Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2017 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays. Welcome http://www.youtube.com/watch?v=oSQJP40PcGI http://www.youtube.com/watch?v=oSQJP40PcGI

A note on doodling

Before next exam (March 3rd) Schedule of readings Before next exam (March 3rd) Please read chapters 1 - 8 in OpenStax textbook Please read Chapters 10, 11, 12 and 14 in Plous Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability and Risk Chapter 14: The Perception of Randomness

By the end of lecture today 2/17/17 Counting ‘standard deviationses’ – z scores Connecting raw scores, z scores and probability Connecting probability, proportion and area of curve Percentiles

No New Homework Assignment Just review assignments 10 & 11 Finding z scores and areas under the curve. Both extended to Monday, February 20th

Lab sessions Everyone will want to be enrolled in one of the lab sessions Labs continue With Project 2

Hand out z tables

z score = raw score - mean standard deviation If we go up one standard deviation z score = +1.0 and raw score = 105 z = -1 z = +1 68% If we go down one standard deviation z score = -1.0 and raw score = 95 85 90 95 100 105 110 115 If we go up two standard deviations z score = +2.0 and raw score = 110 z = -2 95% z = +2 If we go down two standard deviations z score = -2.0 and raw score = 90 85 90 95 100 105 110 115 If we go up three standard deviations z score = +3.0 and raw score = 115 99.7% z = -3 z = +3 If we go down three standard deviations z score = -3.0 and raw score = 85 85 90 95 100 105 110 115 z score: A score that indicates how many standard deviations an observation is above or below the mean of the distribution z score = raw score - mean standard deviation

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

Always draw a picture! Homework worksheet

1 .6800 1 sd 1 sd 28 30 32 Homework worksheet .6800 also fine: 68% z =-1 z = 1 28 30 32

2 .9500 2 sd 2 sd 26 28 30 32 34 Homework worksheet .9500 also fine: 95% also fine: .9544 .9500 2 sd 2 sd z =-2 z = 2 26 28 30 32 34

3 .9970 3 sd 3 sd 24 26 28 30 32 34 36 Homework worksheet .9970 also fine: 99.7% also fine: .9974 .9970 3 sd 3 sd z =-3 z = 3 24 26 28 30 32 34 36

4 .5000 24 26 28 30 32 34 36 Homework worksheet .5000 also fine: 50% z = 0 24 26 28 30 32 34 36

5 .4332 24 26 28 30 32 34 36 Homework worksheet z = 33-30 z = 1.5 Go to table .4332 2 5 also fine: 43.32% .4332 z = 1.5 24 26 28 30 32 34 36

z = 33-30 2 z = 1.5 Go to table .4332 Add area Lower half .4332 + .5000 = .9332 6 also fine: 93.32% .9332 .4332 .5000 z = 1.5 24 26 28 30 32 34 36

7 .4332 .0668 24 26 28 30 32 34 36 Homework worksheet z = 33-30 = 1.5 = 1.5 Go to table .4332 Subtract from .5000 .5000 - .4332 = .0668 2 7 also fine: 6.68% .4332 .0668 z = 1.5 24 26 28 30 32 34 36

z = 29-30 2 = -.5 Go to table .1915 Add to upper Half of curve .5000 - .1915 = .6915 8 also fine: 69.15% .6915 .1915 .5000 z = -.5 24 26 28 30 32 34 36

= 25-30 2 = -2.5 .4938 Go to table = 31-30 2 =.5 .1915 Go to table .4938 + .1915 = .6853 9 also fine: 68.53% .6853 .1915 .4938 z =-2.5 z = .5 24 26 28 30 32 34 36

z = 27-30 2 = -1.5 Go to table .4332 Subtract From .5000 .5000 - .4332 = .0668 10 also fine: 6.68% .5000 .0668 .4332 z =-1.5 24 26 28 30 32 34 36

z = 25-30 2 = -2.5 Go to table .4938 Add lower Half of curve .5000 + .4938 = .9938 11 also fine: 99.38% .9938 .5000 .4938 z =-2.5 24 26 28 30 32 34 36

z = 32-30 2 = 1.0 Go to table .3413 Subtract from .5000 .5000 - .3413 = .1587 12 .5000 also fine: 15.87% .1587 .3413 z =1 24 26 28 30 32 34 36

13 24 26 28 30 32 34 36 50th percentile = median 30 In a normal curve Median= Mean = Mode z =0 24 26 28 30 32 34 36

28 32 14 .6800 1 sd 1 sd z =-1 z = 1 24 26 28 30 32 34 36

z table provides area from mean to score x = mean + z σ = 30 + (.74)(2) = 31.48 77th percentile Find area of interest .7700 - .5000 = .2700 Find nearest z = .74 15 .2700 .7700 z table provides area from mean to score .5000 31.48 z =.74 24 ? 30 36

z table provides area from mean to score 13th percentile Find area of interest .5000 - .1300 = .3700 Find nearest z = -1.13 x = mean + z σ = 30 + (-1.13)(2) = 27.74 16 Note: .13 +.37 =.50 z table provides area from mean to score .3700 .1300 z =-1.13 27.74 ? 24 30 36

Please use the following distribution with a mean of 200 and a standard deviation of 40. 80 120 160 200 240 280 320

17 .6800 1 sd 1 sd 160 200 240 .6800 also fine: 68% also fine: .6826 z =-1 z = 1 160 200 240

18 .9500 2 sd 2 sd 120 200 280 .9500 also fine: 95% also fine: .9544 z =-2 z = 2 120 200 280

19 .9970 3 sd 3 sd 80 200 320 .9970 also fine: 99.7% also fine: .9974 z =-3 z = 3 80 200 320

230-200 Go to table = = .75 .2734 40 20 also fine: 27.34% .2734 z =.75 80 120 160 200 240 280 320

Go to table Add to upper Half of curve z = 180-200 40 = -.5 .1915 .5000 + .1915 = .6915 22 also fine: 69.15% .5000 .1915 .6915 z =-.5 80 120 160 200 240 280 320

z = 236-200 40 = 0.9 Go to table .3159 Subtract from .5000 .5000 - .3159 = .1841 23 .3159 also fine: 18.41% .1841 z =.9 80 120 160 200 240 280 320

z = 192 - 200 40 = -.2 .0793 Go to table .0793 + .2088 = .2881 z = 222 - 200 40 =.55 .2088 Go to table 24 also fine: 28.81% .2881 .2088 .0793 z =-.2 z =.55 80 120 160 200 240 280 320

.4693 + .5000 = .9693 z = 275-200 = 1.875 Go to table Add area Lower half .4693 or .4699 .4699 + .5000 = .9699 40 25 Please note: If z-score rounded to 1.88, then percentile = 96.99% also fine: 96.93% .9693 .4693 .5000 z =1.875 80 120 160 200 240 280 320

Add area Lower half .5000 - .4911 = .0089 .5000 - .4913 = .0087 z = 295-200 40 z = 2.375 Go to table .4911 or .4913 26 Please note: If z-score rounded to 2.38, then area = .0087 also fine: 0.89% .4911 .0089 z =2.375 80 120 160 200 240 280 320

z = 130-200 40 = -1.75 .4599 Add to upper Half of curve Go to table .5000 + .4599 = .9599 27 also fine: 95.99% .9599 .5000 .4599 z =-1.75 80 120 160 200 240 280 320

40 z = 130-200 = -1.75 .4599 Subtract from .5000 .5000 - .4599 = .0401 Go to table 28 .0401 .4599 .5000 also fine: 4.01% z =-1.75 80 120 160 200 240 280 320

z table provides area from mean to score x = mean + z σ = 200 + (2.33)(40) = 293.2 99th percentile Find area of interest .9900 - .5000 = .4900 Find nearest z = 2.33 29 .4900 .9900 z table provides area from mean to score .5000 293.2 z =2.33 80 ? 120 160 200 240

z table provides area from mean to score 33rd percentile Find area of interest .5000 - .3300 = .1700 Find nearest z = .44 x = mean + z σ = 200 + (-.44)(40) = 182.4 30 z table provides area from mean to score Note: .33 +.17 =.50 .3300 .1700 182.4 z =-.44 ? 80 200 240 280 320

z table provides area from mean to score 40th percentile Find area of interest .5000 - .4000 = .1000 Find nearest z = -.25 x = mean + z σ = 200 + (-.25)(40) = 190 31 z table provides area from mean to score Note: .40 +.10 =.50 190 .1000 .4000 z =-.25 ? 80 200 240 280 320

z table provides area from mean to score 67th percentile Find area of interest .6700 - .5000 = .1700 Find nearest z = .44 x = mean + z σ = 200 + (.44)(40) = 217.6 32 z table provides area from mean to score .1700 z =.44 80 200 217.6 ? 320

Thank you! See you next time!!