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BNAD 276: Statistical Inference in Management Spring 2016 Welcome Green sheets

By the end of lecture today 2/2/16 Use this as your study guide By the end of lecture today 2/2/16 Revisit data collection using questionnaires Correlation is called an “r” Positive or Negative Strong, Moderate or Weak (ranges from 0 – 1) Measures of Central Tendency Mean, median and mode

writing assignment forms notebook and clickers to each lecture Remember bring your writing assignment forms notebook and clickers to each lecture A note on doodling Remember to register your clicker soon

Homework Assignment #3 & 4 (Has 2 parts) Questionnaire construction using Likert scales instructions Important additional materials to help with homework assignments 3 & 4 How to report findings in a formal memorandum Example of formal memorandum for homework assignments 3 & 4 Rubric for homework assignments 3 & 4 Due: Thursday February 4th (both handed in together)

Schedule of readings Before next exam: February 18th Please read Chapters 1 - 4 in OpenStax Supplemental reading (Appendix D) Supplemental reading (Appendix E) Supplemental reading (Appendix F) 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

Preview of Questionnaire Homework There are five parts: Statement of Objectives Questionnaire itself (which is the operational definitions of the objectives) Data collection and creation of database Creation of graphs representing results Generate a formal memorandum describing results

Preview of Questionnaire Homework There are five parts: Statement of Objectives Questionnaire itself (which is the operational definitions of the objectives) Data collection and creation of database Creation of graphs representing results Generate a formal memorandum describing results

Designed our study / observation / questionnaire Collected our data Organize and present our results

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 The closer to zero the weaker the relationship and the worse the prediction Positive or negative

Correlation Range between -1 and +1 +1.00 perfect relationship = perfect predictor +0.80 strong relationship = good predictor +0.20 weak relationship = poor predictor 0 no relationship = very poor predictor -0.20 weak relationship = poor predictor -0.80 strong relationship = good predictor -1.00 perfect relationship = perfect predictor

Positive correlation: as values on one variable go up, so do values Positive correlation: as values on one variable go up, so do values for the other variable Negative correlation: as values on one variable go up, the values for the other variable go down Height of Mothers by Height of Daughters Height of Mothers Positive Correlation Height of Daughters

Positive correlation: as values on one variable go up, so do values Positive correlation: as values on one variable go up, so do values for the other variable Negative correlation: as values on one variable go up, the values for the other variable go down Brushing teeth by number cavities Brushing Teeth Negative Correlation Number Cavities

Perfect correlation = +1.00 or -1.00 One variable perfectly predicts the other Height in inches and height in feet Speed (mph) and time to finish race Positive correlation Negative correlation

Correlation The more closely the dots approximate a straight line, (the less spread out they are) the stronger the relationship is. Perfect correlation = +1.00 or -1.00 One variable perfectly predicts the other No variability in the scatterplot The dots approximate a straight line

Correlation

Correlation does not imply causation Is it possible that they are causally related? Yes, but the correlational analysis does not answer that question What if it’s a perfect correlation – isn’t that causal? No, it feels more compelling, but is neutral about causality Number of Birthdays Number of Birthday Cakes

Positive correlation: as values on one variable go up, so do values for other variable Negative correlation: as values on one variable go up, the values for other variable go down Number of bathrooms in a city and number of crimes committed Positive correlation Positive correlation

Linear vs curvilinear relationship Linear relationship is a relationship that can be described best with a straight line Curvilinear relationship is a relationship that can be described best with a curved line

Correlation - How do numerical values change? http://neyman.stat.uiuc.edu/~stat100/cuwu/Games.html http://argyll.epsb.ca/jreed/math9/strand4/scatterPlot.htm Correlation - How do numerical values change? Let’s estimate the correlation coefficient for each of the following r = +.80 r = +1.0 r = -1.0 r = -.50 r = 0.0

This shows a strong positive relationship (r = 0 This shows a strong positive relationship (r = 0.97) between the price of the house and its eventual sales price r = +0.97 Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

r = +0.97 r = -0.48 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 = -0.91 Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number) This shows a strong negative relationship (r = -0.91) between the distance that a golf ball is hit and the accuracy of the drive r = -0.91

r = -0.91 r = 0.61 Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number) This shows a moderate positive relationship (r = 0.61) between the price of the length of stay in a hospital and the number of services provided r = -0.91 r = 0.61

r = +0.97 r = -0.48 r = -0.91 r = 0.61

Height of Daughters (inches) Height of Mothers (in) 48 52 56 60 64 68 72 76 48 52 5660 64 68 72 This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches). Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number) Both axes have real numbers listed Both axes and values are labeled Variable name is listed clearly

Height of Daughters (inches) Height of Mothers (in) 48 52 56 60 64 68 72 76 48 52 5660 64 68 72 This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches). Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number) Both axes have real numbers listed Both axes and values are labeled Variable name is listed clearly

Height of Daughters (inches) Height of Mothers (in) 48 52 56 60 64 68 72 76 48 52 5660 64 68 72 This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches). Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number) Both axes have real numbers listed Both axes and values are labeled Variable name is listed clearly

Height of Daughters (inches) Height of Mothers (in) 48 52 56 60 64 68 72 76 48 52 5660 64 68 72 This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches). Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number) Both axes have real numbers listed Both axes and values are labeled Variable name is listed clearly

Height of Daughters (inches) Height of Mothers (in) 48 52 56 60 64 68 72 76 48 52 5660 64 68 72 This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches). Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number) Both axes have real numbers listed Both axes and values are labeled Variable name is listed clearly

Use examples that are different from those is lecture 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 1. Describe one positive correlation Draw a scatterplot (label axes) You have 12 minutes (approximately 2 minutes per example) 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)

Height of Daughters (inches) Height of Mothers (in) 48 52 56 60 64 68 72 76 48 52 5660 64 68 72 This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches). Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number) Both axes have real numbers listed Both axes and values are labeled Variable name is listed clearly 1. Describe one positive correlation Draw a scatterplot (label axes) 2. Describe one negative correlation Draw a scatterplot (label axes) Hand in Correlation worksheet 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)

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

Another example: How many kids in your family? Number of kids in family 1 4 3 2 1 8 4 2 2 14 14 4 2 1 4 2 2 3 1 8

Mean: The balance point of a distribution. Found 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: Σx / n = mean = x Mean for a population: ΣX / N = mean = µ (mu) Measures of “location” Where on the number line the scores tend to cluster Note: Σ = add up x or X = scores n or N = number of scores

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: Σx / n = mean = x 41/ 10 = mean = 4.1 Number of kids in family 1 4 3 2 1 8 4 2 2 14 Note: Σ = add up x or X = scores n or N = number of scores

How many kids are in your family? What is the most common family size? Number of kids in family 1 3 1 4 2 4 2 8 2 14 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)

Number of kids in family 1 4 3 2 1 8 4 2 2 14 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, 1, 2, 2, 2, 3, 4, 4, 8, 14

Number of kids in family 1 3 1 4 2 4 2 8 2 14 Number of kids in family 1 4 3 2 1 8 4 2 2 14 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, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 8, 8, 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 Median also called the 2nd Quartile

Number of kids in family 1 4 3 2 1 8 4 2 2 14 Number of kids in family 1 3 1 4 2 4 2 8 2 14 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, 1, 2, 2, 2, 2, 3, 3, 4, 4, 8, 14 Lower half Upper half 2.5 2nd Quartile Middle number of all scores (Median) 1, 1, 1, 1, 2, 2, 2, 3, 8, 14 2, 2, 3, 4, 4, 4, 2, 4, 4, 8, 14 1st Quartile Middle number of lower half of scores 3rd Quartile Middle number of upper half of scores

Number of kids in family Mode: The value of the most frequent observation Score f . 1 2 2 3 3 1 4 2 5 0 6 0 7 0 8 1 9 0 10 0 11 0 12 0 13 0 14 1 Number of kids in family 1 3 1 4 2 4 2 8 2 14 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

Thank you! See you next time!!