chapter11

# chapter11 - Introduction to Probability and Statistics and...

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Introduction to Probability Introduction to Probability and Statistics and Statistics Thirteenth Edition Thirteenth Edition Chapter 11 The Analysis of Variance

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Experimental Design Experimental Design The sampling plan sampling plan or experimental experimental design design determines the way that a sample is selected. In an observational study, observational study, the experimenter observes data that already exist. The sampling plan sampling plan is a plan for collecting this data. In a designed experiment, designed experiment, the experimenter imposes one or more experimental conditions on the experimental units and records the response.
Definitions Definitions An experimental unit experimental unit is the object on which a measurement or measurements) is taken. A factor factor is an independent variable whose values are controlled and varied by the experimenter. A level level is the intensity setting of a factor. A treatment treatment is a specific combination of factor levels. The response response is the variable being measured by the experimenter.

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Example Example A group of people is randomly divided into an experimental and a control group. The control group is given an aptitude test after having eaten a full breakfast. The experimental group is given the same test without having eaten any breakfast. Experimental unit = Factor = Response = Levels = Treatments: person Score on test meal Breakfast or no breakfast Breakfast or no breakfast
Example Example The experimenter in the previous example also records the person’s gender. Describe the factors, levels and treatments. Experimental unit = Response = Factor #1 = Factor #2 = Levels = Levels = Treatments: person score meal breakfast or no breakfast gender male or female male and breakfast, female and breakfast, male and no breakfast, female and no breakfast

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The Analysis of The Analysis of Variance (ANOVA) Variance (ANOVA) All measurements exhibit variability variability . . The total variation in the response measurements is broken into portions that can be attributed to various factors factors . These portions are used to judge the effect of the various factors on the experimental response.
The Analysis of Variance The Analysis of Variance If an experiment has been properly designed, Total variation Factor 2 Random variation Factor 1 We compare the variation due to any one factor to the typical random variation in the experiment. The variation between the sample means is larger than the typical variation within the samples. The variation between the sample means is about the same as the typical variation within the samples.

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Assumptions Assumptions Similar to the assumptions required in Chapter 10.
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