ANOVA l The FDistribution l 1 Way ANOVA

ANOVA l. The F-Distribution l 1 -Way ANOVA l. What Test to Use?

The F-Distribution

1 -Way ANOVA: Objective 1 -Way ANalysis Of VAriance (ANOVA) is used when we want to test the claim that three or more populations have the same mean.

Requirements of 1 -Way ANOVA l l l All population distributions are approximately normal. All populations have the same standard deviations (or not too different if the sample sizes are nearly equal). Data collection uses the Simple Random Sampling technique. The samples are independent of each other. The categorization of the sample is done in the same way.

All Roads the Same? Are the mean driving speeds the same for Highway 50, Highway 89, and Pioneer Trail? Hwy 50 58 Hwy 89 43 Pioneer Tr. 51 52 47 55 51 56 50 47 49 56 49 42 54 60 47 55 56 58 50 STAT ->TESTS -> ANOVA, ANOVA(L 1, L 2, L 3) Fail to reject H 0. There is insufficient evidence to conclude that the population mean speeds on the three roads are not the same.

GPA’s By Student Type A study was done to see if the mean GPAs for in-state, out-of-state, and foreign students are different. What can be concluded at the 0. 01 level of significance? Reject H 0. There is statistically significant evidence to conclude that at least two of the population mean GPA’s differ.

How Long Will You Live? Are the mean life spans for dogs the same for different living conditions? Fenced Yard 15 16 11 8 17 14 Indoor Only 18 3 16 12 15 9 17 Indoor/Outdoor 12 16 3 11 10 Stray 9 6 14 12 2 5 8 STAT ->TESTS -> ANOVA, ANOVA(L 1, L 2, L 3, L 4) Fail to reject H 0. There is insufficient evidence to conclude that the population mean life span for the four dog lifestyles differ.

What Test to Use? l Qualitative Data: Try c 2 l Test for Independence or relationship between categories l Same Distribution? With known population and unknown sample or checking for Uniform or Normal: GOF l Same Distribution? Neither known: Homogeneity

What Test to Use? l Just one Sample Taken Yes/No question and np, nq > 5: 1 -Prop. ZTest l Quantitative question and n > 30 and s known: Z-Test l Quantitative question and n > 30 and s unknown: T-Test l

What Test to Use? l Two Samples Predict y given x: Regression Analysis l Yes/No question and np, nq > 5 for both: 2 -Prop. ZTest l Difference between dependent (paired) quantitative variables, ndiff > 30: T-Test (L 1 – L 2 -> L 3) l

What Test to Use? l Two Samples Quantitative question and both n’s > 30 independent samples and s‘s known: 2 -Samp. ZTest l Quantitative question and both n’s > 30 independent samples and s‘s unknown: 2 -Samp. TTest l l >2 Samples: Quantitative questions (many assumptions): ANOVA