Six-sigma12

# Six-sigma12 - Analysis of Variance and Comparative...

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1 Analysis of Variance and Comparative Experiment An example: An independent automobile evaluation company wants to compare the qualities of 4 different cars, Ford Taurus, Chevy Lumina, Honda Accord and Toyota Camry. Evaluation cars are driven and evaluated by 7 evaluators, each evaluator is asked to give a composite score ranging from 1-10, 10 is the best and 1 is the worst. The result is as follows: Car Models Evaluation scores by evaluators Evaluator1 Evaluator2 Evaluato r3 Evaluator4 Evaluator5 Evaluator6 Evaluator7 Ford Taurus 6.5 8.2 3.9 9.4 7.5 5.8 7.9 Chevy Lumina 6.3 8.3 3.5 9.2 7.6 5.4 7.4 Honda Accord 7.2 8.6 3.9 9.5 7.3 6.1 8.2 Toyota Camry 7.3 8.5 4.1 9.4 7.2 6.3 8.1

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2 The Analysis of Variance (ANOVA) The ANOVA procedure is one of the most powerful statistical techniques . ANOVA is a general technique that can be used to test the hypothesis that the means among two or more groups are equal, under the assumption that the sampled populations are normally distributed. To begin, let us study the effect of temperature on a passive component such as a resistor. We select three different temperatures and observe their effect on the resistors. This experiment can be conducted by measuring all the participating resistors before placing n resistors each in three different ovens. Each oven is heated to a selected temperature. Then we measure the resistors again after, say, 24 hours and analyze the responses, which are the differences between before and after being subjected to the temperatures. The temperature is called a factor . The different temperature settings are called levels . In this example there are three levels or settings of the factor Temperature.
3 What is a factor? A factor is an independent treatment variable whose settings (values) are controlled and varied by the experimenter. The intensity setting of a factor is the level. Levels may be quantitative numbers or, in many cases, simply "present" or "not present" ("0" or "1"). For example, the temperature setting in the resistor experiment may be: 100 o F, 200 o F and 300 o F We can simply call them: Level 1; Level 2 and Level 3

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4 The 1-way ANOVA In the experiment above, there is only one factor, temperature, and the analysis of variance that we will be using to analyze the effect of temperature is called a one-way or one-factor ANOVA . The 2-way or 3-way ANOVA We could have opted to also study the effect of positions in the oven. In this case there would be two factors, temperature and oven position. Here we speak of a two-way or two-factor ANOVA . Furthermore, we may be interested in a third factor, the effect of time. Now we deal with a three-way or three-factor ANOVA. In each of these ANOVA's we test a variety of hypotheses of equality of means (or average responses when the factors are varied).
5 Example 1: The tensile strength of Portland cement is being studied.

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## This note was uploaded on 05/09/2010 for the course IE IE7610 taught by Professor Dr.kaiyang during the Winter '10 term at Wayne State University.

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Six-sigma12 - Analysis of Variance and Comparative...

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