Business 205

Review

Two Group Independent Sample T-testUsing Excel’s Add-In for Statistical

AnalysisEntering 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+ timeswith a manager

Didn’t interact with a manager

Took a job satisfaction survey

Interacted 1-19 timeswith a manager

Analysis of Variance (ANOVAs)

Factors Independent variables

LevelsHow 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+ timeswith a manager

Didn’t interact with a manager

Took a job satisfaction survey

Interacted 1-19 timeswith 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 timesNo 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

Symbol Definition

k number of treatment conditions

n number in each treatment condition

N total number in the study (across all conditions)

T sum of each individual score per treatment

SS sum of squares (X – Mean)2 for each treatment

G grand total; sums of all scores in an experiment

∑X2 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 ∑ (X2) = sum of all individual scores squared in all

treatments

Degrees Freedom

dfbetween = k - 1

dfwithin = N - k

dftotal = dfbetween + dfwithin

dftotal = N - 1

Sums of Squares Formulas

withinbetweentotal SSSSSS

N

GXSStotal

22 )(

nwithin SSSSSSSSSS ...21menteach treat inside

N

G

n

TSSbetween

22

)(

Mean Squares

between

betweenbetween

df

SSMS

within

withinwithin

df

SSMS

ANOVA F-Ratio

within

between

MS

MSF

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

0 4 1

1 3 2

3 6 2

1 3 0

0 4 0

ANOVA Example

Group 1

50 degrees

Group 2

75 degrees

Group 3

90 degrees

0 4 1

1 3 2

3 6 2

1 3 0

0 4 0

T1 = 5 T2 = 20 T3 = 5n1 = 5 n2 = 5 n3 = 5M1 = 1 M2 = 4 M3 = 1SS1 = 6 SS2 = 6 SS3 = 4

ANOVA Example

T1 = 5 T2 = 20 T3 = 5n1 = 5 n2 = 5 n3 = 5M1 = 1 M2 = 4 M3 = 1SS1 = 6 SS2 = 6 SS3 = 4

G = 5 + 20 + 5 = 30N = 15k = 3∑(X2) = 106

ANOVA Example

dfbetween = k - 1 = 3 – 1 = 2dfwithin = N – k = 15 – 3 = 12dftotal = N – 1 = 15 – 1 = 14

SSbetween =[(25/5)+(400/5)+(25/5)] – (900/15) = 30

SSwithin = 6 + 6 + 4 = 16SStotal = 30 + 16 = 46

ANOVA Example

MSbetween = 30/2 = 15

MSwithin= 16/12 = 1.33

F = 15/1.33 = 11.28

Fcritical (2, 12) = ± 3.88

ANOVA Example

11.28

We accept our hypothesis; it is statistically significant.

Reporting Results in Table Form

-------------------------------------------------------------------------ANOVA summary

Source SS df MS-------------------------------------------------------------------------Between treatments 30 2 15 F = 11.28Within treatments 16 12 1.33Total 46 14-------------------------------------------------------------------------

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

0 4 1

1 3 2

3 6 2