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 (November 6 th ) Please read chapters 7 – 11 in Ha & Ha Please read Chapters 2, 3, and 4 in Plous Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence

Homework due – Wednesday (October 22 nd ) On class website: Please print and complete homework worksheet #14 Calculating Confidence Intervals

By the end of lecture today 10/20/14 Use this as your study guide Confidence Intervals

Raw Scores Area & Probability Z Scores Formula z table Have raw score Find z Have z Find raw score Have area Find z Have z Find area Normal distribution Raw scores z-scores probabilities

. 75 th percentile Go to table.2500 nearest z =.67 x = mean + z σ = 30 + (.67)(2) = z =.67

. 25 th percentile Go to table.2500 nearest z = -.67 x = mean + z σ = 30 + (-.67)(2) = z = -.67

Variability and means What might the standard deviation be? The variability is different…. The mean is the same … Remember to keep number lines same for both examples

Variability and means What might this be an example of? What might the standard deviation be? Other examples? Grades Grades Grades of “C” students Grades of all students in the class

Variability and means Remember, there is an implied axis measuring frequency f f Remember to keep number lines equally spaced Variable must be numeric Remember to keep number lines same for both examples

Variability and means What might this be an example of? What might the standard deviation be? Other examples? Birth weight in pounds Birth weight in pounds Notice: number lines equally spaced Birth weight for infants From entire population Birth weight for infants from a “typical family”

Variability and means Distributions same mean different variability Final exam scores “C” students versus whole class Birth weight within a typical family versus within the whole community Running speed 30 year olds vs. 20 – 40 year olds Number of violent crimes Milwaukee vs. whole Midwest Social distance (personal space) California vs international community

Variability and means Distributions different mean same variability Performance on a final exam Before versus after taking the class Score on final (before taking class) Notice: number lines equally spaced

Variability and means Distributions different mean same variability Inches in height (women) Height of men versus women Inches in height (men) Notice: number lines equally spaced

Variability and means Distributions different mean same variability Number of errors (not on phone) Driving ability Talking on a cell phone or not Number of errors (on phone) Notice: number lines equally spaced

Variability and means Comparing distributions different mean same variability Performance on a final exam Before versus after taking the class Height of men versus women Driving ability Talking on a cell phone or not Notice: number lines equally spaced

. Writing Assignment Comparing distributions (mean and variability) Think of examples for these three situations same mean but different variability same variability but different means same mean and same variability (different groups) estimate standard deviation calculate variance for each curve find the raw score for the z’s given Remember: number lines equally spaced

. Writing Assignment Comparing distributions (mean and variability) Think of examples for these three situations same mean but different variability same variability but different means same mean and same variability (different groups) estimate standard deviation calculate variance for each curve find the raw score for the z’s given

. Please find the raw scores that border the middle 99% of the curve Please find the raw scores that border the middle 95% of the curve 95% Confidence Interval: We can be 95% confident that the estimated score really does fall between these two scores 99% Confidence Interval: We can be 99% confident that the estimated score really does fall between these two scores

We now know all components of actually calculating confidence intervals: When to use confidence intervals: when you are estimating (guessing) a single number by providing likely range that the number appears in How to calculate confidence intervals Simply finding the raw score that is a certain distance from the mean that is associated with an area under the curve The relevance of the Central Limit Theorem When we are predicting a value we will use the standard error of the mean (rather than the standard deviation) Standard Error of the Mean (SEM)

Confidence Intervals (based on z): We are using this to estimate a value such as a population mean, with a known degree of certainty with a range of values The interval refers to possible values of the population mean. We can be reasonably confident that the population mean falls in this range (90%, 95%, or 99% confident) In the long run, series of intervals, like the one we figured out will describe the population mean about 95% of the time. Can actually generate CI for any confidence level you want – these are just the most common Standard Error of the Mean (SEM) Greater confidence implies loss of precision. (95% confidence is most often used) Subjective vs Empirical

Confidence Intervals (based on z): A range of values that, with a known degree of certainty, includes an unknown population characteristic, such as a population mean How can we make our confidence interval smaller? Decrease Variability Increase sample size (This will decrease variability) Decrease level of confidence Decrease variability through more careful assessment and measurement practices (minimize noise). 95%

1) Go to z table - find z score for for area.4750 z = 1.96 Mean = 50 Standard deviation = 10 Find the scores for the middle 95% ? ? ? 95% 2) x = mean + (z)(standard deviation) x = 50 + (-1.96)(10) x = ) x = mean + (z)(standard deviation) x = 50 + (1.96)(10) x = Please note: We will be using this same logic for “confidence intervals” x = mean ± (z)(standard deviation) Scores capture the middle 95% of the curve

Mean = 50 Standard deviation = 10 n = 100 s.e.m. = 1 Find the scores for the middle 95% ? ? ? 95% x = mean ± (z)(s.e.m.) x = 50 + (1.96)(1) x = % Confidence Interval is captured by the scores – Confidence intervals For “confidence intervals” same logic – same z-score But - we’ll replace standard deviation with the standard error of the mean standard error of the mean σ n = = x = 50 + (-1.96)(1) x = 48.04

Confidence intervals Tell me the scores that border exactly the middle 95% of the curve Construct a 95 percent confidence interval around the mean ?? 95% We know this Similar, but uses standard error the mean based on population s.d. raw score = mean ± (z score)(s.d.) raw score = mean ± (z score)(s.e.m.)

Confidence intervals Tell me the scores that border exactly the middle 95% of the curve - use z score of 1.96 Construct a 95 percent confidence interval around the mean z scores for different levels of confidence Level of Alpha 1.96 = = =.10 90% How do we know which z score to use?

Confidence interval uses SEM