Lecturer’s desk Physics- atmospheric Sciences (PAS) - Room 201 s c r e e n Row A Row B Row C Row D Row E Row F Row G Row H Row A Row B Row C Row D Row E Row F Row G Row H table Row A Row B Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M Row N Row P Row J Row K Row L Row M Row N Row P Row Q table

MGMT 276: Statistical Inference in Management Fall 2015

Just for Fun Assignments Go to D2L - Click on “Content” Click on “Interactive Online Just-for-fun Assignments” Complete Assignments 1 – 7 Please note: These are not worth any class points and are different from the required homeworks

Schedule of readings Before next exam: September 24 th Please read chapters & Appendix D & E in Lind Please read Chapters 1, 5, 6 and 13 in Plous Chapter 1: Selective Perception Chapter 5: Plasticity Chapter 6: Effects of Question Wording and Framing Chapter 13: Anchoring and Adjustment

By the end of lecture today 9/17/15 Questionnaire design and evaluation Surveys and questionnaire design Correlational methodology Positive, Negative and Zero correlation Strength and direction Writing Summaries of results

Review of Homework Worksheet , , , , ,000 Notice Gillian asked 1300 people = /1300 =.10.10x100=10.10 x 1,000,000 = 100,000

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Review of Homework Worksheet

Age Dollars Spent Strong Negative Down -.9

Review of Homework Worksheet =correl(A2:A11,B2:B11) = Strong Negative Down

Review of Homework Worksheet =correl(A2:A11,B2:B11) = Strong Negative Down This shows a strong negative relationship (r = ) between the amount spent on snacks and the age of the moviegoer Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Correlation r (actual number)

Review of Homework Worksheet =correl(A2:A11,B2:B11) = Strong Negative Down Must be complete and must be stapled Hand in your homework

Homework Assignment Assignment 5 Descriptive Statistics in Consulting Due: Thursday, September 22 nd

Overview Frequency distributions The normal curve Mean, Median, Mode, Trimmed Mean Challenge yourself as we work through characteristics of distributions to try to categorize each concept as a measure of 1) central tendency 2) dispersion or 3) shape Skewed right, skewed left unimodal, bimodal, symmetric

A little more about frequency distributions An example of a normal distribution

A little more about frequency distributions An example of a normal distribution

A little more about frequency distributions An example of a normal distribution

A little more about frequency distributions An example of a normal distribution

A little more about frequency distributions An example of a normal distribution

Measure of central tendency: describes how scores tend to cluster toward the center of the distribution Normal distribution In a normal distribution: mode = mean = median In all distributions: mode = tallest point median = middle score mean = balance point

Measure of central tendency: describes how scores tend to cluster toward the center of the distribution Positively skewed distribution In a positively skewed distribution: mode < median < mean In all distributions: mode = tallest point median = middle score mean = balance point Note: mean is most affected by outliers or skewed distributions With Bill Gates our Average Income would be $38 million a year

Measure of central tendency: describes how scores tend to cluster toward the center of the distribution Negatively skewed distribution In a negatively skewed distribution: mean < median < mode In all distributions: mode = tallest point median = middle score mean = balance point Note: mean is most affected by outliers or skewed distributions

Mode: The value of the most frequent observation Bimodal distribution: Distribution with two most frequent observations (2 peaks) Example: Ian coaches two boys baseball teams. One team is made up of 10-year-olds and the other is made up of 16-year-olds. When he measured the height of all of his players he found a bimodal distribution

Overview Frequency distributions The normal curve Mean, Median, Mode, Trimmed Mean Standard deviation, Variance, Range Mean Absolute Deviation Skewed right, skewed left unimodal, bimodal, symmetric

Frequency distributions The normal curve

Variability Some distributions are more variable than others 6’ 7’ 5’ 5’6” 6’6” Let’s say this is our distribution of heights of men on U of A baseball team Mean is 6 feet tall 6’ 7’ 5’ 5’6” 6’6” 6’ 7’ 5’ 5’6” 6’6” What might this be?

6’ 7’ 5’ 5’6” 6’6” 6’ 7’ 5’ 5’6” 6’6” 6’ 7’ 5’ 5’6” 6’6” Dispersion: Variability Some distributions are more variable than others Range: The difference between the largest and smallest observations Range for distribution A? Range for distribution B? Range for distribution C? A B C The larger the variability the wider the curve tends to be The smaller the variability the narrower the curve tends to be

Range: The difference between the largest and smallest scores 84” – 70” = 14” Tallest player = 84” (same as 7’0”) (Kaleb Tarczewski and Dusan Ristic) Shortest player = 70” (same as 5’10”) (Parker Jackson-Cartwritght) Wildcats Basketball team: Range is 14” Fun fact: Mean is 78 x max - x min = Range

Range: The difference between the largest and smallest score 77” – 69” = 8” Tallest player = 77” (same as 6’5”) (Austin Schnabel) Shortest player = 69” (same as 5’9”) (Justin Behnke and Ernie DeLaTrinidad ) Wildcats Baseball team: Range is 8” (77” – 69” ) Fun fact: Mean is 72 x max - x min = Range Please note: No reference is made to numbers between the min and max Baseball

Variability Standard deviation: The average amount by which observations deviate on either side of their mean Mean is 6’ Generally, (on average) how far away is each score from the mean?

Let’s build it up again… U of A Baseball team Diallo Diallo is 6’0” Diallo is 0” Deviation scores 6’0” – 6’0” = 0 5’8” 5’10” 6’0” 6’2” 6’4” Diallo’s deviation score is 0

Preston Preston is 6’2” 6’2” – 6’0” = 2 5’8” 5’10” 6’0” 6’2” 6’4” Diallo is 0” Preston is 2” Deviation scores Preston’s deviation score is 2” Diallo is 6’0” Diallo’s deviation score is 0 Let’s build it up again… U of A Baseball team

Mike Hunter Mike is 5’8” Hunter is 5’10” 5’8” – 6’0” = -4 5’10” – 6’0” = -2 5’8” 5’10” 6’0” 6’2” 6’4” Diallo is 0” Mike is -4” Hunter is -2 Preston is 2” Deviation scores Preston is 6’2” Preston’s deviation score is 2” Diallo is 6’0” Diallo’s deviation score is 0 Mike’s deviation score is -4” Hunter’s deviation score is -2” Let’s build it up again… U of A Baseball team

David Shea Shea is 6’4” David is 6’ 0” 6’4” – 6’0” = 4 6’ 0” – 6’0” = 0 5’8” 5’10” 6’0” 6’2” 6’4” Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David is 0” Preston is 2” Deviation scores Preston’s deviation score is 2” Diallo’s deviation score is 0 Mike’s deviation score is -4” Hunter’s deviation score is -2” Shea’s deviation score is 4” David’s deviation score is 0 Let’s build it up again… U of A Baseball team

David Shea 5’8” 5’10” 6’0” 6’2” 6’4” Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David is 0” Preston is 2” Deviation scores Preston’s deviation score is 2” Diallo’s deviation score is 0 Mike’s deviation score is -4” Hunter’s deviation score is -2” Shea’s deviation score is 4” David’s deviation score is 0” Let’s build it up again… U of A Baseball team

5’8” 5’10” 6’0” 6’2” 6’4” Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David is 0” Preston is 2” Deviation scores Let’s build it up again… U of A Baseball team

Standard deviation: The average amount by which observations deviate on either side of their mean 5’8” 5’10” 6’0” 6’2” 6’4” Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David is 0” Preston is 2” Deviation scores

Standard deviation: The average amount by which observations deviate on either side of their mean 5’8” 5’10” 6’0” 6’2” 6’4” Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David is 0” Preston is 2” Deviation scores

Standard deviation: The average amount by which observations deviate on either side of their mean 5’8” 5’10” 6’0” 6’2” 6’4” Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David is 0” Preston is 2” Deviation scores

How do we find each deviation score? 5’8” - 6’0” = - 4” 5’9” - 6’0” = - 3” 5’10’ - 6’0” = - 2” 5’11” - 6’0” = - 1” 6’0” - 6’0 = 0 6’1” - 6’0” = + 1” 6’2” - 6’0” = + 2” 6’3” - 6’0” = + 3” 6’4” - 6’0” = + 4” Deviation scores: The amount by which observations deviate on either side of their mean (x - µ ) = ? Diallo Mike Hunter Preston Mean Mike Shea Preston Diallo How far away is each score from the mean? ( x - µ ) Diallo Mike Hunter Preston Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David is 0” Preston is 2” Deviation scores ( x - µ ) Find distance of each person from the mean (subtract their score from mean) ( x - µ ) Deviation score

5’8” - 6’0” = - 4” 5’9” - 6’0” = - 3” 5’10’ - 6’0” = - 2” 5’11” - 6’0” = - 1” 6’0” - 6’0 = 0 6’1” - 6’0” = + 1” 6’2” - 6’0” = + 2” 6’3” - 6’0” = + 3” 6’4” - 6’0” = + 4” Deviation scores: The amount by which observations deviate on either side of their mean (x - µ ) = ? Mean Mike Shea Preston Diallo How far away is each score from the mean? Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David is 0” Preston is 2” Deviation scores ( x - µ ) Based on difference from the mean Remember It’s relative to the mean ( x - µ ) Deviation score

How do we find the average height? 5’8” - 6’0” = - 4” 5’9” - 6’0” = - 3” 5’10’ - 6’0” = - 2” 5’11” - 6’0” = - 1” 6’0” - 6’0 = 0 6’1” - 6’0” = + 1” 6’2” - 6’0” = + 2” 6’3” - 6’0” = + 3” 6’4” - 6’0” = + 4” Standard deviation: The average amount by which observations deviate on either side of their mean Σ(x - x) = 0 Σ (x - µ ) = ? Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David is 0” Preston is 2” Deviation scores Σ(x - µ ) = 0 = average height N ΣxΣx = average deviation Σ(x - µ ) N How do we find the average spread? Mean Mike Shea Preston Diallo How far away is each score from the mean? ( x - µ ) Add up Deviation scores

5’8” - 6’0” = - 4” 5’9” - 6’0” = - 3” 5’10’ - 6’0” = - 2” 5’11” - 6’0” = - 1” 6’0” - 6’0 = 0 6’1” - 6’0” = + 1” 6’2” - 6’0” = + 2” 6’3” - 6’0” = + 3” 6’4” - 6’0” = + 4” Standard deviation: The average amount by which observations deviate on either side of their mean Σ(x - x) = 0 Σ (x - µ ) = ? Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David is 0” Preston is 2” Deviation scores Σ(x - µ ) = 0 Mean Mike Shea Preston Diallo How far away is each score from the mean? ( x - µ ) Big problem Σ(x - x) 2 Square the deviations Σ(x - µ ) 2 N 2

Standard deviation: The average amount by which observations deviate on either side of their mean These would be helpful to know by heart – please memorize these formula

Standard deviation: The average amount by which observations deviate on either side of their mean What do these two formula have in common?

Standard deviation: The average amount by which observations deviate on either side of their mean What do these two formula have in common?

Standard deviation: The average amount by which observations deviate on either side of their mean How do these formula differ? “n-1” is Degrees of Freedom”

Standard deviation: The average amount by which observations deviate on either side of their mean Based on difference from the mean Mean Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David 0” Preston is 2” Deviation scores Mike Shea Preston Diallo Generally, (on average) how far away is each score from the mean? Remember, it’s relative to the mean Please memorize these “Sum of Squares” “n-1” is “Degrees of Freedom” “n-1” is “Degrees of Freedom” Remember, We are thinking in terms of “deviations”

Standard deviation (definitional formula) - Let’s do one _ X_ Step 1: Find the mean ΣX = 45 ΣX / N = 45/9 = 5 Step 2: Subtract the mean from each score _ X - µ _ = = = = = = = = = 4 0 Step 3: Square the deviations (X - µ ) Step 4: Find standard deviation a) 60 / 9 = Σ(x - µ ) = 0 This is the Variance! This is the standard deviation! Each of these are deviation scores b) square root of = This numerator is called “sum of squares”

Another example: How many kids in your family?

Standard deviation - Let’s do one _ X_ Step 1: Find the mean = 30 = 30/10 = 3 Step 2: Subtract the mean from each score (deviations) X - µ _ = = = = = = = = = = 1 Step 3: Square the deviations (X - µ ) Step 5: Find standard deviation a) 38 / 10 = 3.8 b) square root of 3.8 = 1.95 Step 4: Add up the squared deviations Σx = 30 Σ(x - µ ) = 0 Σ(x - µ ) 2 = 38 This is the Variance! This is the standard deviation! Definitional formula How many kids?

These would be helpful to know by heart – please memorize areas 1 sd above and below mean 68% 2 sd above and below mean 95% 3 sd above and below mean 99.7%

Raw scores, z scores & probabilities 68% 95%99.7% Please note spatially where 1 standard deviation falls on the curve

Raw scores, z scores & probabilities Please note spatially where 1 standard deviation falls on the curve

Raw scores, z scores & probabilities Mean = 50 S = 10 (Note S = standard deviation) If we go up one standard deviation z score = +1.0 and raw score = 60 If we go down one standard deviation z score = -1.0 and raw score = 40 1 sd above and below mean 68% z = -1 z = +1

Mean = 50 S = 10 (Note S = standard deviation) If we go up two standard deviations z score = +2.0 and raw score = 70 If we go down two standard deviations z score = -2.0 and raw score = 30 2 sd above and below mean 95% Raw scores, z scores & probabilities z = -2 z = +2

Mean = 50 S = 10 (Note S = standard deviation) If we go up three standard deviations z score = +3.0 and raw score = 80 If we go down three standard deviations z score = -3.0 and raw score = 20 3 sd above and below mean 99.7% Raw scores, z scores & probabilities z = -3 z = +3