Lecturing (leading a class, giving a talk, etc.)

Lecturing(leading a class,

giving a talk, etc.)

Kari Lock MorganSTA 790: Teaching Statistics

10/3/12

It’s not what you teach, it’s what they learn

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

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

• Randomized experiments are the “gold standard” for estimating causal effects

• WHY?

1. They yield unbiased estimates 2. They eliminate confounding factors

The Gold Standard

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

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???

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

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

• 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

Control Treatment

2030

4050

60A

ge

Control Treatment

-10

-50

5W

eigh

t Cha

nge

p-value = .01 p-value = .001

Mind-Set Matters

Use Visuals• Often, visuals are much easier to understand

than text

• Flowcharts are a great way to enforce conceptual understanding of a procedure

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

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

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?

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

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

Ma

MMa

Ma

Distribution of M

RERANDOMIZE

Acceptable Randomizations

pa = Probability of accepting a randomization

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

How can we make this more clear?• Pictures/visuals

• Concrete examples

• Special cases

• Ask students questions to gauge understanding

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

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

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

If the acceptance probability (pa) is increased, va will…

Incre

ase

Decrease

0%0%

1. Increase2. Decrease

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

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

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

va

Difference in Outcome Means

Outcome Variance Reduction

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

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

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

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

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

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

Powerpoint or Board?• Which is better for lecturing?

• It depends on your style… both have pros and cons

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

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”

• 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?