Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2019 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays. February 15 http://www.youtube.com/watch?v=oSQJP40PcGI

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Before next exam (March 1st) Schedule of readings Before next exam (March 1st) 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

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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

Hand out z tables

Writing Assignment Let’s do some problems Mean = 50 Standard deviation = 10 Writing Assignment Let’s do some problems

Find the percentile rank for score of 550 Mean = 500 Standard deviation = 100 ? Find the percentile rank for score of 550 550 .1915 .5 1) Find z score z score = 550 - 500 100 z score = 50 100 = 0.5 2) Go to z table 3) Look at your picture - add .5000 +.1915 = .6915 4) Percentile rank or score of 550 = 69.15% Review

Find the score that is associated New Mean & Standard Deviation Mean = 50 Standard deviation = 10 ? 30 Hint always draw a picture! Find the score for z = -2 Find the score that is associated with a z score of -2 raw score = mean + (z score)(standard deviation) Raw score = 50 + (-2)(10) Raw score = 50 + (-20) = 30 Review

percentile rank of 77%ile Mean = 50 Standard deviation = 10 ? Find the score for percentile rank of 77%ile .7700 ? Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion Problem 1

percentile rank of 77%ile Mean = 50 Standard deviation = 10 .27 ? Find the score for percentile rank of 77%ile .5 .5 + .27 = .77 .5 .27 .7700 ? 1) Go to z table - find z score for for area .2700 (.7700 - .5000) = .27 Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion area = .2704 (closest I could find to .2700) z = 0.74 Problem 1

percentile rank of 77%ile Mean = 50 Standard deviation = 10 .27 ? Find the score for percentile rank of 77%ile .5 x = 57.4 .5 .27 .7700 ? 2) x = mean + (z)(standard deviation) x = 50 + (0.74)(10) x = 57.4 x = 57.4 Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion Problem 1

percentile rank of 55%ile Mean = 50 Standard deviation = 10 ? Find the score for percentile rank of 55%ile .5500 ? Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion Problem 2

percentile rank of 55%ile Mean = 50 Standard deviation = 10 .05 ? Find the score for percentile rank of 55%ile .5 .5 + .05 = .55 .5 .05 .5500 ? 1) Go to z table - find z score for for area .0500 (.5500 - .5000) = .05 Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion area = .0517 (closest I could find to .0500) z = 0.13 Problem 2

percentile rank of 55%ile Mean = 50 Standard deviation = 10 .05 ? Find the score for percentile rank of 55%ile .5 .5 .05 .5500 ? 1) Go to z table - find z score for for area .0500 (.5500 - .5000) = .05 Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion area = .0517 (closest I could find to .0500) z = 0.13 Problem 2

percentile rank of 55%ile Mean = 50 Standard deviation = 10 .05 ? Find the score for percentile rank of 55%ile .5 x = 51.3 .5 .05 .5500 ? 1) Go to z table - find z score for for area .0500 (.5500 - .5000) = .0500 area = .0517 (closest I could find to .0500) z = 0.13 2) x = mean + (z)(standard deviation) x = 50 + (0.13)(10) x = 51.3 Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion x = 51.3 Problem 2

? .7500 .25 .5000 . Find score associated with the 75th percentile Go to table nearest z = .67 .2500 x = mean + z σ = 30 + (.67)(2) = 31.34 .7500 .25 .5000 24 26 28 30 ? 34 36 31.34 Problem 3 z = .67

? .2500 .25 .25 . Find the score associated with the 25th percentile Go to table nearest z = -.67 .2500 x = mean + z σ = 30 + (-.67)(2) = 28.66 .2500 .25 .25 24 26 28.66 28 ? 30 34 36 Problem 4 z = -.67

A word on “add-in” Using Excel ?

t-tests Using Excel

t-tests Using Excel

Homework Assignment Worksheet Distributed in Class Interpreting t-tests

Whether or not feed had corn oil No, feed had no corn oil Yes, the feed had corn oil Weight of eggs 60 grams if no corn oil 63 grams if corn oil weight of eggs based on corn oil in food weight of eggs based on corn oil in food true experiment between nominal ratio 200 100 100 198 99 99

-3.35 1.97 Yes Yes Yes 0.0009638 Yes 0.05 The weights of eggs for chickens who received the corn oil was 63 grams, while the weights of the eggs for chickens who did not receive the corn oil was 60 grams. A t-test found this to be a significant difference t(198) = -3.35; p < 0.05

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