MGMT 276: Statistical Inference in Management.

MGMT 276: Statistical Inference in Management. Welcome http://www.youtube.com/watch?v=tKH2oLjQIAA

Please read: Chapters 5 - 9 in Lind book & Chapters 10, 11, 12 & 14 in Plous book: Lind Chapter 5: Survey of Probability Concepts Chapter 6: Discrete Probability Distributions Chapter 7: Continuous Probability Distributions Chapter 8: Sampling Methods and CLT Chapter 9: Estimation and Confidence Interval Plous Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability and Risk Chapter 14: The Perception of Randomness We’ll be jumping around some…we will start with chapter 7

Use this as your study guide By the end of lecture today2/15/11 • Objectives of research in business • Characteristics of a distribution • Central Tendency • Dispersion • Shape • What are the three primary types of “measures of central • tendency”? • Mean • Median • Mode • Measures of variability • Range, Standard deviation and Variance • Definitional versus calculation formula

Please click in Homework due next class - (Due February 17th) My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z Complete memo homework available on class website Please double check – All cell phones other electronic devices are turned off and stowed away Turn your clicker on

Homework Worksheet

Homework Worksheet -22= 4 3 – 5 = -2 -2 1 4 1 9 36 3 6 12= 1 6 – 5 = +1

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It went really well! Exam 1 – Last Tuesday Thanks for your patience and cooperation Average grade for class is 83%

Remember… In a negatively skewed distribution: mean < median < mode 90 = mode = tallest point 85 = median = middle score 83 = mean = balance point Median Mode Mean

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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 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, 1, 2, 2, 2, 4, 4, 2, 2, 1, 1, 8, 8, 3, 4, 4, 14 14 2.5 2 + 3 µ=2.5 If there appears to be two medians, take the mean of the two Median always has a percentile rank of 50% regardless of shape of distribution (section 1 only)

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 Median: The middle value when observations are ordered from least to most (or most to least) Mode: The value of the most frequent observation 1, 2, 2, 4, 2, 1, 8, 3, 4, 14 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 (section 1 only)

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 (section 1 only)

Overview Frequency distributions The normal curve 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 Mean, Median, Mode, Trimmed Mean Standard deviation, Variance, Range Mean Absolute Deviation Skewed right, skewed left unimodal, bimodal, symmetric (section 1 only)

Measure of central tendency: describes how scores tend to cluster toward the center of the distribution Normal distribution In all distributions: mode = tallest point median = middle score mean = balance point In a normal distribution: mode = mean = median (section 1 only)

Measure of central tendency: describes how scores tend to cluster toward the center of the distribution Positively skewed distribution In all distributions: mode = tallest point median = middle score mean = balance point In a positively skewed distribution: mode < median < mean Note: mean is most affected by outliers or skewed distributions (section 1 only)

Measure of central tendency: describes how scores tend to cluster toward the center of the distribution Negatively skewed distribution In all distributions: mode = tallest point median = middle score mean = balance point In a negatively skewed distribution: mean < median < mode Note: mean is most affected by outliers or skewed distributions (section 1 only)

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 (section 1 only)

Remember… Frequency 10 20 30 40 50 60 70 80 90 100 Score on Exam Note: Label and Numbers Note: Always “frequency” (section 1 only)

Examples of data that would produce three of these shapes (section 1 only)

Take-home Writing Assignment: Generate an example of data that would produce three of these possible nine shapes (3 examples altogether) Be sure to include 1) Identify the shape 2) Labels for both axes 3) Numbers on both axes 4) A sentence describing the distribution and why it has the shape that it does

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 Start both sections

5’ 7’ 6’ 6’6” 5’6” 5’ 7’ 6’ 6’6” 5’6” 5’ 7’ 6’ 6’6” 5’6” Variability The larger the variability the wider the curve tends to be The smaller the variability the narrower the curve tends to be

Dispersion: Variability 5’ 7’ 6’ 6’6” 5’6” 5’ 7’ 6’ 6’6” 5’6” 5’ 7’ 6’ 6’6” 5’6” Some distributions are more variable than others A Range: The difference between the largest and smallest observations B Range for distribution A? Range for distribution B? Range for distribution C? C

Fun fact: Mean is 72 Wildcats Baseball team: Tallest player = 76” (same as 6’4”) Shortest player = 68” (same as 5’8”) Range: The difference between the largest and smallest scores 76” – 68” = 8” Range is 8” (76” – 68”) xmax - xmin = Range Please note: No reference is made to numbers between the min and max

Fun fact: Mean is 78 Wildcats Basketball team: Tallest player = 83” (same as 6’11”) Shortest player = 70” (same as 5’10”) Range is 13” (83” – 70”) Range: The difference between the largest and smallest scores 83” – 70” = 13” xmax - xmin = Range

Frequency distributions The normal curve

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

5’ 7’ 6’ 6’6” 5’6” 5’ 7’ 6’ 6’6” 5’6” 5’ 7’ 6’ 6’6” 5’6” Variability 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

Let’s build it up again…U of A Baseball team Diallo is 6’0” Diallo 5’8” 5’10” 6’0” 6’2” 6’4”

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

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

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

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

Let’s build it up again…U of A Baseball team 5’8” 5’10” 6’0” 6’2” 6’4” 5’8” 5’10” 6’0” 6’2” 6’4”

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

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

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

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

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

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

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

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

Σ(x - x) = 0 Deviation scores Standard deviation: The average amount by which observations deviate on either side of their mean Diallo is 0” Preston is 2” Mike is -4” Hunter is -2 Shea is 4 David is 0” Mike Σ x - x = ? Hunter 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” Diallo 5’8” 5’10” 6’0” 6’2” 6’4” How do we find the average deviation? Preston Σx / n = mean Σ(x - µ) = 0

Σ(x - x) Σ(x - x) = 0 Deviation scores Standard deviation: The average amount by which observations deviate on either side of their mean Diallo is 0” Preston is 2” Mike is -4” Hunter is -2 Shea is 4 How do we find the average deviation? David is 0” Square the deviations!! (and later take square root) Σx / n = mean Σ x - x = ? 2 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” 2 Σ(x - µ) How do we get rid of the negatives??!? Big problem!! Σ(x - µ) = 0

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

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

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 Fun Fact: Standard deviation squared = variance

MGMT 276: Statistical Inference in Management.