Lecture 03: Chapter 2 Statistics for Psychology David Wallace Croft 2005 May 20 Fri Copyright 2005 David Wallace Croft This work is licensed under the Creative Commons Attribution License 2.0. Creative Commons Attribution License 2.0

Quiz Please mute your mobile phones Write your name on a blank piece of paper Quiz will begin at 09:00 When done, turn your paper over At 09:02, I will say, “Pens down” Writing after “Pens down” is cheating Pass your quizzes to your left

Outline Previous Material Textbook Slides Emphasis Homework Exam

Previous Material Syllabus Research Exposure Credits Requirement Lecture Slides on Website Mailing List

Textbook Slides Chapter 2

Emphasis Mean, Median, and Mode See Saw Variance vs. Standard Deviation Computational Formula Division by N – 1 Average Absolute vs. Standard Deviation Z Score

Mean, Median, and Mode Mean: average Median: 50% scores below, 50% above Mode: Most frequently occurring Central Tendency Median Household Income

See Saw Torque = Force * Distance Balanced when net is zero 1 N * (-1 m) N * (2 m) = 0 M = ( ∑ X i ) / N ∑ X i = N * M ∑ ( X i – M ) = 0 ∑ X i – ∑ M = 0 N * M – N * M = 0

Variance vs. Standard Deviation Variance: average of squared deviations [ ∑ ( X i – M ) 2 ] / N Standard Deviation: square root of average of squared deviations √ ( [ ∑ ( X i – M ) 2 ] / N ) “Root Mean Square (RMS) deviation from the average.” -- “Standard Deviation”, Wikipedia

Computational Formula Variance = [ ∑ ( X i – M ) 2 ] / N = [ ∑ ( X i 2 – 2 * M * X i + M 2 ) ] / N = [ ∑ X i 2 – ∑ 2 * M * X i + ∑ M 2 ] / N = [ ∑ X i 2 – 2 * M * ∑ X i + N * M 2 ] / N = [ ∑ X i 2 – 2 * M * ( N * M) + N * M 2 ] / N = [ ∑ X i 2 – 2 * N * M 2 + N * M 2 ] / N = [ ∑ X i 2 – N * M 2 ] / N = [ ∑ X i 2 – ( N * M ) 2 / N ] / N = [ ∑ X i 2 – (∑ X i ) 2 / N ] / N Use Definitional Formula

Division by N - 1 Variance = SS / N Chapter 9: Variance = SS / ( N – 1 ) A mystery Divide by N for now

Average Absolute vs. Standard Deviation Average Absolute Deviation ( ∑ √ [( X i – M ) 2 ] ) / N Averages out influence of highly deviant points Standard Deviation √ ( [ ∑ ( X i – M ) 2 ] / N ) Rubber Bands Exaggerates influence of highly deviant points Shows up in Normal Distribution

Z Score Letter grades based on z score B-: Z >= -1 B: Z >= -2/3 B+: Z >= -1/3 A-: Z >= 0 A: Z >= 1/3 A+: Z >= 2/3 84% expected to make A or B More in Chapter 5 on the Normal Distribution

Homework Chapter 2 Mean, median, standard deviation, z score Do practice problems 1 and 2 You must be able to do these Seek help if you cannot Problems 5 and 6 also interesting Do the rest if you have time

Exam Review Monday at 09:00 Ends at 10:15 (75 minutes) No calculators, no electronic devices Closed book, closed notes 50 multiple choice (1.5 minutes each) Probably less than 45 minutes for most Review questions?

Protocol Objective grading Packing up distracting Wait to be dismissed Foreign instructors Graduate school

Questions Questions for Class? Post to list unless personal –