Stage Screen Row B Gallagher Theater Row R Lecturer’s desk Row A Row B Row C Row A Row A Row C Row D Row D Row E Row E Row F Row F Row G Row G Row H Row H Row I Row I Row J Row J Row K Row K Row L Row L Row M Row M Row N Row N Row O Row O Row P Row P Row Q Row Q 4 4 Row R Row S Row B Row C Row D Row E Row F Row G Row H Row I Row J Row K Row L Row M Row N Row O Row P Row Q 26Left-Handed Desks A14, B16, B20, C19, D16, D20, E15, E19, F16, F20, G19, H16, H20, I15, J16, J20, K19, L16, L20, M15, M19, N16, P20, Q13, Q16, S4 5 Broken Desks B9, E12, G9, H3, M17 Need Labels B5, E1, I16, J17, K8, M4, O1, P16 Left handed

Stage Screen Row A Row B Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 17 Row C Row D Row E Projection Booth 65 4 table Row C Row D Row E R/L handed broken desk Social Sciences 100 Row N Row O Row P Row Q Row R Row F Row G Row H Row J Row K Row L Row M Row N Row O Row P Row Q Row R Row I Row I Lecturer’s desk Row F Row G Row H Row J Row K Row L Row M Row N Row O Row P Row Q Row R Row I Row B

MGMT 276: Statistical Inference in Management Fall, 2014 Green sheets

Just a reminder Talking or whispering to your neighbor can be a problem for us – please consider writing short notes. A note on doodling

Homework due - (September 23 rd ) Assignment 5 & 6 Calculating Descriptive Statistics And Presenting Findings in a Memorandum Due: Tuesday, September 23 rd

Schedule of readings Before next exam: September 25 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 9/18/14 Use this as your study guide Characteristics of a distribution Standard Deviation Variance Empirical Rule (areas under the curve) Measures of variability Understanding and memorization of the following four definitional formulae Standard Deviation for sample Standard Deviation for population Variance for sample Variance for population

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

Review of Homework Worksheet , , , , ,000

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)

Height of Daughters (inches) Height of Mothers (in) This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches). Both axes and values are labeled Both axes have real numbers listed 1. Describe one positive correlation Draw a scatterplot (label axes) 2. Describe one negative correlation Draw a scatterplot (label axes) 3. Describe one zero correlation Draw a scatterplot (label axes) 4. Describe one perfect correlation (positive or negative) Draw a scatterplot (label axes) 5. Describe curvilinear relationship Draw a scatterplot (label axes) Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number) Hand in Homework and Correlation worksheet

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 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

Another example: How many kids in your family? Number of kids in family

Measures of Central Tendency (Measures of location) The mean, median and mode Mean: The balance point of a distribution. Found by adding up all observations and then dividing by the number of observations Mean for a sample: Mean for a population: ΣX / N = mean = µ (mu) Note: Σ = add up x or X = scores n or N = number of scores Σx / n = mean = x Measures of “location” Where on the number line the scores tend to cluster

Measures of Central Tendency (Measures of location) The mean, median and mode Mean: The balance point of a distribution. Found by adding up all observations and then dividing by the number of observations Mean for a sample: Note: Σ = add up x or X = scores n or N = number of scores Σx / n = mean = x Number of kids in family / 10 = mean = 4.1

How many kids are in your family? What is the most common family size? Number of kids in family Median: The middle value when observations are ordered from least to most (or most to least)

How many kids are in your family? What is the most common family size? Median: The middle value when observations are ordered from least to most (or most to least) 1, 3, 1, 4, 2, 4, 2, 8, 2, 14 1, 2, 3, 4, 8, 14 Number of kids in family

Number of kids in family , 4, 2, 1, How many kids are in your family? What is the most common family size? Number of kids in family Median: The middle value when observations are ordered from least to most (or most to least) 1, 3, 1, 4, 2, 4, 2, 8, 2, , 3, 1, 2, 4, 2, 4,8, 1, 14 2, 3, 1, Median always has a percentile rank of 50% regardless of shape of distribution µ = 2.5 If there appears to be two medians, take the mean of the two

Mode: The value of the most frequent observation Number of kids in family Score f Please note: The mode is “2” because it is the most frequently occurring score. It occurs “3” times. “3” is not the mode, it is just the frequency for the value that is the mode Bimodal distribution: If there are two most frequent observations

What about central tendency for qualitative data? Mode is good for nominal or ordinal data Median can be used with ordinal data Mean can be used with interval or ratio data

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

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

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” – 71” = 13” Tallest player = 84” (same as 7’0”) (Kaleb Tarczewski and Dusan Ristic) Shortest player = 71” (same as 5’11”) (Parker Jackson-Cartwritght) Wildcats Basketball team: Range is 13” Fun fact: Mean is 78 x max - x min = Range

Range: The difference between the largest and smallest score 77” – 70” = 7” Tallest player = 77” (same as 6’5”) (Austin Schnabel) Shortest player = 70” (same as 5’10”) (Five players are 5’10”) Wildcats Baseball team: Range is 7” (77” – 70” ) Fun fact: Mean is 72 x max - x min = Range Please note: No reference is made to numbers between the min and max Baseball

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” The larger the variability the wider the curve the larger the deviations scores tend to be The smaller the variability the narrower the curve the smaller the deviations scores tend to be 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 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 Mike Hunter Preston 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 Σ(x - µ ) = 0 = average height N ΣxΣx = average deviation Σ(x - µ ) N How do we find the average spread?

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 - x = ? 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 Σ(x - µ ) = 0 Big problem Σ(x - x) 2 Square the deviations Σ(x - µ ) 2 N ΣxΣx N Big problem 2

Mean: The average value in the data Standard deviation: The average amount scores deviate on either side of their mean Standard deviation is typical “spread” (typical size of deviations or distance from mean) – can never be negative Mean is a measure of typical “value” (where the typical scores are positioned on the number line)

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? n-1 is “Degrees of Freedom” More, next lecture

Standard deviation Standard deviation: The average amount by which observations deviate on either side of their mean Fun Fact: Standard deviation squared = variance Note this is for population

Standard deviation Standard deviation: The average amount by which observations deviate on either side of their mean Note this is for sample Fun Fact: Standard deviation squared = variance

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”

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”

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?

Review notation 1. What does this symbol refer to? 2. What does this symbol refer to? 5. What does this symbol refer to? 3. What does this symbol refer to? 4. What does this symbol refer to? What is it called? What does it mean? Is it referring to a sample or population? What is it called? What does it mean? Is it referring to a sample or population? What is it called? What does it mean? Is it referring to a sample or population? What is it called? What does it mean? Is it referring to a sample or population?

Review notations 6. What does this refer to? 7. What does this refer to? 8. What do these two refer to? 9. What does this refer to? What are they called? How are they different What is it called? Use it for sample data or population? What are they called? What do they refer to? How are they different What are they called? How are they different

Review notations 9. What does this refer to? What are they called? What do they refer to? How are they different 10. What does this refer to? What are they called? What do they refer to? How are they different

Review Notations 1. What does this symbol refer to? 2. What does this symbol refer to? 5. What does this symbol refer to? 3. What does this symbol refer to? 4. What does this symbol refer to? What is it called? What does it mean? Is it referring to a sample or population? What is it called? What does it mean? Is it referring to a sample or population? What is it called? What does it mean? Is it referring to a sample or population? What is it called? What does it mean? Is it referring to a sample or population? The standard deviation (population) The mean (population) The mean (sample) The standard deviation (sample) Each individual score sigma population mu x-bar population sample s

6. What does this refer to? 7. What does this refer to? 8. What do these two refer to? 9. What does this refer to? What are they called? How are they different What is it called? Use it for sample data or population? What are they called? What do they refer to? How are they different What are they called? How are they different Variance population sample Sigma squared S squared Deviation scores population sample Sum of squares population sample Degrees of freedom sample Review Notations

Review notations 9. What does this refer to? What are they called? What do they refer to? How are they different 10. What does this refer to? What are they called? What do they refer to? How are they different Variance population sample Standard Deviation population sample

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” Review Remember, We are thinking in terms of “deviations”