Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Chapter 24 Statistical Inference: Conclusion

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Identifying the Correct Technique… Tools > Data Analysis Plus > Technique Identification High Tech

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Identifying the Correct Technique…

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Identifying the Correct Technique…

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Identifying the Correct Technique… Textbook > Figure 24.1 > Flowchart of Techniques Low Tech

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Identifying the Correct Technique… Flowchart of Techniques…

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Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 24.9

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Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Twelve Statistical Concepts… …you need for life after the statistics final exam

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Concept One… Statistical techniques are processes that convert data into information. Descriptive techniques describe and summarize. Inferential techniques allow us to make estimates and draw conclusions about populations from samples. Data Statistics Information

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Concept Two… We need a large number of techniques because there are numerous objectives and types of data. There are three types of data: interval (real numbers), nominal (categories), and ordinal (ratings). Each combination of data type and objective requires specific techniques.

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Concept Three… We gather data by various sampling plans. However, the validity of any statistical outcome is dependent on the validity of the sampling. “Garbage in-garbage out” very much applies in statistics.

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Concept Four… The sampling distribution is the source of statistical inference. The confidence interval estimator and the test statistic are derived directly from the sampling distribution. All inferences are actually probability statements based on the sampling distribution.

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Concept Five… All tests of hypotheses are conducted similarly. We assume that the null hypothesis is true. We then compute the value of the test statistic. If the difference between what we have observed (and calculated) and what we expect to observe is too large, we reject the null hypothesis. The standard that decides what is “too large” is determined by the probability of a Type I error.

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Concept Six… In any test of hypothesis (and in most decisions) there are two possible errors, Type I and Type II errors. The relationship between the probabilities of these errors helps us decide where to set the standard. If we set the standard so high that the probability of a Type I error is very small, we increase the probability of a Type II error (and vice versa).

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Concept Seven… We can improve the exactitude of a confidence interval estimator or decrease the probability of a Type II error by increasing the sample size. More data means more information, which results in narrower intervals or lower probabilities of making mistakes, which in turn leads to better decisions.

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Concept Eight… The sampling distributions that are used for interval data are the Student t and the F. These distributions are related so that the various techniques for interval data are themselves related. We can use the analysis of variance in place of the t-test of two means. We can use regression analysis with indicator variables in place of the analysis of variance. We often build a model to represent relationships among interval variables, including indicator variables.

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Concept Nine… In analyzing interval data, we attempt to explain as much of the variation as possible. By doing so, we can learn a great deal about whether populations differ and what variables affect the response (dependent) variable.

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Concept Ten… The techniques used on nominal data require that we count the number of times each category occurs. The counts are then used to compute statistics. The sampling distributions we use for nominal data are the standard normal and the chi-squared. These distributions are related, as are the techniques.

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Concept Eleven… The techniques used on ordinal data are based on a ranking procedure. We call these techniques nonparametric. Because the requirements for the use of nonparametric techniques are less stringent than those for a parametric procedure, we often use nonparametric techniques in place of parametric ones when the required conditions for the parametric test are not satisfied. To ensure the validity of a statistical technique, we must check the required conditions.

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc Concept Twelve… We can obtain data through experimentation or by observation. Observational data lend themselves to several conflicting interpretations. Data gathered by an experiment are more likely to lead to a definitive interpretation. In addition to designing experiments, statistics practitioners can also select particular sample sizes to produce the accuracy and confidence they desire.

Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc In today’s world… …we are constantly being bombarded with statistics and statistical information… Customer Surveys Medical News Political Polls Economic Predictions Marketing Information Scanner Data How can we make sense out of all this data? How do we differentiate valid from flawed claims? What is Statistics?! “Statistics is a way to get information from data. That’s it!” – Gerald Keller