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

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Schedule of readings Before next exam: February 18 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 2/6/14 Use this as your study guide Correlational methodology Strength of correlation versus direction Positive vs Negative correlation Strong, vs Moderate vs Weak correlation Characteristics of a distribution Remember to hold onto homework until we have a chance to cover it

Homework due - (February 13 th ) On class website: please print and complete homework worksheet # 5

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)

Scatterplot displays relationships between two continuous variables Correlation: Measure of how two variables co-occur and also can be used for prediction Range between -1 and +1 Range between -1 and +1 The closer to zero the weaker the relationship The closer to zero the weaker the relationship and the worse the prediction Positive or negative Positive or negative

Correlation - How do numerical values change? Let’s estimate the correlation coefficient for each of the following r = +1.0r = -1.0 r = +.80 r = -.50r =

r = This shows a strong positive relationship (r = 0.97) between the appraised price of the house and its eventual sales price Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

r = +0.97r = This shows a moderate negative relationship (r = -0.48) between the amount of pectin in orange juice and its sweetness Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

r = This shows a strong negative relationship (r = -0.91) between the distance that a golf ball is hit and the accuracy of the drive Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

r = r = 0.61 This shows a moderate positive relationship (r = 0.61) between the length of stay in a hospital and the number of services provided Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

r = +0.97r = r = r = 0.61

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 Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (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 Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (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 Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (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 Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (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 Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

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) Break into groups of 2 or 3 Each person hand in own worksheet. Be sure to list your name and names of all others in your group Use examples that are different from those is lecture 4. Describe one perfect correlation (positive or negative) Draw a scatterplot (label axes) 5. Describe curvilinear relationship Draw a scatterplot (label axes)

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)

Height of Daughters (inches) Height of Mothers (in) This shows the strong positive (.8) relationship between the heights of daughters (measured in inches) with heights of their mothers (measured in inches). Both axes and values are labeled Both variables are listed, as are direction and strength

Height of Daughters (inches) Height of Mothers (in) This shows the strong positive (.8) relationship between the heights of daughters (measured in inches) with heights of their mothers (measured in inches). Both axes and values are labeled Both variables are listed, as are direction and strength

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) Break into groups of 2 or 3 Each person hand in own worksheet. Be sure to list your name and names of all others in your group Use examples that are different from those is lecture 4. Describe one perfect correlation (positive or negative) Draw a scatterplot (label axes) 5. Describe curvilinear relationship Draw a scatterplot (label axes)

Height of Daughters (inches) Height of Mothers (in) This shows the strong positive (.8) relationship between the heights of daughters (measured in inches) with heights of their mothers (measured in inches). Both axes and values are labeled Both variables are listed, as are direction and strength 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)

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

Sample versus census How is a census different from a sample? Census measures each person in the specific population Sample measures a subset of the population and infers about the population – representative sample is good What’s better? Use of existing survey data U.S. Census Family size, fertility, occupation The General Social Survey Surveys sample of US citizens over 1,000 items Same questions asked each year You’ve completed constructing your questionnaire…what’s the best way to get responders??

Parameter – Measurement or characteristic of the population Usually unknown (only estimated) Usually represented by Greek letters (µ) Population (census) versus sample Parameter versus statistic pronounced “mu ” pronounced “mew ” Statistic – Numerical value calculated from a sample Usually represented by Roman letters (x) pronounced “x bar ”

Simple random sampling: each person from the population has an equal probability of being included Sample frame = how you define population Sample frame = how you define population =RANDBETWEEN(1,115) Let’s take a sample …a random sample Question: Average weight of U of A football player Sample frame population of the U of A football team Or, you can use excel to provide number for random sample Random number table – List of random numbers Random number table – List of random numbers 64 Pick 64 th name on the list (64 is just an example here) Pick 24 th name on the list

Systematic random sampling: A probability sampling technique that involves selecting every technique that involves selecting every kth person from a sampling frame You pick the number Other examples of systematic random sampling 1) check every 2000 th light bulb 2) survey every 10 th voter

Stratified sampling: sampling technique that involves dividing a sample into subgroups (or strata) and then selecting samples from each of these groups - sampling technique can maintain ratios for the different groups Average number of speeding tickets 17.7% of sample are Pre-business majors 4.6% of sample are Psychology majors 4.6% of sample are Psychology majors 2.8% of sample are Biology majors 2.8% of sample are Biology majors 2.4% of sample are Architecture majors 2.4% of sample are Architecture majors etc etc Average cost for text books for a semester 12% of sample is from California 7% of sample is from Texas 6% of sample is from Florida 6% from New York 4% from Illinois 4% from Ohio 4% from Pennsylvania 3% from Michigan etc

Cluster sampling: sampling technique divides a population sample into subgroups (or clusters) by region or physical space. Can either measure everyone or select samples for each cluster Textbook prices Southwest schools Southwest schools Midwest schools Midwest schools Northwest schools Northwest schools etc etc Average student income, survey by Old main area Old main area Near McClelland Around Main Gate etc Patient satisfaction for hospital 7 th floor (near maternity ward) 7 th floor (near maternity ward) 5 th floor (near physical rehab) 5 th floor (near physical rehab) 2 nd floor (near trauma center) 2 nd floor (near trauma center) etc etc

Snowball sampling: a non-random technique in which one or more members of a population are located and used to lead the researcher to other members of the population Used when we don’t have any other way of finding them - also vulnerable to biases Convenience sampling: sampling technique that involves sampling people nearby. A non-random sample and vulnerable to bias Judgment sampling: sampling technique that involves sampling people who an expert says would be useful. A non-random sample and vulnerable to bias Non-random sampling is vulnerable to bias

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? 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

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)

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