1. STAT 101 Dr. Kari Lock Morgan
Synthesis
Big Picture Essential Synthesis
Review
Speed Dating

2. Final Monday, April 28th, 2 – 5pm No make-ups, no excuses
30% of your course grade
Cumulative from the entire course
Open only to a calculator and 3 double-sided pages of notes prepared only by you

3. Help Before Final Wednesday, 4/23: Thursday, 4/24: Friday, 4/25:
3 – 4pm, Prof Morgan, Old Chem 216
4 – 9pm, Stat Ed Help, Old Chem 211A
Thursday, 4/24:
5 – 7pm, Yating, Old Chem 211A
Friday, 4/25:
1 – 3pm, Prof Morgan, Old Chem 216
3 – 4 pm, REVIEW SESSION, room tbd
Sunday, 4/27:
4 – 6pm, Tori, Old Chem 211A
6 – 7pm, Stat Ed Help, Old Chem 211A
7 – 9pm, David, Old Chem 211A
Monday, 4/28:
12:30 – 1:30, Prof Morgan, Old Chem 216

4. Review What is Bayes Rule?
A way of getting from P(A if B) to P(B if A)
A way of calculating P(A and B)
A way of calculating P(A or B)

5. Data Collection
The way the data are/were collected determines the scope of inference
For generalizing to the population: was it a random sample? Was there sampling bias?
For assessing causality: was it a randomized experiment?
Collecting good data is crucial to making good inferences based on the data

6. Exploratory Data Analysis
Before doing inference, always explore your data with descriptive statistics
Always visualize your data! Visualize your variables and relationships between variables
Calculate summary statistics for variables and relationships between variables – these will be key for later inference
The type of visualization and summary statistics depends on whether the variable(s) are categorical or quantitative

7. Estimation
For good estimation, provide not just a point estimate, but an interval estimate which takes into account the uncertainty of the statistic
Confidence intervals are designed to capture the true parameter for a specified proportion of all samples
A P% confidence interval can be created by
bootstrapping (sampling with replacement from the sample) and using the middle P% of bootstrap statistics

8. Hypothesis Testing
A p-value is the probability of getting a statistic as extreme as observed, if H0 is true
The p-value measures the strength of the evidence the data provide against H0
“If the p-value is low, the H0 must go”
If the p-value is not low, then you can not reject H0 and have an inconclusive test

9. p-value A p-value can be calculated by
A randomization test: simulate statistics assuming H0 is true, and see what proportion of simulated statistics are as extreme as that observed
Calculating a test statistic and comparing that to a theoretical reference distribution (normal, t, 2, F)

10. Hypothesis Tests Variables Appropriate Test One Quantitative
Single mean (t)
One Categorical
Single proportion (normal)
Chi-square Goodness of Fit
Two Categorical
Difference in proportions (normal)
Chi-square Test for Association
One Quantitative,
Difference in means (t)
Matched pairs (t)
ANOVA (F)
Two Quantitative
Correlation (t)
Slope in Simple Linear Regression (t)
More than two
Multiple Regression (t, F)

11. Regression
Regression is a way to predict one response variable with multiple explanatory variables
Regression fits the coefficients of the model
The model can be used to
Analyze relationships between the explanatory variables and the response
Predict Y based on the explanatory variables
Adjust for confounding variables

12. Probability

13. Romance Do these variables differ for males and females?
What variables help to predict romantic interest?
Do these variables differ for males and females?
All we need to figure this out is DATA!
(For all of you, being almost done with STAT 101, this is the case for many interesting questions!)

14. Speed Dating
We will use data from speed dating conducted at Columbia University,
276 males and 276 females from Columbia’s various graduate and professional schools
Each person met with people of the opposite sex for 4 minutes each
After each encounter each person said either “yes” (they would like to be put in touch with that partner) or “no”

15. Speed Dating Data What are the cases?
Students participating in speed dating
Speed dates
Ratings of each student

16. Speed Dating What is the population? Ideal population?
More realistic population?

17. Speed Dating
It is randomly determined who the students will be paired with for the speed dates.
We find that people are significantly more likely to say “yes” to people they think are more intelligent.
Can we infer causality between perceived intelligence and wanting a second date?
Yes No

18. Successful Speed Date?
What is the probability that a speed date is successful (results in both people wanting a second date)?
To best answer this question, we should use
Descriptive statistics
Confidence Interval
Hypothesis Test
Regression
Bayes Rule

19. Successful Speed Date?
63 of the 276 speed dates were deemed successful (both male and female said yes).
A 95% confidence interval for the true proportion of successful speed dates is
(0.2, 0.3)
(0.18, 0.28)
(0.21, 0.25)
(0.13, 0.33)

20. Pickiness and Gender
Are males or females more picky when it comes to saying yes?
Guesses?
Males
Females

21. Pickiness and Gender
Yes No
Males
146
130
Females
127
149
Are males or females more picky when it comes to saying yes? How could you answer this?
Test for a single proportion
Test for a difference in proportions
Chi-square test for association
ANOVA
Either (b) or (c)

22. Pickiness and Gender
Do males and females differ in their pickiness? Using α = 0.05, how would you answer this?
a) Yes b) No c) Not enough information

23. Reciprocity
Male says Yes
Male says No
Female says Yes 63 64
Female says No 83 66
Are people more likely to say yes to someone who says yes back? How would you best answer this?
Descriptive statistics
Confidence Interval
Hypothesis Test
Regression
Bayes Rule

24. Reciprocity
Male says Yes
Male says No
Female says Yes 63 64
Female says No 83 66
Are people more likely to say yes to someone who says yes back? How could you answer this?
Test for a single proportion
Test for a difference in proportions
Chi-square test for association
ANOVA
Either (b) or (c)

25. Reciprocity
Are people more likely to say yes to someone who says yes back?
p-value =
Based on this data, we cannot determine whether people are more likely to say yes to someone who says yes back.

26. Race and Response: Females
Does the chance of females saying yes to males differ by race?
How could you answer this question?
Test for a single proportion
Test for a difference in proportions
Chi-square goodness of fit
Chi-square test for association
ANOVA
Asian
Black
Caucasian
Latino
Other
0.50
0.57
0.42
0.48
0.53

27. Race and Response: Males
Each person rated their date on a scale of based on how much they liked them overall.
Does how much males like females differ by race?
How would you test this?
Chi-square test
t-test for a difference in means
Matched pairs test
ANOVA
Either (b) or (d)

28. Physical Attractiveness
Each person also rated their date from 1-10 on the physical attractiveness. Do males rate females higher, or do females rate males higher?
Which tool would you use to answer this question?
Two-sample difference in means
Matched pair difference in means
Chi-Square
ANOVA
Correlation

29. Physical Attractiveness
The histogram shown is of the
data
bootstrap distribution
randomization distribution
sampling distribution
𝑥 𝑀 − 𝑥 𝐹 =0.406
95% CI: (0.10, 0.71)
p-value =0.01

30. Other Ratings
Each person also rated their date from 1-10 on the following attributes:
Attractiveness
Sincerity
Intelligence
How fun the person seems
Ambition
Shared interests
Which of these best predict how much someone will like their date?

31. Multiple Regression
MALES RATING FEMALES:
FEMALES RATING MALES:

32. Ambition and Liking
Do people prefer their dates to be less ambitious???
How does the perceived ambition of a date relate to how much the date is liked?
How would you answer this question?
Inference for difference in means
ANOVA
Inference for correlation
Inference for simple linear regression
Either (b), (c) or (d)

33. Simple Linear Regression
MALES RATING FEMALES:
FEMALES RATING MALES:

34. Ambition and Liking r = 0.44, SE = 0.05 Find a 95% CI for .
Test whether 1 differs from 0.

35. ALL YOU NEED IS DATA!!! After taking STAT 101: Thank You!!!
If you have a question that needs answering…
ALL YOU NEED IS DATA!!!
Thank You!!!