1. Lecture 3 zLast Day: 1.4, 1.6, 1.7 and 1.9 zToday: Finish notes from last day; Sections 2.1-2.3 zNext Day: Finish 2.1-2.3 zPlease read these sections. You are responsible for all material in these sections…even those not discussed in class zAssignment #1: yChapter 1: 11, 13, 16, 18(i)

2. Example (Boys Shoes) zCompany wishes to run an experiment to determine if a new synthetic material is better than the existing one used for making the soles of boys' shoes zExperiment was run to see if the new, cheaper sole wears at the same rate at which the soles wear out zHave enough resources to make 10 pairs of shoes zHow should one sun the experiment?

3. Are These the Same? zExperiment 1: z10 boys were selected at random zEach boy was given a pair of shoes z5 boys received a pair of shoes with the old sole (Sole A) and 5 boys received shoes with the the new sole (sole B) zEach boy wears the shoes for 1 month and the amount of wear is measured z Experiment 2 z 10 boys were selected at random z Each boy was given a pair of shoes z Each pair had 1 shoe with the old sole and 1 shoe with the new sole z For each pair of shoes, the sole type was randomly assigned to the right or left foot z Each boy wears the shoes for 1 month and the amount of wear is measured

4. Analysis zHow would you analyze the data from Experiment 1?

5. Completely Random Design zObjective: Comparing two treatments - A and B zMethod: yN experimental units available for the experiment yrandomly assign treatment A to n 1 exp. units and treatment B to n 2 units (N = n1 + n2) yConduct experiment yresults: A: y A1, y A2, …, y An1 ; B: y B1, y B2, … y Bn2 zAnalysis Objective: yCompare the average responses, A vs. B yIs there evidence that one treatment is better than other, on average? How much better?

6. Model and Analysis

7. Analysis zHow would you analyze the data from Experiment 2? zCan we use a 2-sample t-test or ANOVA here? zWould the 2-sample t-test or ANOVA detect a significant difference?

8. Paired Comparison Designs zObjective - Compare two treatments zMethod ySelect N experimental units yEach experimental unit receives both treatments yConduct the experiment assigning the treatments in random order yMeasure the responses yResults, N pairs: (y A1, y B1 ), (y A2, y B2 ), …, (y AN, y BN )

9. Model and Analysis

10. Benefits of Paired Experiment zPaired experiment used to eliminate possible sources of variability (noise) yIf one receives sole A and another sole B, then the experimental error (variability among experimental units that receive the same treatment) reflects variability between boys and the variability within each boy yIf each boys receives both soles, then the comparison within boy eliminates the variability among boys from the reference noise. The variability of repeated measurements within each boy is the pertinent experimental error in this case zCan be cheaper

11. Data

15. Analyzing the Data

16. Comments zExperimental results must be interpreted and thought about in terms of the subject-matter, not just the statistical results zIn a good experiment, the message should be reasonably clear in a good plot of the data zFormal statistical procedures quantify the impressions that good plots convey

17. Something to Help You Get to Sleep zRead the following news item and in groups of 2-4 discuss the question below: Headline: Xeriscaping May Use Up More Water MESA, AZ – Desert landscaping (called xeriscaping), often planted by residents to conserve water, may actually be using more water. ASU botanist Chris Martin and two students have been measuring the amount of irrigation used in the yards of 18 homes in Tempe and Phoenix. Half have desert plantings; the others have conventional plantings. In the 18 months of the study so far, homeowners put an average of 2.24 gallons per square foot on the xeriscaped yards, compared with 1.67 gallons per square foot on the other yards. zWhat questions would you like to ask Prof. Martin to help you interpret and evaluate these results?

18. You should know … zhow to design, conduct, and analyze: ycompletely randomized design yrandomized paired comparison design zhow to recognize design from description of experiment

19. Blocking and Randomization zBlocking yeliminate sources of variability zRandomization ybalance possible effects of uncontrolled sources of variability yprovide fair estimate of noise variability zGeneral Guidance: “Block what you can and randomize what you cannot”