Transcript Statistics for Psychology

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
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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
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Previous Material
Textbook Slides
Emphasis
Homework
Exam
Previous Material
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Syllabus
Research Exposure Credits Requirement
Lecture Slides on Website
Mailing List
Textbook Slides
• Chapter 2
Emphasis
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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
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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
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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
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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
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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
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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
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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