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Lecturing(leading a class,
giving a talk, etc.)
Kari Lock MorganSTA 790: Teaching Statistics
10/3/12
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It’s not what you teach, it’s what they learn
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It’s What They Learn• It doesn’t matter what or how much you cover if
they aren’t paying attention or don’t understand
• Always keep your focus on the students – are they with you? Do they seem to be getting it?
• Focus on getting them to really learn what you do cover, not on getting through as much material as possible
• Make them think during class
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Get them Thinking• Ask them questions, get them involved and
invested in the material
• Ask questions that either
– are clear and have specific answers
– are open-ended and have a variety of possible responses
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• Randomized experiments are the “gold standard” for estimating causal effects
• WHY?
1. They yield unbiased estimates 2. They eliminate confounding factors
The Gold Standard
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RR R R
R R R R
R R R R
R R R R
R R R R
R R R R
R R R R
R R R R
R R R
R R R R R
R R R R R
R R R R R
R R R
R R R R R
R R R R R
R R R R R
Randomize
RR R R R R R R
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12 Females, 8 Males 8 Females, 12 Males5 Females, 15 Males 15 Females, 5 Males
Covariate Balance - Gender
• Suppose you get a “bad” randomization
• What would you do???
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Suppose you get a “bad” randomization and notice it before the experiment takes place. What would you do?
0%0%1. Conduct the experiment as is2. Rerandomize
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Start with Motivation• Why is what you are teaching important for the
students to know?
• Get them curious, and get them to want to understand what you are teaching
• Depending on the class and topic, this may or may not use real data
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• In 2007, Dr. Ellen Langer tested her hypothesis that “mind-set matters” with a randomized experiment
• She recruited 84 maids working at 7 different hotels, and randomly assigned half to a treatment group and half to control
• The “treatment” was simply informing the maids that their work satisfies the Surgeon General’s recommendations for an active lifestyle
Crum, A.J. and Langer, E.J. (2007). “Mind-Set Matters: Exercise and the Placebo Effect,” Psychological Science, 18:165-171.
Mind-Set Matters
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Control Treatment
2030
4050
60A
ge
Control Treatment
-10
-50
5W
eigh
t Cha
nge
p-value = .01 p-value = .001
Mind-Set Matters
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Use Visuals• Often, visuals are much easier to understand
than text
• Flowcharts are a great way to enforce conceptual understanding of a procedure
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Randomize subjects to treated and control
Collect covariate dataSpecify criteria determining when a
randomization is unacceptable; based on covariate balance
(Re)randomize subjects to treated and control
Check covariate balance
1)
2)
Conduct experiment
unacceptable acceptable
Analyze results (with a randomization test)
3)
4)
RERANDOMIZATION
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Confidence Intervals
Population Sample
Sample
Sample
SampleSampleSample
. . .
Calculate statistic for each sample
Sampling Distribution
Standard Error (SE): standard deviation of sampling distribution
Margin of Error (ME)(95% CI: ME = 2×SE)
Confidence Interval
statistic ± ME
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Have them discuss possibilities• Sometimes, you can have students discuss
possibilities before you give them the answer
• Decision: have them read before or after class?
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We use Mahalanobis Distance, M, to represent multivariate distance between group means:
Choose a and rerandomize when M > a
1' cov )(T C T CM X X X X X
Criteria for Acceptable Balance
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Make Connections• Try to connect new concepts back to what they
already know
• Mahalanobis distance is just the (scaled) test statistic for the multivariate t-test
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Ma
MMa
Ma
Distribution of M
RERANDOMIZE
Acceptable Randomizations
pa = Probability of accepting a randomization
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Theorem: If nT = nC, the covariate means are normally distributed, and rerandomization occurs when M > a, then
|T CE M a X X 0and
cov cov| .T C T CaM a v X X X X
1,2 2 2 ,
,2 2
a
k a
vk ak
Covariates After Rerandomization
1
0
where is the incomplete gamma function: ( , )
c b yb c y e dy
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How can we make this more clear?• Pictures/visuals
• Concrete examples
• Special cases
• Ask students questions to gauge understanding
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Difference in Mean Age-10 -5 0 5 10
Pure RandomizationRerandomization
Variance of covariate difference in means under rerandomizationVariance of covariate difference in means under pure randomizationav
Variance Reduction
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Standardized Difference in Covariate Means
-4 -2 0 2 4
Diastolic
Systolic
Waist-Hip Ratio
Body Fat
BMI
Weight
Age
Work as Exercise
Exercise Hours
Exercise
Pure RandomizationRerandomization
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Difference in Mean Age-10 -5 0 5 10
Pure RandomizationRerandomization
Covariate Variance Reduction
101, 1,2 22 2 2 2 .12
1010, ,2 2 2
1.48
1.482
a
k a
av
kk
• In the maids example:• 10 covariates (k = 10)• pa = .001• Want a such that P(2
10 < a) = .001 => a = 1.48
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If the acceptance probability (pa) is increased, va will…
Incre
ase
Decrease
0%0%
1. Increase2. Decrease
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Difference in Mean Age-10 -5 0 5 10
Pure RandomizationRerandomization
Covariate Variance Reduction
1.48101, 1,
2 22 2 2 2 .121010, ,
2 2 2
10, .001 1.48
12.48
a
a
k p
v
ak a
k ak
4.87101, 1,
2 22 2 2 2 .381010, ,
10, .1 4.87
4.82 2 2 2
7
a
a
ak a
k ak
k p
v
Difference in Mean Age-10 -5 0 5 10
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0.0
0.2
0.4
0.6
0.8
1.0
v a
10 20 30 40 50
-6
-5
-4
-3
-2
-1
0
Proportion of Original Variance After Re-Randomization
k: Number of Covariates
Acc
epta
nce
Pro
babi
lity:
log 1
0 s
cale
Covariate Variance Reduction
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Theorem: If nT = nC , the covariate means are normally distributed, and rerandomization occurs when M > a, then
| 0T CE Y Y M a and
2| 1 (1 ) varvar ,T C T CaM a vY Y Y YR
where R2 is the coefficient of determination (squared canonical correlation).
Estimated Treatment Effect After Rerandomization
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va
Difference in Outcome Means
Outcome Variance Reduction
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Outcome Variance Reduction10, .001 .12a avk p
Outcome: Weight ChangeR2 = .1 Variance Reduction = 1 – (1 – va )R2 = 1 – (1 – .12 )(.1) = .91
Outcome: Change in Diastolic Blood PressureR2 = .64Variance Reduction = 1 – (1 – va )R2 = 1 – (1 – .12 )(.64) = .44
Equivalent to increasing the sample size by
1/.44 = 2.27
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Use Examples!• Examples make everything more clear
• Often, it’s easiest to start with a specific example to help understanding, then generalize
• Choose examples that are interesting or relevant to the students
• Examples solidify abstract concepts.
• Everything should be illustrated with an example
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Key Points• What are the key points you want your students
to get during the lecture?
• Make sure they learn these points, and fill in around this as needed
• Don’t allow yourselves to get sidetracked too far from the point
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Preparation!!!• Make sure you take the time to prepare your
lectures in advance
• Save time for finding interesting data/examples, making helpful visuals, etc.
• Make sure everything you say is accurate
• Think hard about ordering, where examples could be helpful, etc.
• Keep time in mind
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Time Management• Perhaps have a couple of different endpoints
• End with an activity that could take as long as needed
• Err on the side of having to explain things a bit more, rather than having to rush through important material
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Note Taking• Make sure students will have enough details in
their notes
• If using the board, don’t just verbally say important information… students will need to see it when studying
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Powerpoint or Board?• Which is better for lecturing?
• It depends on your style… both have pros and cons
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PowerPoint• Allows seamless integration of technology
• Allows you to have continuous eye contact with your students• Forces you to fully prepare in advance
• Frees students to think about what you are saying rather than frantically copying it all down
• Lets you use color
graphics
animationssound effects
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Blackboard• When you have your text already typed on
PowerPoint it’s easy to just read the slides and go too fast and entirely lose the attention of the students who don’t have to pay attention anyway because the notes are all online for them to go back to and look at later if they need them…
• Forcing the students to take notes ensures that they continue to pay attention and don’t fog out
• “The only way to keep the students engaged is to be engaged myself”
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• People have many different strategies for keeping students engaged… experiment and find what works for you
• It’s often not what you do, but how you do it
Powerpoint or Board?