ANOVA-A (Key Even)

12.2 Bronchial reactivity.

(A) Explore the data with side-by-side boxplots. Not yet done.

(B) Test the means for a difference with a one-way ANOVA procedure. Descriptive statistics are

n Mean StdDev SO₂ 5 18.840 9.692 NO 6 6.617 3.945 O₂ 4 4.975 3.409 Total 15 10.253

Testing H₀: �₁ = �₂ = �₃ vs. H₁: at least one population mean differs
SS_B = (5)(18.84 - 10.253)² + (6)(6.617 - 10.253)² + (4)(4.975 - 10.253)² = 559.435 with df_B = 3 - 1= 2 and s²_B = 559.435 / 2 = 279.717
SS_w = 488.418 with df_w = 15 - 3 = 12 and s²_{w =} 488.418 / 12 = 40.702
F_stat = 279.717 / 40.702 = 6.87 with 2 and 12 df; P = .010.
Comment: Sample variances differ by quite a bit and Levene's test produces P = 0.06, making ANOVA suspect. Maybe a non-parametric is warranted?

12.4 Fever reduction. Conduct an ANOVA.

SS_B = 5.6575 with df_B = 2 and s²_B = 2.829
SS_W = 5.2056 with df_W = 12 and s²_{W =} 0.4338
F_stat = 6.52 with 2 and 12 df, P = 0.012

Interpret your results. The ANOVA show the differences to be significant.

12.6 Maternal smoking 1. Stemplots were not requested by are helpful in getting organized.

4| 5| 6| 29 7| 45 8| 3 9| 2 �10

Group 1 (non-smokers)

4| 5|8 6| 7| 138 8| 2 9| �10

Group 2 (Ex-smokers)

4|7 5|89 6|22 7| 8|3 9| �10

Group 3 (< half)

4|9 5|478 6|228 7|1 8| 9| �10

Group 4 (> half)

(A) Explore the data with a side-by-side boxplot. The boxplots are shown below. Because of the small ns it is hard to say anything other than group 1 and group 2 seem to have higher averages than groups 3 and 4. The three outside values warrant further scrutiny.

(B) Conduct an ANOVA.

(C) ...discuss your findings.

Testing H₀: �₁ = �₂ = �₃ = �₄ versus H₁: at least one population mean differs

F_stat = 4.15 w/ df₁ = 3 and df₂ = 21; P = 0.019.

The difference is significant, confirming non-random differences among the groups.

The descriptive statistics should be discussed in this context.