Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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. 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) + 0.5 N * (2 m) = 0 M = ( ∑ Xi ) / N ∑ Xi = N * M ∑ ( Xi – M ) = 0 ∑ Xi – ∑ M = 0 N*M–N*M=0 Variance vs. Standard Deviation • Variance: average of squared deviations [ ∑ ( Xi – M )2 ] / N • Standard Deviation: square root of average of squared deviations √ ( [ ∑ ( Xi – M ) 2 ] / N ) • “Root Mean Square (RMS) deviation from the average.” -- “Standard Deviation”, Wikipedia Computational Formula • Variance = [ ∑ ( Xi – M )2 ] / N = [ ∑ ( Xi2 – 2 * M * Xi + M2 ) ] / N = [ ∑ Xi2 – ∑ 2 * M * Xi + ∑ M2 ] / N = [ ∑ Xi2 – 2 * M * ∑ Xi + N * M2 ] / N = [ ∑ Xi2 – 2 * M * ( N * M) + N * M2 ] / N = [ ∑ Xi2 – 2 * N * M2 + N * M2 ] / N = [ ∑ Xi2 – N * M2 ] / N = [ ∑ Xi2 – ( N * M )2 / N ] / N = [ ∑ Xi2 – (∑ Xi)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 ( ∑ √ [( Xi – M )2 ] ) / N • Averages out influence of highly deviant points • Standard Deviation √ ( [ ∑ ( Xi – 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 e-mail list unless personal – http://egroups.com/group/utd-statistics