Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Fall 2015 Room 150 Harvill Building 10: :50 Mondays, Wednesdays & Fridays.

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

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

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

Homework Assignment Using Excel ?

Homework Assignment Using Excel

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Schedule of readings Before next exam (September 25 th ) Please read chapters 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

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

How do we find each deviation score? 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” Deviation scores: The amount by which observations deviate on either side of their mean (x - µ ) = ? Diallo Mike Hunter Preston Mean Mike Shea Preston Diallo How far away is each score from the mean? ( x - µ ) Diallo Mike Hunter Preston Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David is 0” Preston is 2” Deviation scores ( x - µ ) Find distance of each person from the mean (subtract their score from mean) ( x - µ ) Deviation score Rev iew

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” Deviation scores: The amount by which observations deviate on either side of their mean (x - µ ) = ? Mean Mike Shea Preston Diallo How far away is each score from the mean? Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David is 0” Preston is 2” Deviation scores ( x - µ ) Based on difference from the mean Remember It’s relative to the mean ( x - µ ) Deviation score Rev iew

How do we find the average height? 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” Standard deviation: The average amount by which observations deviate on either side of their mean Σ(x - x) = 0 Σ (x - µ ) = ? Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David is 0” Preston is 2” Deviation scores Σ(x - µ ) = 0 = average height N ΣxΣx = average deviation Σ(x - µ ) N How do we find the average spread? Mean Mike Shea Preston Diallo How far away is each score from the mean? ( x - µ ) Add up Deviation scores Rev iew

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

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 Rev iew

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

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

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

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

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%

Summary of 7 facts to memorize