Experimental Designs 1 Completely Randomized Design 2 Randomized

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Experimental Designs 1. Completely Randomized Design 2. Randomized Block 3. Matched Pairs

Experimental Designs 1. Completely Randomized Design 2. Randomized Block 3. Matched Pairs

Let’s recap some ideas. Random assignment removes the potential for confounding variables. Direct control

Let’s recap some ideas. Random assignment removes the potential for confounding variables. Direct control holds extraneous variables constant so their effects are not confounded with the treatments. Blocking uses extraneous variables to create groups (blocks) that are similar. All treatments are then tried in each block.

Experimental Designs Experimental Units Random Assignment 1. Completely randomized design – experimental units are

Experimental Designs Experimental Units Random Assignment 1. Completely randomized design – experimental units are assigned at random to treatments or treatments are assigned at random to trials Treatment A Measure response for A Compare treatments Treatment B Measure response for B

Example 1: A farm-product manufacturer wants to determine if the yield of a crop

Example 1: A farm-product manufacturer wants to determine if the yield of a crop is different when the soil is treated with three different types of fertilizers. Fifteen similar plots of land are planted with the same type of seed but are fertilized differently. At the end of the growing season, the mean yield from the sample plots is compared. Experimental units? Plots of land Factors? Type of fertilizer Response variable? Yield of crop How many treatments? 3

Fertilizer experiment continued: A farm-product manufacturer wants to determine if the yield of a

Fertilizer experiment continued: A farm-product manufacturer wants to determine if the yield of a crop is different when the soil is treated with three different types of fertilizers. Fifteen similar plots of land are planted with the same type of seed but are fertilized differently. At the end of the growing season, the mean yield from the sample plots is compared. Why is the same type of seed used on all 15 plots? It is part of the controls in the experiment. What are other potential extraneous variables? Type of soil, amount of water, etc. Does this experiment have a placebo? Explain NO – a placebo is not needed in this experiment

Example 2: A consumer group wants to test cake pans to see which works

Example 2: A consumer group wants to test cake pans to see which works the best (bakes evenly). It will test aluminum, glass, and plastic pans in both gas and electric ovens. There are 30 boxes of cake mix to use for this experiment. Experiment units? Factors? Cake mixes Two factors - type of pan (aluminum, glass, and plastic) and type of oven (electric and gas) Response variable? How evenly the cake bakes Name the treatments? Aluminum pan in electric oven, aluminum pan in gas oven, glass pan in electric oven, glass pan in gas oven, plastic pan in electric oven, and plastic pan in gas oven

Cake experiment continued: A consumer group wants to Could wewhich roll a works die

Cake experiment continued: A consumer group wants to Could wewhich roll a works die forthe each box? test cake pans to see best (bakes evenly). If aluminum, we roll a “ 1” assign box to theinfirst It will test glass, andthe plastic pans both gas treatment (aluminum pan 30 in electric oven). If we and electric ovens. There are boxes of cake mix to use nd roll aexperiment. 2, assign the box to the 2 treatment, and so for this on. This is justhow one way you can perform this randomization. Describe to that randomly assign the cake mixes to the treatments so that there is an even number in each treatment. Number the boxes of cake mix from 1 to 30. Write the numbers 1 to 30 on identical slips of paper and place into a hat. Mix well. Randomly select 5 numbers from the hat and assign those boxes to the treatment of aluminum pan in electric oven. Randomly select 5 more numbers and assign those boxes to the treatment aluminum pan in gas oven. Continue this process, randomly assigning 5 boxes to each treatment glass pan in electric oven, glass pan in gas oven, and plastic pan in electric oven. The remaining 5 are assigned to plastic pan in gas oven

2. Randomized block Units should be blocked on a variable that Randomized block –

2. Randomized block Units should be blocked on a variable that Randomized block – units are blocked into affects the response!!! groups (homogeneous) and then randomly Block 2 Treatment A Measure response for A Compare treatments for block 1 Treatment B Measure response for B Treatment A Measure response for A Compare the results from the 2 blocks Create blocks Experimental Units 1 Random Assignment Block Random Assignment assigned to treatments Compare treatments for block 2 Treatment B Measure response for B

Fertilizer experiment revisited: A farm-product manufacturer wants to determine if the yield of a

Fertilizer experiment revisited: A farm-product manufacturer wants to determine if the yield of a crop is different when the soil is treated with two different types of fertilizers. Twenty plots of land (10 plots are along a river and 10 plots are away from the river) are planted with the same type of seed but are fertilized differently. At the end of the growing season, the mean yield from the sample plots is compared. Can the experimenter directly control the types of soil in the different plots of land? No – they must use the plots that are available What can be done to account for this variable? They could block by type of land

Fertilizer experiment revisited: Describe how to create the blocks of land then to randomly

Fertilizer experiment revisited: Describe how to create the blocks of land then to randomly assign plots to the 2 types of fertilizer. • First create 2 blocks of land. Block 1 would be the 10 plots that are by the river. Block 2 would be the 10 plots away from the river. • Number the 10 plots in block 1 from 1 to 10. Write the numbers 1 to 10 on identical slips of paper and place into a hat. Mix well. Randomly select 5 numbers from the hat and assign those boxes to fertilizer A. The remaining 5 are assigned to Fertilizer B. • Number the 10 plots in block 2 from 1 to 10. Write the numbers 1 to 10 on identical slips of paper and place into a hat. Mix well. Randomly select 5 numbers from the hat and assign those boxes to fertilizer A. The remaining 5 are assigned to Fertilizer B.

Example: Comparing cancer therapies The progress of a type of cancer differs in women

Example: Comparing cancer therapies The progress of a type of cancer differs in women and in men. A clinical experiment to compare three therapies for this cancer therefore treats sex as a blocking variable. Two separate randomizations are done. One assigning the female subjects and the other assigning the male subjects. They are groups of subjects that differ in some way (sex in this case) that is apparent BEFORE the experiment.

Here is a mapping of this experiment:

Here is a mapping of this experiment:

3. Matched pairs - a special type of block design where the blocks consist

3. Matched pairs - a special type of block design where the blocks consist of 2 experimental units that are similar (eg. Twins) with each being randomly assigned to a treatment OR the block consist of individual units that are assigned both treatments in random order (Each block in a matched pairs design may consist of just one subject who gets both treatments one after the other.

Each subject serves as his or her own control. The order of the treatments

Each subject serves as his or her own control. The order of the treatments can influence the subject’s response, so we randomize the order for each subject by a coin toss.

Example 3: Two new word-processing programs are to be compared by measuring the speed

Example 3: Two new word-processing programs are to be compared by measuring the speed with which a standard task can be completed. One hundred volunteers will perform the same task on each of the programs in random order and their speeds will be measured. Explain why this is a matched pairs design. Each block consist of an individual who will do both treatments How could we determine which program the volunteers use first? We could flip a coin for each volunteer; heads they do program A first, tails they do program B first.

The ONLY way to show a cause-effect relationship is with a well-designed, well-controlled experiment!!!

The ONLY way to show a cause-effect relationship is with a well-designed, well-controlled experiment!!!

My-tips for AP Exam - Every experiment should include the following components: 1. Randomization

My-tips for AP Exam - Every experiment should include the following components: 1. Randomization 2. Imposing Treatment 3. Control and/or blocking 4. Replication Make sure you show all these 4 components!