Business 205

Review Two Group Independent Sample T-test Using Excel’s Add-In for Statistical Analysis Entering in Survey Responses

Preview Analysis of Variance (ANOVAs)

Designing Experiments Random Sample Took a job satisfaction survey Took a job satisfaction survey Interacted with a manager Didn’t interact with a manager What tests could your use to run an analysis of the survey data?

Designing Experiments Random Sample Took a job satisfaction survey Took a job satisfaction survey Interacted 20+ times with a manager Didn’t interact with a manager Took a job satisfaction survey Interacted 1-19 times with a manager

Analysis of Variance (ANOVAs) Factors Independent variables Levels How many different values are used for the independent variables Example: You want to know the effect of

Designing Experiments Random Sample Took a job satisfaction survey Took a job satisfaction survey Interacted 20+ times with a manager Didn’t interact with a manager Took a job satisfaction survey Interacted 1-19 times with a manager What are the factors? How many levels are there?

How do you classify this? Factors: Interaction levels Levels: 3 Interact 20+ times Interact 1 – 19 times No interaction

Try a few… Example 1: You are test marketing different colas and want to see which one a consumer would enjoy more. You tell them to taste New Coke, Coke Classic, Diet Coke, Coke with Lime. What is your factor? What is the dependent variable? What is the level?

Try a few… Example 2: You are testing different types of gum and would like to see which one blows the biggest bubble. You have hubba-bubba, juicy fruit, and Wrigley’s gum. What is your factor? What is the dependent variable? What is the level?

Components of an ANOVA SymbolDefinition knumber of treatment conditions nnumber in each treatment condition Ntotal number in the study (across all conditions) Tsum of each individual score per treatment SSsum of squares (X – Mean) 2 for each treatment Ggrand total; sums of all scores in an experiment ∑X 2 each individual score squared then summed for each treatment

Formulas k = ∑ all treatments N = ∑ n for all treatments n = number of scores in each INDIVIDUAL treatment T = ∑ X (all scores in each INDIVIDUAL treatment) SS = ∑ (X-M) 2 for each treatment M = mean for each treatment G = ∑ T ∑ (X 2 ) = sum of all individual scores squared in all treatments

Degrees Freedom df between = k - 1 df within = N - k df total = df between + df within df total = N - 1

Sums of Squares Formulas

Mean Squares

ANOVA F-Ratio

For example… You want to see if the office temperature affects employees’ ability to perform their job. You decided to set the temperature of the room at 50, 75, and 90 degrees. What is the hypothesis? What is the factor? What is the level?

ANOVA Example Group 1 50 degrees Group 2 75 degrees Group 3 90 degrees

ANOVA Example Group 1 50 degrees Group 2 75 degrees Group 3 90 degrees T 1 = 5T 2 = 20T 3 = 5 n 1 = 5 n 2 = 5n 3 = 5 M 1 = 1M 2 = 4M 3 = 1 SS 1 = 6SS 2 = 6SS 3 = 4

ANOVA Example T 1 = 5T 2 = 20T 3 = 5 n 1 = 5 n 2 = 5n 3 = 5 M 1 = 1M 2 = 4M 3 = 1 SS 1 = 6SS 2 = 6SS 3 = 4 G = = 30 N = 15 k = 3 ∑(X 2 ) = 106

ANOVA Example df between = k - 1 = 3 – 1 = 2 df within = N – k = 15 – 3 = 12 df total = N – 1 = 15 – 1 = 14 SS between =[(25/5)+(400/5)+(25/5)] – (900/15) = 30 SS within = = 16 SS total = = 46

ANOVA Example MS between = 30/2 = 15 MS within = 16/12 = 1.33 F = 15/1.33 = F critical (2, 12) = ± 3.88

ANOVA Example We accept our hypothesis; it is statistically significant.

Reporting Results in Table Form ANOVA summary SourceSSdfMS Between treatments30215F = Within treatments Total

Reporting results in written form The analysis revealed significant results, F(2, 12) = 11.28, p <.05.

ANOVA In-Class Example Group 1 50 degrees Group 2 75 degrees Group 3 90 degrees