Objective: To learn and use other important principles of experimental design. HW: Read the rest of section 5.2 and complete pink ditto (double sided). Do Now: Take out last nights homework Draw a diagram for yesterdays tomato plant experiment in your notebook.

Designing Experiments An ad for OptiGro plant fertilizer claims that with this product, you will grow juicier, tastier tomatoes. Youd like to taste this claim, and wonder whether you might be able to get away with half the specified dose. How can you set up an experiment to test this claim?

1)State what you want to know: I want to know if OptiGro makes tomato plants tastier or juicier than plants without fertilizer. 2) Specify the response variable: The level of juicy and tastiness in the tomatoes. 3) Specify the factor levels and treatments I will grow tomatoes at three different levels- some with no fertilizer, some with half the specified amount, and some with the full dose. These are the three treatments. 4) Specify the experimental units: 24 lovely tomatoes (possibly organic and of the same variety) from the same store.

Observe the principles of experimental design: -Control any sources of variability you know of and can control -Randomly assign experimental units to treatments to equalize the effects of unknown or uncontrollable variation -Specify how the random numbers needed for randomization will be obtained. -Replicate results by placing more than one plant in each treatment group. Grow tomato plants in the same soil / plot of land, take into account environmental things like trees, etc. Take care of them consistently (same amount of watering, pesticides, etc)… I will use my calculator to randomly select tomatoes to put into 3 different groups. 24 Tomatoes – put 8 in each treatment group

How are we going to measure the response variable? We could get a blind panel of tasters to taste the tomatoes and rate their juiciness and tastiness (rank them and compare rankings or you could do a scale 1-10)…

DIAGRAM IT

Other Details Specify other experiment details. You must give enough details so that another experimenter could exactly replicate your experiment. Its generally better to include details that seem irrelevant than to leave out matters that could turn out to be important. Specify how to measure the response.

Once you have collected the data: You need to display them (visually) and compare the results between the three treatment groups. Conclusion: If the differences in taste and juiciness among groups are greater than I would expect by knowing the usual variation among tomatoes, I may be able to conclude that these differences can be attributed to the treatment with the fertilizer.

Statistical Significance In later chapters, we will find a precise numerical way to actually calculate statistical significance. For now, use your common sense / intuition. Consider these boxplots (see overhead)

Control Treatment & the Control Group What was our control treatment and group in the tomato-fertilizer example? AS – Is a control group really necessary?

BLINDING Who can affect the outcome of an experiment: Those who influence the results (subjects, treatment administrators, technicians) Those who evaluate the results (judges, physicians, etc) Single-blind vs. double-blind Tomato Experiment Again…

PLACEBOS A fake treatment that looks just like the treatments being tested. What is the placebo effect? The tendency of many human subjects (often 20% or more) to show a response even when administered a placebo.

The best experiments are: Randomized Double blind Comparative Placebo-controlled

Randomized Block Design 12 Tomatoes from Store A and 12 Tomatoes from Store B Block A Block B

Adding more Factors There are two kinds of gardeners. Some water frequently and some never do. OptiGro wants to ensure that their product will work under a variety of watering conditions. Lets include the amount of watering as part of our experiment.

Multi-Factor Design 12 Tomato Plants from store Group 1 (2 plants) Group 2 (2 plants) Group 3 (2 plants) Group 4 (2 plants) Group 5 (2 plants) Group 6 (2 plants) Treatment 1 control – no water Treatment 2 ½ dose – no water Treatment 3 Full dose/ no water Treatment 4 Control – water Treatment 5 ½ dose – water Treatment 6 Full dose - water Compare juiciness and tastiness

CONFOUNDING Teacher classroom style example When the levels of one factor are associated with the levels of another factor, we say these two factors are confounded.