Introduction to Statistics for the Social Sciences SBS

Introduction to Statistics for the Social Sciences SBS 200 - Lecture Section 001, Fall 2016 Room 150 Harvill Building 10: 00 - 10: 50 Mondays, Wednesdays & Fridays. http: //www. youtube. com/watch? v=o. SQJP 40 Pc. GI

Use this as your study guide By the end of lecture today 9/16/16 Characteristics of a distribution Central Tendency Dispersion Measures of variability Range Standard deviation Variance Memorizing the four definitional formulae

Schedule of readings Before next exam (September 23 rd) Please read chapters 1 - 5 in Open. Stax 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

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

Another example: How many kids in your family? 3 4 2 1 4 2 2 3 1 8

Standard deviation - Let’s do one This numerator is called “sum of squares” Definitional formula How many kids? Step 1: Find the mean _ X_ = 30 3 2 3 1 2 4 8 2 1 4 = 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 a) 38 / 10 = 3. 8 Σx = 30 This is the Variance! b) square root of 3. 8 = 1. 95 Each of these are deviation scores X- µ_ (X - 3 -3= 0 2 - 3 = -1 3 -3= 0 1 - 3 = -2 2 - 3 = -1 4 -3= 1 8 -3= 5 2 - 3 = -1 1 - 3 = -2 4 -3= 1 µ )2 0 1 0 4 1 1 25 1 4 1 Σ(x - µ) = 0 Σ(x - µ)2 = 38 Σ(x - µ) = 0 This is the standard deviation!

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

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

Raw scores, z scores & probabilities 68% 95% Please note spatially where 1 standard deviation falls on the curve 99. 7%

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

Summary of 7 facts to memorize

We estimated and calculated the standard deviation Now let’s use it as a measure of counting

Raw scores, z scores & probabilities z= Mean = 50 S = 10 -1 z= +1 1 sd above and below mean 68% If we go up one standard deviation z score = +1. 0 and raw score = 60 (Note S = standard deviation) If we go down one standard deviation z score = -1. 0 and raw score = 40

Raw scores, z scores & probabilities z= -2 Mean = 50 S = 10 z= 2 sd above and below mean 95% +2 If we go up two standard deviations z score = +2. 0 and raw score = 70 (Note S = standard deviation) If we go down two standard deviations z score = -2. 0 and raw score = 30

Raw scores, z scores & probabilities 3 sd above and below mean 99. 7% z= -3 Mean = 50 S = 10 z= +3 If we go up three standard deviations z score = +3. 0 and raw score = 80 (Note S = standard deviation) If we go down three standard deviations z score = -3. 0 and raw score = 20

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 3. Mike has a deviation score of -4: What does that tell us about Mike? • Is he taller or shorter than the mean? And by how much? • Are most people in the group taller or shorter than Mike 4. Diallo has a deviation score of 0: What does that tell us about Diallo? • Is he taller or shorter than the mean? And by how much? • Are most people in the group taller or shorter than Diallo? 5. Please write the formula for the standard deviation of a population 6. Please draw 3 curves showing 1, 2 & 3 standard deviations from mean

Writing Assignment – Pop Quiz 7. What does symbol refer to? • What isthis it called? • What does it mean? • Is it referring to a sample or population? 8. What doesisthis symbol refer to? • What it called? • What does it mean? • Is it referring to a sample or population? 9. What does this symbol refer to? • What is it called? • What does it mean? • Is it referring to a sample or population? 10. What does this symbol refer to? • What is it called? • What does it mean? • Is it referring to a sample or population? 11. What does this symbol refer to?

Writing Assignment – Pop Quiz • What are they 12. What does this refer to? called? • What do they refer to? • How are they 13. • What does refer to? What arethis they different called? • How are they different 14. What do these two refer to? • What are they called? • How are they different 15. What does this refer to? • What is it called? • Use it for sample data or population? • “We lose a degree of freedom for every ______”

Writing Assignment – Pop Quiz • What are they 16. What does this refer to? called? • What do they refer to? • How are they different • What are they 17. What does this refer to? called? • What do they refer to? • How are they different

Writing Assignment – Pop Quiz 1. What is a “deviation score” How fa s r aw re f 2: ay i 2. Preston has a deviation scorecoof does that tell us about Preston? rom What s e ah the • Is he taller or shorter than the mean? by how much? Pre mea c. And ston n? mea is 2” • Are most people in the group taller or shorter than Preston n (t talle a l l 3. Mike has a deviation score of -4: What does that tell us about Mike? er t r tha han n th m M • Is he taller or shorter than the mean? i. And ost) e ke i by how much? mea s 4” s • Are most people in the group taller or shorter n (s hort than Mike e h h er t r ttell 4. Diallo has a deviation score of 0: What doesortthat about Diallo? han an thus e mos much? • Is he taller or shorter than the mean? And by how t) Dia • Are most people in the group taller orllo shorter than Diallo? is e xac tly 5. Please write the formula for the standard(hadeviation of a population lf ta same ller heig 6. Please draw 3 curves showing 1, 2 & 3 standard from mean ha deviations h lf sh t orte as me an r)

Writing Assignment – Pop Quiz 7. What does symbol refer to? • What isthis it called? sigm a o • What does it mean? lati u p po or • Is it referring to a sample n population? 8. What doesisthis symbol refer to? • What it called? mu o • What does it mean? lati u p po n or • Is it referring to a sample population? 9. What does this symbol refer to? • What is it called? x-ba r • What does it mean? le amp s • Is it referring to a sample or population? 10. What does this symbol refer to? • What is it called? s • What does it mean? ple sam • Is it referring to a sample or population? 11. What does this symbol refer to? Th es dev tanda (po iati rd pul on ati on) Th (po e me a pul ati n on ) Th e (sa mean mp le) Th es dev tanda (sa iation rd mp le) Each in dividua l score

Writing Assignment – Pop Quiz o ti a ul p po n sa m pl e e • What are they pl m 12. What does this refer to? sa called? • What do they refer Variance to? Sigm S a sq uarosequa • How are they e i d red pl 13. • What does this refer to? at l What are they m different pu n sa o p called? Deviation • How are they scores o different ti a l 14. What do these two refer to? pu n o p • What are they called? Sum of • How are they different squares 15. What does this refer to? Degrees of • What is it called? • Use it for sample data or population? freedom • “We lose a degree of freedom for every parameter we estimate”

rd a d n a t S iation v De Writing Assignment – Pop Quiz pl e o ti la pu n m po sa ce n ia r Va m pl e o ti la pu n sa po • What are they 16. What does this refer to? called? • What do they refer to? • How are they different • What are they 17. What does this refer to? called? • What do they refer to? • How are they different

rd a d n a t S iation v De Writing Assignment – Pop Quiz pl e o ti la pu n m po sa ce n ia r Va m pl e o ti la pu n sa po • What are they 10. What does this refer to? called? • What do they refer to? • How are they different • What are they 11. What does this refer to? called? • What do they refer to? • How are they different