
 State your hypotheses, and define your population parameters
H µ
• 0 : procrastinat≥ 75
• H 1 : µprocrastinat<
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