INTEGRATED LEARNING CENTER Screen Lecturer’s desk Cabinet Cabinet Table Computer Storage Cabinet 4 3 Row A 19 18 5 17 16 15 14 13 12 11 10 9 8 7 6 2 1 Row B 3 23 22 6 5 4 21 20 19 7 18 17 16 15 14 13 12 11 10 9 8 2 1 Row C 24 4 3 23 22 5 21 20 6 19 7 18 17 16 15 14 13 12 11 10 9 8 1 Row D 25 2 24 23 4 3 22 21 20 6 5 19 7 18 17 16 15 14 13 12 11 10 9 8 1 Row E 26 25 2 24 4 3 23 22 5 21 20 6 19 18 17 16 15 14 13 12 11 10 9 8 7 27 26 2 1 Row F 25 24 3 23 4 22 5 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 28 27 26 1 Row G 25 24 3 2 23 5 4 22 29 21 20 6 28 19 18 17 16 15 14 13 12 11 10 9 8 7 27 26 2 1 Row H 25 24 3 23 22 6 5 4 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 26 2 1 Row I 25 24 3 23 4 22 5 21 20 6 19 18 17 16 15 14 13 12 11 10 9 8 7 26 1 25 3 2 Row J 24 23 5 4 22 21 20 6 28 19 7 18 17 16 15 14 13 12 11 10 9 8 27 26 25 3 2 1 Row K 24 23 4 22 5 21 20 6 19 7 18 17 16 15 14 13 12 11 10 9 8 Row L 20 19 18 1 17 3 2 16 5 4 15 14 13 12 11 10 9 8 7 6 INTEGRATED LEARNING CENTER ILC 120 broken desk

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

Schedule of readings Before our next exam (April 7th) OpenStax Chapters 1 – 12 Plous (2, 3, & 4) Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence

By the end of lecture today 3/24/16 Analysis of Variance (ANOVA) Constructing brief, complete summary statements

“df” = degrees of freedom Remember, you should know these two formulas by heart “SS” = “Sum of Squares” “SS” = “Sum of Squares” = s2 = Sample Variance Sample Standard Deviation = s = “SS” = “Sum of Squares” “df” = degrees of freedom

Study Type 3: One-way Analysis of Variance (ANOVA) We are looking to compare two means Study Type 2: t-test Study Type 3: One-way Analysis of Variance (ANOVA) Comparing more than two means

incentive then the means are significantly different from each other Main effect of incentive: Will offering an incentive result in more girl scout cookies being sold? If we have a “effect” of incentive then the means are significantly different from each other we reject the null we have a significant F p < 0.05 To get an effect we want: Large “F” - big effect and small variability Small “p” - less than 0.05 (whatever our alpha is) We don’t know which means are different from which …. just that they are not all the same 8

One way analysis of variance Variance is divided Remember, one-way = one IV Total variability Between group variability (only one factor) Within group variability (error variance) Remember, 1 factor = 1 independent variable (this will be our numerator – like difference between means) Remember, error variance = random error (this will be our denominator – like within group variability

F = MSBetween MSWithin 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)? Still, difference between means Critical statistic (e.g. z or t or F or r) value? Step 3: Calculations MSWithin MSBetween F = Still, variability of curve(s) 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

“Between Groups” Variability Difference between means . “Between Groups” Variability Difference between means Difference between means Difference between means “Within Groups” Variability Variability of curve(s) Variability of curve(s) Variability of curve(s)

The sum of squared deviations of some set of scores about their mean Sum of squares (SS): The sum of squared deviations of some set of scores about their mean Mean squares (MS): The sum of squares divided by its degrees of freedom Mean square between groups: sum of squares between groups divided by its degrees of freedom Mean square total: sum of squares total divided by its degrees of freedom MSWithin MSBetween F = Mean square within groups: sum of squares within groups divided by its degrees of freedom 12

F = ANOVA Variability between groups Variability within groups “Between” variability bigger than “within” variability so should get a big (significant) F Variability Within Groups Variability Within Groups Variability Between Groups Variability Within Groups “Between” variability getting smaller “within” variability staying same so, should get a smaller F Variability Between Groups “Between” variability getting very small “within” variability staying same so, should get a very small F Variability Within Groups

ANOVA Variability between groups F = Variability within groups “Between” variability bigger than “within” variability so should get a big (significant) F Variability Within Groups Variability Within Groups Variability Between Groups “Between” variability getting smaller “within” variability staying same so, should get a smaller F Variability Within Groups “Between” variability getting very small “within” variability staying same so, should get a very small F (equal to 1)

Homework

Homework

Homework

Homework Type of major in school 4 (accounting, finance, hr, marketing) Grade Point Average Homework 0.05 2.83 3.02 3.24 3.37

# scores - number of groups 0.3937 0.1119 If observed F is bigger than critical F: Reject null & Significant! If observed F is bigger than critical F: Reject null & Significant! 0.3937 / 0.1119 = 3.517 Homework 3.517 3.009 If p value is less than 0.05: Reject null & Significant! 3 24 0.03 4-1=3 # groups - 1 # scores - number of groups 28 - 4=24 # scores - 1 28 - 1=27

Yes Homework 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).

Average for each group (We REALLY care about this one) Number of observations in each group

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

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

Type of executive 3 (banking, retail, insurance) Hours spent at computer 0.05 10.8 8 8.4

11.46 2 If observed F is bigger than critical F: Reject null & Significant! If observed F is bigger than critical F: Reject null & Significant! 11.46 / 2 = 5.733 5.733 3.88 If p value is less than 0.05: Reject null & Significant! 2 12 0.0179

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 Average for each group Number of observations in each group Just add up all scores

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

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

Questions?

Writing Assignment - Quiz 1. When do you use a t-test and when do you use an ANOVA 2. What is the formula for degrees of freedom in a two-sample t-test 3. What is the formula for degrees of freedom “between groups” in ANOVA 4. What is the formula for degrees of freedom “within groups” in ANOVA 5. How are “levels”, “groups”, “conditions” “treatments” related? 6. How are “significant difference”, “p< 0.05”, “main effect” and “we reject the null” related? 7. Draw and match each with proper label Within Group Variability Total Variability Between Group Variability

Writing Assignment - Quiz 8. Daphne compared running speed for three types of running shoes. She asked 10 people to run as fast as they could wearing one type of shoe. So, there were 30 people altogether 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)? 9. Complete this ANOVA table 10. Find the critical F value from the table 11. Is there a main effect of type of running shoe? Is “p< 0.05”?

Writing Assignment - Quiz n -1 per group or n-2 or Total n - # of groups 1. When do you use a t-test and when do you use an ANOVA t-tests compare two means ANOVA compares more than two means 2. What is the formula for degrees of freedom in a two-sample t-test 3. What is the formula for degrees of freedom “between groups” in ANOVA # of groups - 1 4. What is the formula for degrees of freedom “within groups” in ANOVA n -1 per group or Total n - # of groups 5. How are “levels”, “groups”, “conditions” “treatments” related? 6. How are “significant difference”, “p< 0.05”, “main effect” and “we reject the null” related? They all mean the same thing They all mean the same thing 7. Draw and match each with proper label Within Group Variability Total Variability Between Group Variability

Writing Assignment - Quiz 8. Daphne compared running speed for three types of running shoes. She asked 10 people to run as fast as they could wearing one type of shoe. So, there were 30 people altogether 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)? Type of running shoe Running Speed Type 1 Type 2 Type 3 3 groups 1 Factor 9. Complete this ANOVA table SSB dfB # groups - 1 n - # groups MSB MSW SSW dfW n - 1 Yes F(2,27)=4.00; p< 0.05 10. Find the critical F value from the table 3.37 11. Is there a main effect of type of running shoe? Is “p< 0.05”?

In a one-way ANOVA we have three types of variability. Let’s try one In a one-way ANOVA we have three types of variability. Which picture best depicts the random error variability (also known as the within variability)? a. Figure 1 b. Figure 2 c. Figure 3 d. All of the above 1. correct 2. 3.

In a one-way ANOVA we have three types of variability. Let’s try one In a one-way ANOVA we have three types of variability. Which picture best depicts the between group variability? a. Figure 1 b. Figure 2 c. Figure 3 d. All of the above correct 1. 2. 3.

Which figure would depict the largest F ratio a. Figure 1 b. Figure 2 Variability between groups F = Let’s try one Variability within groups “F ratio” is referring to "observed F” Which figure would depict the largest F ratio a. Figure 1 b. Figure 2 c. Figure 3 d. All of the above correct 1. 2. 3.

Winnie found an observed F ratio of .9, what should she conclude? Let’s try one Winnie found an observed F ratio of .9, what should she conclude? a. Reject the null hypothesis b. Do not reject the null hypothesis c. Not enough info is given correct 1. 2. 3.

Winnie found an observed z of .74, what should she conclude? If your observed z is within one standard deviation of the mean, you will never reject the null Let’s try one Winnie found an observed z of .74, what should she conclude? (Hint: notice that .74 is less than 1) a. Reject the null hypothesis b. Do not reject the null hypothesis c. Not enough info is given correct x x small observed z score small observed z score

Winnie found an observed t of .04, what should she conclude? Let’s try one Winnie found an observed t of .04, what should she conclude? (Hint: notice that .04 is less than 1) a. Reject the null hypothesis b. Do not reject the null hypothesis c. Not enough info is given correct x small observed t score

F(4, 25) = 3.12; p < 0.05 Let’s try one How many observations within each group? Let’s try one An ANOVA was conducted comparing different types of solar cells and there appears to be a significant difference in output of each (watts) F(4, 25) = 3.12; p < 0.05. In this study there were __ types of solar cells and __ total observations in the whole study? a. 4; 25 b. 5; 30 c. 4; 30 d. 5; 25 F(4, 25) = 3.12; p < 0.05 correct # groups - 1 # scores - # of groups # scores - 1

F(4, 25) = 3.12; p < 0.05 Let’s try one An ANOVA was conducted comparing different types of solar cells and there appears to be significant difference in output of each (watts) F(4, 25) = 3.12; p < 0.05. In this study ___ a. we rejected the null hypothesis b. we did not reject the null hypothesis correct F(4, 25) = 3.12; p < 0.05 Observed F bigger than Critical F p < .05

F(4, 25) = 3.12; p < 0.05 Let’s try one An ANOVA was conducted comparing different types of solar cells. The analysis was completed using an alpha of 0.05. But Julia now wants to know if she can reject the null with an alpha of at 0.01. In this study ___ a. we rejected the null hypothesis b. we did not reject the null hypothesis correct F(4, 25) = 3.12; p < 0.05 Comparison of the Observed F and Critical F Is no longer are helpful because the critical F is no longer correct. We must use the p value p < .05 p > .01

Let’s try one An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark) . For each neighborhood we measured the price of four homes. Please complete this ANOVA table. Degrees of freedom between is _____; degrees of freedom within is ____ a. 16; 4 b. 4; 16 c. 12; 3 d. 3; 12 correct .

Let’s try one An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark) . For each neighborhood we measured the price of four homes. Please complete this ANOVA table. Mean Square between is _____; Mean Square within is ____ a. 300, 300 b. 100, 100 c. 100, 25 d. 25, 100 correct .

Let’s try one An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark) . For each neighborhood we measured the price of four homes. Please complete this ANOVA table. The F ratio is: a. .25 b. 1 c. 4 d. 25 correct .

a. reject the null hypothesis b. not reject the null hypothesis Let’s try one An ANOVA was conducted comparing home prices in four neighborhoods (Southpark, Northpark, Westpark, Eastpark) . For each neighborhood we measured the price of four homes. Please complete this ANOVA table, alpha = 0.05. We should: a. reject the null hypothesis b. not reject the null hypothesis correct Observed F bigger than Critical F p < .05

Thank you! See you next time!!