Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Spring 2016 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays Welcome http://www.youtube.com/watch?v=oSQJP40PcGI

By the end of lecture today 2/5/16 Use this as your study guide By the end of lecture today 2/5/16 Characteristics of a distribution Central Tendency Dispersion Measures of variability Range Standard deviation Variance Memorizing the four definitional formulae Empirical Rule for Normal Curve (68% vs 95% vs 99.7%)

Schedule of readings Before next exam (February 12th) Please read chapters 1 - 5 in OpenStax textbook Please read Appendix D, E & F online On syllabus this is referred to as online readings 1, 2 & 3 Please read Chapters 1, 5, 6 and 13 in Plous Chapter 1: Selective Perception Chapter 5: Plasticity Chapter 6: Effects of Question Wording and Framing Chapter 13: Anchoring and Adjustment

Lab sessions Everyone will want to be enrolled in one of the lab sessions Labs continue next week

Project 1 - Likert Scale - Correlations - Comparing two means (bar graph) Questions?

Homework due Monday, Feb 8th On class website: please print and complete homework worksheet # 7 & 8 Calculating Descriptive Statistics And Presenting Findings in a Memorandum

Review From the lab review IV: Nominal IV: Nominal Ordinal Interval or Ratio? Independent Variable? Type of Cow Chow Mariska works at a cattle ranch, and wants cattle to gain as much weight as possible. Mariska wants to know if the new feed makes a difference in how much weight the cattle gain. She gathers the first 100 cows that she finds in the meadow, and then randomly assigns those 100 cows into two groups (50 each group) One group gets the new feed for 6 months, while the other group of cattle gets the old feed. She is not looking for any trends over time, but is just looking for a difference between the two types of cow chow (feed). IV: Continuous or discrete? IV: Discrete Random Sampling? No, only convenience sampling Random Assignment (True Expt) Random Assignment? DV: Ratio DV: Nominal Ordinal Interval or Ratio? Dependent Variable? Weight DV: Continuous or discrete? DV: Continuous Between or within? Between Participant Design Cross Sectional Cross Sectional or Time Series Review

Overview Frequency distributions The normal curve Mean, Median, Mode, Trimmed Mean Standard deviation, Variance, Range Mean Absolute Deviation Skewed right, skewed left unimodal, bimodal, symmetric

How far away is each score from the mean? Standard deviation: The average amount by which observations deviate on either side of their mean Deviation scores (x - µ) Diallo is 0” Preston is 2” How far away is each score from the mean? Mike is -4” Hunter is -2 Shea is 4 Mean David is 0” Add up Deviation scores Diallo Preston Σ (x - µ) = ? Shea Mike 5’8” - 6’0” = - 4” 5’9” - 6’0” = - 3” 5’10’ - 6’0” = - 2” 5’11” - 6’0” = - 1” 6’0” - 6’0 = 0 6’1” - 6’0” = + 1” 6’2” - 6’0” = + 2” 6’3” - 6’0” = + 3” 6’4” - 6’0” = + 4” How do we find the average height? N Σx = average height How do we find the average spread? Σ(x - x) = 0 Σ(x - µ) N = average deviation Σ(x - µ) = 0 Review

How far away is each score from the mean? Standard deviation: The average amount by which observations deviate on either side of their mean Deviation scores (x - µ) Diallo is 0” Preston is 2” How far away is each score from the mean? Mike is -4” Hunter is -2 Shea is 4 Mean David is 0” Diallo Preston Σ (x - µ) = ? Shea Mike 5’8” - 6’0” = - 4” 5’9” - 6’0” = - 3” 5’10’ - 6’0” = - 2” 5’11” - 6’0” = - 1” 6’0” - 6’0 = 0 6’1” - 6’0” = + 1” 6’2” - 6’0” = + 2” 6’3” - 6’0” = + 3” 6’4” - 6’0” = + 4” Square the deviations Big problem Σ(x - x) 2 2 Σ(x - x) = 0 Σ(x - µ) N Σ(x - µ) 2 Σ(x - µ) = 0 Review

These would be helpful to know by heart – please memorize Standard deviation: The average amount by which observations deviate on either side of their mean These would be helpful to know by heart – please memorize these formula Review

What do these two formula have in common? Standard deviation: The average amount by which observations deviate on either side of their mean What do these two formula have in common? Review

What do these two formula have in common? Standard deviation: The average amount by which observations deviate on either side of their mean What do these two formula have in common? Review

How do these formula differ? Standard deviation: The average amount by which observations deviate on either side of their mean “n-1” is Degrees of Freedom” How do these formula differ? Review

Standard deviation - Let’s do one Definitional formula How many kids? Step 1: Find the mean X - µ_ 3 - 3 = 0 2 - 3 = -1 1 - 3 = -2 4 - 3 = 1 8 - 3 = 5 (X - µ)2 1 4 25 _ X_ 3 2 1 4 8 = 30 = 30/10 = 3 Step 2: Subtract the mean from each score (deviations) Step 3: Square the deviations Step 4: Add up the squared deviations Step 5: Find standard deviation Σ(x - µ) = 0 Σx = 30 Σ(x - µ)2 = 38 This is the Variance! a) 38 / 10 = 3.8 b) square root of 3.8 = 1.95 This is the standard deviation!

“Sum of Squares” “Sum of Squares” “Sum of Squares” “Sum of Squares” Standard deviation: The average amount by which observations deviate on either side of their mean “Sum of Squares” “Sum of Squares” “Sum of Squares” “Sum of Squares” Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David 0” Preston is 2” Deviation scores “n-1” is “Degrees of Freedom” “n-1” is “Degrees of Freedom” Remember, it’s relative to the mean Generally, (on average) how far away is each score from the mean? Based on difference from the mean Mean Remember, We are thinking in terms of “deviations” Diallo Please memorize these Preston Shea Mike

Raw scores, z scores & probabilities Please note spatially where 1 standard deviation falls on the curve

These would be helpful to know by heart – please memorize areas 1 sd above and below mean 68% 2 sd above and below mean 95% 3 sd above and below mean 99.7% These would be helpful to know by heart – please memorize areas

Raw scores, z scores & probabilities Please note spatially where 1 standard deviation falls on the curve 68% 95% 99.7%

Summary of 7 facts to memorize

Writing Assignment – Pop Quiz 1. What is a “deviation score” 2. Preston has a deviation score of 2: What does that tell us about Preston? Is he taller or shorter than the mean? And by how much? Are most people in the group taller or shorter than Preston Mike has a deviation score of -4: What does that tell us about Mike? Are most people in the group taller or shorter than Mike Diallo has a deviation score of 0: What does that tell us about Diallo? Are most people in the group taller or shorter than Diallo? Please write the formula for the standard deviation of a population Please draw 3 curves showing 1, 2 & 3 standard deviations from mean

Writing Assignment – Pop Quiz 1. What is a “deviation score” 2. Preston has a deviation score of 2: What does that tell us about Preston? Is he taller or shorter than the mean? And by how much? Are most people in the group taller or shorter than Preston Mike has a deviation score of -4: What does that tell us about Mike? Are most people in the group taller or shorter than Mike Diallo has a deviation score of 0: What does that tell us about Diallo? Are most people in the group taller or shorter than Diallo? Please write the formula for the standard deviation of a population Please draw 3 curves showing 1, 2 & 3 standard deviations from mean How far away is each score from the mean? Preston is 2” taller than the mean (taller than most) Mike is 4” shorter than the mean (shorter than most) Diallo is exactly same height as mean (half taller half shorter)

Thank you! See you next time!!