#### Transcript anova

**S519: Evaluation of Information Systems**

Social Statistics Inferential Statistics Chapter 11: ANOVA

**This week**

When to use F statstic How to compute and interpret Using FTEST and FDIST functions How to use the ANOVA

**The problem with t tests…**

We could compare three groups with multiple ttests: M1 vs. M2, M1 vs. M3, M2 vs. M3

**What is ANOVA?**

“

**An**

alysis

**o**

f

**Va**

riance” A hypothesis-testing procedure used to evaluate mean differences between two or more treatments (or populations).

Related to: t-tests using independent-measures or repeated- measures design.

Advantages: 1) Can work with more than two samples.

2) Can work with more than one independent variable

**What is ANOVA?**

In ANOVA an independent or quasi independent variable is called a factor.

Factor = independent (or quasi-independent) variable.

Levels = number of values used for the independent variable.

One factor → “single-factor design” More than one factor → “factorial design”

**What is ANOVA?**

An example of a single-factor design A example of a two-factor design

**F value**

Variance between treatments can have two interpretations: Variance is due to differences between treatments.

Variance is due to chance alone. This may be due to individual differences or experimental error.

**Three Types of ANOVA**

Independent measures design: Groups are samples of independent measurements (different people) Dependent measures design: Groups are samples of dependent measurements (usually same people at different times; also matched samples) “Repeated measures” Factorial ANOVA (more than one factor)

**Excel: ANOVA**

Three different ANOVA: Anova: single factor - independent Anova: two factors with replication - factorial Anova: two factors without replication - dependent

**Example (independent)**

Three groups of preschoolers and their language scores, whether they are overall different?

Group 1 Scores 87 Group 2 Scores 86 76 56 78 98 77 66 75 67 87 Group 3 Scores 89 85 99 91 96 85 79 81 82 87 89 90 89 78 85 91 96 96 93

**F test steps**

Step1: a statement of the null and research hypothesis One-tailed or two-tailed (there is no such thing in ANOVA)

*H*

0 : 1 2 3

*H*

1

## : at least one

## is different

**F test steps**

Step2: Setting the level of risk (or the level of significance or Type I error) associated with the null hypothesis 0.05

**F test steps**

Step3: Selection of the appropriate test statistics See Figure 11.1 (S-p227) Simple ANOVA (independent)

**F test steps**

Between-group degree of freedom=k-1 k: number of groups Within-group degree of freedom=N-k N: total sample size

**F test steps**

Step4: determination of the value needed for rejection of the null hypothesis using the appropriate table of critical values for the particular statistic Table B3 (S-p363) df for the denominator = n-k=30-3=27 df for the numerator = k-1=3-1=2

**F test steps**

Step5: comparison of the obtained value and the critical value If obtained value > the critical value, reject the null hypothesis If obtained value < the critical value, accept the null hypothesis 8.80 and 3.36

**F test steps**

Step6 and 7: decision time What is your conclusion? Why?

How do you interpret F (2, 27) =8.80, p<0.05

**Example (dependent)**

Five participants took a series of test on a new drug

**P1 P2 P3 P4 P5 2 0 0 T1 3 0 1 1 1 T2 4 3 4 3 4 T3 6 3 5 4 3 T4 7 6**

**F test steps**

Step1: a statement of the null and research hypothesis One-tailed or two-tailed (there is no such thing in ANOVA)

*H*

0 : 1 2 3 4

*H*

1

## : at least one

## is different

**F test steps**

Step2: Setting the level of risk (or the level of significance or Type I error) associated with the null hypothesis 0.05

**F test steps**

Step3: Selection of the appropriate test statistics See Figure 11.1 (S-p227) Simple ANOVA (independent)

**F test steps**

Between-group degree of freedom=k-1 k: number of groups Within-group degree of freedom=N-k N: total sample size Between-subject degree of freedom=n-1 n: number of subjects Error degree of freedom=(N-k)-(n-1)

**F test steps**

Step4: determination of the value needed for rejection of the null hypothesis using the appropriate table of critical values for the particular statistic Table B3 (S-p363) df for the denominator = (N-k)-(n-1)=16-4=12 df for the numerator = k-1=4-1=3

**F test steps**

Step5: comparison of the obtained value and the critical value If obtained value > the critical value, reject the null hypothesis If obtained value < the critical value, accept the null hypothesis 24.88 and 3.49

**F test steps**

Step6 and 7: decision time What is your conclusion? Why?

How do you interpret F (3, 12) =24.88, p<0.05

**Factorial ANOAVA**

Next week