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

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

Before our next exam (December 4 th ) Lind (10 – 12) Chapter 13: Linear Regression and Correlation Chapter 14: Multiple Regression Chapter 15: Chi-Square Plous (2, 3, & 4) Chapter 17: Social Influences Chapter 18: Group Judgments and Decisions Schedule of readings

Exam 4 – Optional Times for Final Two options for completing Exam 4 Thursday (12/4/14) – The regularly scheduled time Tuesday (12/9/14) – The optional later time Must sign up to take Exam 4 on Tuesday (12/2) Only need to take one exam – these are two optional times

Homework due – Tuesday (November 25 th ) On class website: Please print and complete homework worksheet #18 Hypothesis Testing with correlation coefficients and simple regression

Five steps to hypothesis testing Step 1: Identify the research problem (hypothesis) Describe the null and alternative hypotheses Step 2: Decision rule Alpha level? ( α =.05 or.01)? Step 3: Calculations Step 4: Make decision whether or not to reject null hypothesis If observed t (or F) is bigger then critical t (or F) then reject null Step 5: Conclusion - tie findings back in to research problem Critical statistic (e.g. z or t or F or r) value? MS Within MS Between F = Still, difference between means Still, variability of curve(s)

Homework

Type of major in school 4 (accounting, finance, hr, marketing) Grade Point Average

Homework / = If observed F is bigger than critical F: Reject null & Significant! If p value is less than 0.05: Reject null & Significant! # groups - 1 # scores - number of groups # scores = = =27

Homework Yes F (3, 24) = 3.517;p < 0.05 The GPA for four majors was compared. The average GPA was 2.83 for accounting, 3.02 for finance, 3.24 for HR, and 3.37 for marketing. An ANOVA was conducted and there is a significant difference in GPA for these four groups (F (3,24) = 3.52; p < 0.05).

Number of observations in each group Just add up all scores (we don’t really care about this one) Average for each group (We REALLY care about this one)

“SS” = “Sum of Squares” - will be given for exams Number of groups minus one (k – 1)  4-1=3 Number of people minus number of groups (n – k)  28-4=24

MS between MS within SS between df between SS within df within

Type of executive 3 (banking, retail, insurance) Hours spent at computer

/ 2 = If observed F is bigger than critical F: Reject null & Significant! If p value is less than 0.05: Reject null & Significant!

Yes F (2, 12)= 5.73; p < 0.05 The number of hours spent at the computer was compared for three types of executives. The average hours spent was 10.8 for banking executives, 8 for retail executives, and 8.4 for insurance executives. An ANOVA was conducted and we found a significant difference in the average number of hours spent at the computer for these three groups, (F (2,12) = 5.73; p < 0.05).

Number of observations in each group Just add up all scores (we don’t really care about this one) Average for each group (We REALLY care about this one)

“SS” = “Sum of Squares” - will be given for exams Number of groups minus one (k – 1)  3-1=2 Number of people minus number of groups (n – k)  15-3=12

MS between MS within SS between df between SS within df within

Five steps to hypothesis testing Step 1: Identify the research problem (hypothesis) Describe the null and alternative hypotheses Step 2: Decision rule Alpha level? ( α =.05 or.01)? Step 3: Calculations Step 4: Make decision whether or not to reject null hypothesis If observed t (or F) is bigger then critical t (or F) then reject null Step 5: Conclusion - tie findings back in to research problem Critical statistic (e.g. z or t or F or r) value? MS Within MS Between F = Still, difference between means Still, variability of curve(s)

Writing Assignment - Quiz 2. When do you use a t-test and when do you use an ANOVA 3. What is the formula for degrees of freedom in a two-sample t-test 4. What is the formula for degrees of freedom “between groups” in ANOVA 5. What is the formula for degrees of freedom “within groups” in ANOVA 9. Draw and match each with proper label Between Group Variability Within Group Variability Total Variability 6. Daphne compared running speed for three types of running shoes What is the independent variable? What is the dependent variable? How many factors do we have (what are they)? How many treatments do we have (what are they)? 7. How are “levels”, “groups”, “conditions” “treatments” related? 8. How are “significant difference”, “p< 0.05”, “we reject the null”, and “we found a main effect” related? 1.When do you use a z-test and when do you use a t-test?

Next couple of lectures 11/18/14 Use this as your study guide Logic of hypothesis testing with Correlations Interpreting the Correlations and scatterplots Simple and Multiple Regression Using correlation for predictions r versus r 2 Regression uses the predictor variable (independent) to make predictions about the predicted variable (dependent) Coefficient of correlation is name for “r” Coefficient of determination is name for “r 2 ” (remember it is always positive – no direction info) Standard error of the estimate is our measure of the variability of the dots around the regression line (average deviation of each data point from the regression line – like standard deviation) Coefficient of regression will “b” for each variable (like slope)

Five steps to hypothesis testing Step 1: Identify the research problem (hypothesis) Describe the null and alternative hypotheses Step 2: Decision rule Alpha level? ( α =.05 or.01)? Step 3: Calculations Step 4: Make decision whether or not to reject null hypothesis If observed r is bigger than critical r then reject null Step 5: Conclusion - tie findings back in to research problem Critical statistic (e.g. critical r) value from table? For correlation null is that r = 0 (no relationship) Degrees of Freedom = (n – 2) df = # pairs - 2

Finding a statistically significant correlation The result is “statistically significant” if: the observed correlation is larger than the critical correlation we want our r to be big if we want it to be significantly different from zero!! (either negative or positive but just far away from zero) the p value is less than 0.05 (which is our alpha) we want our “p” to be small!! we reject the null hypothesis then we have support for our alternative hypothesis

Correlation 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 and the worse the prediction The closer to zero the weaker the relationship and the worse the prediction Positive or negative Positive or negative Remember, We’ll call the correlations “r”

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

Positive correlation Positive correlation: as values on one variable go up, so do values for other variable pairs of observations tend to occupy similar relative positions higher scores on one variable tend to co-occur with higher scores on the second variable lower scores on one variable tend to co-occur with lower scores on the second variable scatterplot shows clusters of point from lower left to upper right Remember, Correlation = “r”

Negative correlation Negative correlation: as values on one variable go up, values for other variable go down pairs of observations tend to occupy dissimilar relative positions higher scores on one variable tend to co-occur with lower scores on the second variable lower scores on one variable tend to co-occur with higher scores on the second variable scatterplot shows clusters of point from upper left to lower right Remember, Correlation = “r”

Zero correlation as values on one variable go up, values for the other variable go... anywhere pairs of observations tend to occupy seemingly random relative positions scatterplot shows no apparent slope

Correlation Perfect correlation = or The more closely the dots approximate a straight line, the stronger the relationship is. One variable perfectly predicts the other No variability in the scatterplot The dots approximate a straight line

Perfect correlation = or One variable perfectly predicts the other Negative correlation Positive correlation Height in inches and height in feet Speed (mph) and time to finish race Percent correct on exam by number correct on exam Percent Correct Number Correct Positive correlation Time in the house by time outside of house Negative Correlation Time outside Time in house

Is it possible that they are causally related? Correlation does not imply causation 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 Birthday Cakes Number of Birthdays Remember the birthday cakes!

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

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

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

Correlation - How do numerical values change? r = r = 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)

Let’s estimate the correlation coefficient for each of the following r = +.98 r = Remember, Correlation = “r”

Let’s estimate the correlation coefficient for each of the following r = r = -. 63

Let’s estimate the correlation coefficient for each of the following r = r = -. 43

Correlation The more closely the dots approximate a straight line, the stronger the relationship is. One variable perfectly predicts the other No variability in the scatter plot The dots approximate a straight line Perfect correlation = or -1.00

Five steps to hypothesis testing Step 1: Identify the research problem (hypothesis) Describe the null and alternative hypotheses Step 2: Decision rule Alpha level? ( α =.05 or.01)? Step 3: Calculations Step 4: Make decision whether or not to reject null hypothesis If observed r is bigger than critical r then reject null Step 5: Conclusion - tie findings back in to research problem Critical statistic (e.g. critical r) value from table? For correlation null is that r = 0 (no relationship) Degrees of Freedom = (n – 2) df = # pairs - 2

Five steps to hypothesis testing Problem 1 Is there a relationship between the: Price Square Feet We measured 150 homes recently sold

Five steps to hypothesis testing Step 1: Identify the research problem (hypothesis) Describe the null and alternative hypotheses Step 2: Decision rule – find critical r (from table) Alpha level? ( α =.05) null is that there is no relationship (r = 0.0) Degrees of Freedom = (n – 2) df = # pairs - 2 Is there a relationship between the cost of a home and the size of the home alternative is that there is a relationship (r ≠ 0.0) 150 pairs – 2 = 148 pairs

Critical r value from table df = # pairs - 2 df = 148 pairs α =.05 Critical value r (148) = 0.195

Five steps to hypothesis testing Step 3: Calculations

Five steps to hypothesis testing Step 3: Calculations

Five steps to hypothesis testing Step 3: Calculations Step 4: Make decision whether or not to reject null hypothesis If observed r is bigger than critical r then reject null r = Critical value r (148) = Observed correlation r (148) = Yes we reject the null > 0.195

Conclusion: Yes we reject the null. The observed r is bigger than critical r (0.727 > 0.195) Yes, this is significantly different than zero – something going on These data suggest a strong positive correlation between home prices and home size. This correlation was large enough to reach significance, r(148) = 0.73; p < 0.05

Finding a statistically significant correlation The result is “statistically significant” if: the observed correlation is larger than the critical correlation we want our r to be big if we want it to be significantly different from zero!! (either negative or positive but just far away from zero) the p value is less than 0.05 (which is our alpha) we want our “p” to be small!! we reject the null hypothesis then we have support for our alternative hypothesis