Six sigma and beyond problem solving and basic mathematics volume ii
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Take a well-defined population — the owners of a particular product X. You cannot tell whether your observed results are biased one way or another, and you cannot tell by how much. After all, no two things are exactly the same. Unless the experimenter plans a study appropriately, accounts for certain issues that are inherent in any study, and understands what is needed for a successful experiment, all will be for naught. Conversely, if you made a bar chart of the ages, on the other hand, no space would be left for the particular category. Height, weight, distance, age, and education can all be measured on a ratio scale. Three say they do, and two say they do not.

To avoid the effect, you should prevent subjects from knowing which experimental group they are in, and you should not tell them anything about the expected results. Why are we going around in circles? Each of the cells also contains a second number. In some situations, however, the mean may not really represent the data well. Eighty percent had seven or fewer tickets a year. Thus, the new treatment may work quite differently for those who are motivated versus those who are not. The result, the standard deviation of the distribution of sample means, is called the standard error of the mean. For example, on one occasion, researchers at a hospital compared two treatments for a particular disease.

I would like to thank as always my personal inspiration, bouncing board, navigator and editor, Carla, for her continually enthusiastic attitude during my most trying times. Your population is well defined. The next step is to resolve it. By comparing the ranges of the two samples, you can tell that the number of problems per vehicle in the sedan sample differed more from each other than those in the truck sample. For the set of data shown in Table 3.

This approach turns out to be more manageable and more expedient. It would be more useful to make another frequency table in which each line represents not a single response but several ones. This procedure should result in about the same number of subjects in the two groups. This number links the paper form and the computer record. As for the terminology and the conventional interpretation of the plot, we owe it all to the statistician John Tukey.

Of course, you can never tell whether your particular sample mean is one of the unlikely ones in the shaded region. What you have to figure out from your sample of respondents is this: How likely is this sample mean of 112 if the population mean for everybody who ever bought this product X is 100? You can also see whether one of the responses was an overwhelming favorite, and which responses are about equally likely. When you have two means from independent samples, the variance of their difference equals the sum of their variances. If you are going to invest a lot of time and money in a study, you owe it to yourself to get expert advice. However, now you are ready to do more. For a variable measured on an interval or ratio scale, however, you can compute some better measures. In this chapter, you will look more closely at some characteristics of the normal distribution.

The next step is to resolve it. By identifying the subcommand percentiles in the frequency command, you will get the percentiles. Sometimes, though, they provide too much information. Differences may occur for many reasons. However, if a sample is reasonably large and it comes from a normal population, its distribution should look more or less normal.

You cannot just make up a table of numbers that you think are random. Current patients may have been diagnosed earlier than previous patients, so they have a better chance of surviving. It turns out, though, that a better way by far is to 1. The intent of the introduction is to sensitize the reader to the importance of taking statistics into consideration in the design and planning of experiments. Questions like these, which do not specify the possible responses, are known as open-ended questions. Or you may want to try product A and product B and then compare the results to see which one is better. On the other hand, if only half of the voters plan to vote for your candidate, your samples would show more variability.

Does the interval include the unknown population value? Show your plans to someone who has actually carried out similar surveys, and ask for advice — before you take any big steps such as printing the questionnaires. Every chapter has been revised and expanded to better tell the story of Lean production—its history, applications, practices, and methods. He reviews basic parametric and non-parametric statistics, probability concepts and applications, and addresses topics for both measurable and attribute characteristics. Would it not be much more informative if I told you that I own the average number of books, or that I am two standard deviations above the average? The normal distribution is very important in data analysis, as you will see throughout the rest of this book and in volumes 4, 5, and 6 of this series. This book gives you a detailed rationale and a theoretical explanation of the problem solving process. Get the raw numbers, and let the machine do the arithmetic.

Design for Six Sigma Statistics is a rigorous mathematical roadmap to help companies reach this goal. Suppose that you are a company personnel manager, and you want to study why people miss work. Since its sign is positive, it indicates that I have more books than average. You also identify values that appear to be unusual, such as ages in the one hundreds or incomes in the millions, and you check the original records to make sure that these values were picked up correctly. You settle on a definition of rich.

Negative values indicate that a distribution has lighter tails than a normal distribution does. No doubt, you and your advisor would be delighted if you could come up with an explanation for absenteeism that would apply to all sorts of workers in all sorts of places. In short, you can do everything possible to make sure the survey will help you answer your specific questions of interest. Owning 20 cars is much more extraordinary than owning 20 shirts. The two types of studies differ in important ways. Medical studies are often characterized as single blind or double blind.