Lecturer’s desk INTEGRATED LEARNING CENTER ILC 120 Screen Row A Row B Row C Row D Row E Row F Row G Row H Row I Row J Row K Row L Computer Storage Cabinet Cabinet Table broken desk

Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Fall, 2014 Room 120 Integrated Learning Center (ILC) 10: :50 Mondays, Wednesdays & Fridays.

Reminder A note on doodling

Labs continue this week

Schedule of readings Before next exam (October 17 th ) Please read chapters 5, 6, & 8 in Ha & Ha Please read Chapters 10, 11, 12 and 14 in Plous Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability and Risk Chapter 14: The Perception of Randomness

By the end of lecture today 10/15/14 Use this as your study guide Central Limit Theorem Law of Large Numbers Dan Gilbert Readings Review for Exam 2

No homework due Just study for Exam 2

Exam 2 – This Friday (10/17/14) Study guide is online now Bring 2 calculators (remember only simple calculators, we can’t use calculators with programming functions) Bring 2 pencils (with good erasers) Bring ID

Dan Gilbert Reading Hand in homework

Proposition 1: If sample size ( n ) is large enough (e.g. 100) The mean of the sampling distribution will approach the mean of the population Central Limit Theorem Proposition 2: If sample size ( n ) is large enough (e.g. 100) The sampling distribution of means will be approximately normal, regardless of the shape of the population XXXXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXX XXXXXX XXXX XXXX X X XXXXXXXXXX XXXXXXXXXX X XXXXXXXXXX Proposition 3: The standard deviation of the sampling distribution equals the standard deviation of the population divided by the square root of the sample size. As n increases SEM decreases. As n ↑ x will approach µ As n ↑ curve will approach normal shape As n ↑ curve variability gets smaller

Proposition 1: If sample size ( n ) is large enough (e.g. 100) The mean of the sampling distribution will approach the mean of the population Central Limit Theorem Law of large numbers: As the number of measurements increases the data becomes more stable and a better approximation of the true (theoretical) probability. Larger sample sizes tend to be associated with stability. As the number of observations ( n ) increases or the number of times the experiment is performed, the estimate will become more accurate.

Proposition 2: If sample size (n) is large enough (e.g. 100), the sampling distribution of means will be approximately normal, regardless of the shape of the population population sampling distribution n = 5 sampling distribution n = 30 sampling distribution n = 2 sampling distribution n = 5 sampling distribution n = 4 sampling distribution n = 25 Population Take sample (n = 5) – get mean Repeat over and over

Central Limit Theorem Proposition 2: If sample size (n) is large enough (e.g. 100) The sampling distribution of means will be approximately normal, regardless of the shape of the population

Central Limit Theorem Proposition 2: If sample size (n) is large enough (e.g. 100) The sampling distribution of means will be approximately normal, regardless of the shape of the population

Central Limit Theorem Proposition 2: If sample size (n) is large enough (e.g. 100) The sampling distribution of means will be approximately normal, regardless of the shape of the population

Central Limit Theorem XXXXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXX XXXXXX XXXX XXXX X X XXXXXXXXXX XXXXXXXXXX X XXXXXXXXXX Proposition 3: The standard deviation of the sampling distribution equals the standard deviation of the population divided by the square root of the sample size. As n increases SEM decreases.

Proposition 1: If sample size ( n ) is large enough (e.g. 100) The mean of the sampling distribution will approach the mean of the population Central Limit Theorem Proposition 2: If sample size ( n ) is large enough (e.g. 100) The sampling distribution of means will be approximately normal, regardless of the shape of the population XXXXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXX XXXXXX XXXX XXXX X X XXXXXXXXXX XXXXXXXXXX X XXXXXXXXXX Proposition 3: The standard deviation of the sampling distribution equals the standard deviation of the population divided by the square root of the sample size. As n increases SEM decreases. As n ↑ x will approach µ As n ↑ curve will approach normal shape As n ↑ curve variability gets smaller

Central Limit Theorem: If random samples of a fixed N are drawn from any population (regardless of the shape of the population distribution), as N becomes larger, the distribution of sample means approaches normality, with the overall mean approaching the theoretical population mean. Animation for creating sampling distribution of sample means Eugene Melvin Mean for sample 12 Mean for sample 7 Distribution of Raw Scores Sampling Distribution of Sample means Distribution of single sample Sampling Distribution of Sample means

Central Limit Theorem: If random samples of a fixed N are drawn from any population (regardless of the shape of the population distribution), as N becomes larger, the distribution of sample means approaches normality, with the overall mean approaching the theoretical population mean. Sampling distribution for continuous distributions XXXXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXX XXXXXX XXXX XXXX X X XXXXXXXXXX XXXXXXXXXX X XXXXXXXXXX Melvin Eugene Sampling Distribution of Sample means Distribution of Raw Scores 2 nd sample 23 rd sample

Proposition 1: If sample size ( n ) is large enough (e.g. 100) The mean of the sampling distribution will approach the mean of the population Central Limit Theorem Proposition 2: If sample size ( n ) is large enough (e.g. 100) The sampling distribution of means will be approximately normal, regardless of the shape of the population XXXXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXX XXXXXX XXXX XXXX X X XXXXXXXXXX XXXXXXXXXX X XXXXXXXXXX Proposition 3: The standard deviation of the sampling distribution equals the standard deviation of the population divided by the square root of the sample size. As n increases SEM decreases. As n ↑ x will approach µ As n ↑ curve will approach normal shape As n ↑ curve variability gets smaller

. Writing Assignment: Writing a letter to a friend Imagine you have a good friend (pick one). This is a good friend whom you consider to be smart and interested in stuff generally. They are teaching themselves stats (hoping to test out of the class) but need your help on a couple ideas. For this assignment please write your friend/mom/dad/ favorite cousin a letter answering these five questions: (Feel free to use diagrams and drawings if you think that can help) Dear Friend, 1. I’m struggling with this whole Central Limit Theorem idea. Could you describe for me the difference between a distribution of raw scores, and a distribution of sample means? 2. I also don’t get the “three propositions of the Central Limit Theorem”. They all seem to address sample size, but I don’t get how sample size could affect these three things. If you could help explain it, that would be really helpful.

. Imagine you have a good friend (pick one). This is a good friend whom you consider to be smart and interested in stuff generally. They are teaching themselves stats (hoping to test out of the class) but need your help on a couple ideas. For this assignment please write your friend/mom/dad/ favorite cousin a letter answering these five questions: (Feel free to use diagrams and drawings if you think that can help) Dear Friend, 1. I’m struggling with this whole Central Limit Theorem idea. Could you describe for me the difference between a distribution of raw scores, and a distribution of sample means? 2. I also don’t get the “three propositions of the Central Limit Theorem”. They all seem to address sample size, but I don’t get how sample size could affect these three things. If you could help explain it, that would be really helpful.