M316 Chapter 22 - M316 Chapter 22 Dr. Berg Inference About...

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Unformatted text preview: M316 Chapter 22 Dr. Berg Inference About Variables: Part III Review The procedures of Chapters 18 to 21 are among the most common of all statistical inference methods. There are three key questions: • What population parameter does you problem concern? • What type of design produced the data? • Are the conditions of the procedure met? Here is a flowchart: Here are some necessary skills. A. Recognition 1 Recognize when a problem requires inference about population means (quantitative response variable) or population proportions (usually categorical response variable). 2 Recognize from the design of a study whether one‐sample, matched pairs, or two‐sample procedures are needed. 3 Based on recognizing the problem setting, choose among the one‐ and two‐ sample t procedures for means, and the one‐ and two‐sample z procedures for proportions. 1 M316 B. Inference About One Mean Chapter 22 Dr. Berg 1 Verify that the t procedures are appropriate in a particular setting. Check the study design and the distribution of the data and take advantage of robustness against lack of Normality. 2 Recognize when poor study design, outliers, or a small sample from a skewed distribution make the t procedures risky. 3 Use the one‐sample t procedure to obtain a confidence interval at a stated level of confidence for the mean µ of a population. 4 Carry out a one‐sample t test for the hypothesis that a population mean µ has a specified value against either a one‐sided or a two‐sided alternative. Use software to find the P‐value or Table C to get an approximate value. 5 Recognize matched pairs data and use the t procedures to obtain confidence intervals an to perform tests of significance for such data. C. Comparing Two Means 1 Verify that the two‐sample t procedures are appropriate in a particular setting. Check the study design and the distribution of the data and take advantage of robustness against lack of Normality. 2 Give a confidence interval for the difference between two means. Use software if you have it. Use the two‐sample t statistic with conservative degrees of freedom and Table C if you do not have statistical software. 3 Test the hypothesis that two populations have equal means against either a one‐sided or a two‐sided alternative. Use software if you have it. Use the two‐sample t test with conservative degrees of freedom and Table C if you do not have statistical software. 4 Know that procedures for comparing the standard deviations of two Normal populations are available, but that these procedures are risky because they are not robust against non‐Normal distributions. D. Inference About One Proportion 1 Verify that you can safely use either the large‐sample or the plus four z procedures in a particular setting. Check the study design and the guidelines for sample size. 2 Use the large‐sample z procedure to give a confidence interval for a population proportion p. Understand that the true confidence level may be substantially less than you ask for unless the sample is very large and the true p is not close to 0 or 1. 3 Use the plus four modification of the z procedure to give a confidence interval for p that is accurate even for small samples and for any value of p. 4 Use the z statistic to carry out a test of significance for the hypothesis H 0 : p = p0 about a population proportion p against either a onesided or a two‐ € 2 M316 Chapter 22 Dr. Berg sided alternative. Use software or Table A to find the P‐value, or Table C to get an approximate value. E. Comparing Two Proportions 1 Verify that you can safely use either the large‐sample or the plus four z procedures in a particular setting. Check the study design and the guidelines for sample sizes. 2 Use the large‐sample z procedure to give a confidence interval for the difference p1 − p2 between proportions in two populations based on independent samples from the populations. Understand that the true confidence level may be less than you ask for unless the samples are quite large. 3 Use the plus four modification of the z procedure to give a confidence € interval for p1 − p2 that is accurate even for very small samples and for any values of p1 and p2. 4 Use a z statistic to test the hypothesis H 0 : p1 = p2 that proportions in two distinct populations are equal. Use software or Table A to find the P‐value, or Table € C to get an approximate value. € 3 ...
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This note was uploaded on 09/02/2010 for the course BIO 325 taught by Professor Saxena during the Spring '08 term at University of Texas at Austin.

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