Introduction to Statistics for the Social Sciences

1. Introduction to Statistics for the Social SciencesSBS200, COMM200, GEOG200, PA200, POL200, or SOC200Lecture Section 001, Fall 2015Room 150 Harvill Building10:00 - 10:50 Mondays, Wednesdays & Fridays. Welcome

2. Lab sessions Everyone will want to be enrolled in one of the lab sessions Lab continue this week, Project 1

3. Project 1- Likert Scale- Correlations- Comparing two means (bar graph)

4. Project 1- Likert Scale- Correlations- Comparing two means (bar graph)

5. Project 1- Likert Scale- Correlations- Comparing two means (bar graph)

7. Homework Assignment No new homework assignments (Time to get caught up if you’ve fallen behind)

8. Homework Assignment Using Excel ?

9. Homework Assignment Using Excel

10. More information on registering clickers coming soon

11. Schedule of readings Before next exam (September 25th) Please read chapters 1 - 5 in OpenStax textbook Please read Appendix D, E & F onlineOn 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

12. IV: Nominal IV: Nominal Ordinal Interval or Ratio? Type of Cow Chow Independent Variable? From the lab review 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: Discrete IV: Continuous or discrete? No, only convenience sampling Random Sampling? Random Assignment? Random Assignment (True Expt) DV: Ratio DV: Nominal Ordinal Interval or Ratio? Weight Dependent Variable? DV: Continuous DV: Continuous or discrete? Between Participant Design Between or within? Cross Sectional Cross Sectional or Time Series Review

14. Deviation scores Deviation scores: The amount by which observations deviate on either side of their mean (x- µ) (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 Deviation score Mike Preston (x - µ) = ? Shea Hunter 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” Diallo How do we find each deviation score? (x- µ) Preston Hunter Diallo Mike Preston Find distance of each person from the mean (subtract their score from mean) Review

15. Deviation scores Deviation scores: The amount by which observations deviate on either side of their mean (x- µ) (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 Deviation score Preston (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” Remember It’s relative to the mean Based on difference from the mean Review

16. Σ(x - x) = 0 Deviation scores Standard deviation: The average amount by which observations deviate on either side of their mean (x- µ) Diallo is 0” Preston is 2” Mike is -4” How far away is each score from the mean? 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? = average height Σx N How do we find the average spread? Σ(x - µ) = average deviation Σ(x - µ) = 0 Review N

17. Σ(x - x) = 0 Σ(x - x) Deviation scores Standard deviation: The average amount by which observations deviate on either side of their mean (x- µ) Diallo is 0” Preston is 2” Mike is -4” How far away is each score from the mean? Hunter is -2 Shea is 4 Mean David is 0” Diallo Preston Σ(x - µ) = ? Shea 2 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 2 Σ(x - µ) 2 Σ(x - µ) Σ(x - µ) = 0 Review N

18. 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

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

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

21. 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

22. Standard deviation(definitional formula) - Let’s do one This numerator is called “sum of squares” Each of these are deviation scores _ X - µ_ 1 - 5 = - 4 2 - 5 = - 3 3 - 5 = - 2 4 - 5 = - 1 5 - 5 = 0 6 - 5 = 1 7 - 5 = 2 8 - 5 = 3 9 - 5 = 4 0 (X - µ)2 16 9 4 1 0 1 4 9 16 60 Step 1: Find the mean _ X_ 1 2 3 4 5 6 7 8 9 45 ΣX = 45 ΣX / N = 45/9 = 5 Step 2:Subtract the mean from each score Step 3:Square the deviations Step 4:Find standard deviation a) 60 / 9 = 6.6667 This is the Variance! b) square root of 6.6667 = 2.5820 Σ(x - µ) = 0 This is the standard deviation!

23. 2 sd above and below mean 95% 1 sd above and below mean 68% 3 sd above and below mean 99.7% These would be helpful to know by heart – please memorize areas

24. Summary of 7 facts to memorize

25. Thank you! See you next time!!