SLIDE 1 Unit 1: Introduction to data
- 3. Introduction to statistical inference
Sta 101 - Spring 2015
Duke University, Department of Statistical Science
January 22, 2015
Slides posted at http://bitly.com/windle2
To do:
▶ Performance Assessment 1: by 11:59pm on Friday. ▶ Problem Set 3: by next Thursday before class. ▶ Lab 2: by next Wednesday. ▶ Readiness Assessment 2: next Tuesday in class.
My OH today: 4:30-6pm.
1
Themes/Ideas/Tools of the day
Today: probability fundamentals and their connection to inference. Ideas:
- 1. Proportion and probability are connected.
- 2. A bucket of cards.
- 3. Larger random samples provide more reliable information.
- 4. In statistics, you often need to think about how you would
act/decide before seeing the actual data. Tools:
- 1. probability distribution / probability mass function
- 2. bar plot
- 3. h-plot
2
Definition of probability
Probability:
- 1. The chance that something will happen.
- 2. A branch of mathematics that studies chance.
- 3. The long-run relative frequency of an event.
3
SLIDE 2 Idea: Proportion and probability are intimately connected.
Examples:
▶ A coin ▶ A die
4
For categorical or discrete numerical variables:
Tool: A “probability distribution” or a “probability mass function” is a table that describes the possible outcomes of a random process and the probabilities of those possible
Rolling a die possible outcomes 1 2 3 4 5 6 probability 1/6 1/6 1/6 1/6 1/6 1/6
5
Visualizations
6
Visualizations
7
SLIDE 3
Probability and proportion
Rolling a die possible outcomes 1 2 3 4 5 6 probability 1/6 1/6 1/6 1/6 1/6 1/6 relative frequency table Number of dots 1 2 3 4 5 6 Relative Frequency 1/6 1/6 1/6 1/6 1/6 1/6
8
Visualizations
9
Visualizations
10
Cards analogy
Clicker question
What proportion of cards are red? (b) 1/6 (b) 1/2 (b) 13/52 (b) 4/52
11
SLIDE 4
Cards analogy
Clicker question
What is the probability of drawing a face card? (a) 12/52 (b) 16/52 (c) 26/52 (d) 13/52
12
Question: If we think of this deck of cards as a population what are the attributes/variables of interest? Case Suit Number Color 1 Clubs Ace Black 2 Clubs 2 Black 3 Clubs 3 Black . . . . . . . . . . . . 51 Diamonds Queen Red 52 Diamonds King Red
13
Idea: Lots of things in statistics can be thought of as a deck of cards / a bucket of cards.
Example: Duke students.
14
Sample size demo Rolling two dice 1 2 3 4 5 6 1 1,1 1,2 1,3 1,4 1,5 1,6 2 2,1 2,2 2,3 2,4 2,5 2,6 3 3,1 3,2 3,3 3,4 3,5 3,6 4 4,1 4,2 4,3 4,4 4,5 4,6 5 5,1 5,2 5,3 5,4 5,5 5,6 6 6,1 6,2 6,3 6,4 6,5 6,6 Rolling two dice and summing 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 12
15
SLIDE 5 Application Exercise 1.4b: bitly.com/windle2
16
Asch conformity experiments
Idea: In statistics, you often need to think about how you would act before seeing the actual data.
17
Asch conformity experiments
18
Asch conformity experiments
Null hypothesis: there is a little conformity.
- Alt. hypothesis: there is more than a little conformity.
19
SLIDE 6
Asch conformity experiments
H0: proportion of the population that will conform is 0.1. HA: proportion of the population that will conform is > 0.1.
20
Asch conformity experiments
H0: proportion of the population that will conform is 0.1. HA: proportion of the population that will conform is 0.3.
21
Asch conformity experiments
Question: based on these plots, how many conformers do you need to see before you reject the null?
22
Asch conformity experiments
Often we ask ourselves: How can I avoid making the wrong decision in the case that the null hypothesis is true?
23
SLIDE 7
We decide to reject based on seeing a relatively unlikely observation. This is ONE WAY to come up with a PROCEDURE for deciding to stick with/reject the null.
24
