Lesson 4:

More 1-way ANOVA

Why can’t we do 3 individual 2 population tests?

• A.

• B.

• C.• If each test has a 5% significance level (the

single comparison-wise type one error) then the overall (experiment-wise type one error) significance level, denoted by alpha sub EW would be

Experimental Design

• Experimental Study

• Observational Study

• Completely Randomized Design

Example 1

• Four different paints are advertised as having the same drying time. To check the manufacturers’ claim, 5 random samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied were recorded. The following table summarizes the results.

Paint 1 Paint 2 Paint 3 Paint 4

Mean 133 139 136 144

Std. Dev 6.89 7.07 4.58 7.38

n 5 5 5 5

Use a 5% significance level to see whether the mean drying time is the

same for each.• SSTR

• MSTR

• SSE

• MSE

ANOVA Table

Source DF SS MS F p

Factor

Error

Total

Example 2: Fabric Flammability Tests

• Flammability tests were conducted on children’s sleep wear. The Vertical Semi-restrained Test was used, in which pieces of fabric were burned under controlled conditions. After burning stopped, the length of the charred portion was measured and recorded. Random samples using the same material were obtained from each of 5 testing labs. Because the same fabric was used, the different labs should have obtained the same results. Is there sufficient evidence to support the claim that the mean lengths for the different labs are the same?

Lab 1 Lab 2 Lab 3 Lab 4 Lab 5

2.9 2.7 3.3 3.3 4.1

3.1 2.9 3.3 3.2 4.1

3.7 3.2 3.5 2.7 4.2

3.1 3.7 2.8 2.7 3.1

4.2 3.2 2.8 3.3 3.5

3.1 3.4 3.5 2.7 4.2

ANOVA Table

Source DF SS MS F p

Factor

Error

Total

Calculate Fisher LSD and determine where the differences liePopulations Mean Dif LSD Dif Y/N??

Lab 1 & 2

Lab 1 & 3

Lab 1 & 4

Lab 1 & 5

Lab 2 & 3

Lab 2 & 4

Lab 2 & 5

Lab 3 & 4

Lab 3 & 5

Lab 4 & 5