The sample variance Version 12.0 Revision Date: July 2009 David J. Moriarty Biological Sciences Department California State Polytechnic University ()DFSSnXXsnii=−−=∑=1122BIO 211 Test Pac Version 12.0 Page 1 The BIO 211 TEST PAC contains a variety of information critical to your success in the course. Bring the TEST PAC to class with you, and be sure to bring it to exams. Use the TEST PAC regularly and become very familiar with its contents. It will help you. Information in the TEST PAC includes: (1) test summary sheets; (2) class examples; (3) supplemental reading material; (4) practice exams; and (5) practice problems. These are discussed below. See the Table of Contents to locate various items. Test Summary Sheets The test summary sheets contain a summary of basic information on all the inferential statistical tests covered in the course. You are required to have this information committed to memory. Much of this information will appear on the closed book portion of exams. Another important use for this information is to help you select the appropriate statistical test on the open book portion of the exam. When you read a problem, do not expect the choice of test needed to solve the problem to be obvious. You must have a systematic method of going through the tests available to you, and selecting the correct one. Remember that the choice of tests depends on two factors: 1) the biological question; and 2) characteristics of the data. The test summaries should aid you in your search for the appropriate test. You are allowed (and expected) to bring the TEST PAC to exams and use it on the open book portion of the exams. While these sheets present a summary of many important facts on the various analyses, they are not complete. Do not attempt to substitute these sheets for class attendance. Class Examples The examples used in class for many of the statistical tests are found in the TEST PAC. We will use the examples extensively in class. You’ll need the TEST PAC! Supplemental Reading Material The TEST PAC contains text on critical areas are not adequately covered in the text. Your course syllabus references these reading assignments. Practice Exams Read the discussion on how to use the practice exams about one week prior to the first exam. See the Table of Contents for the section of practice exams. Practice Problems - Werner Blood Chemistry Data The practice problems are designed to help you on the final exam. Read the discussion on the practice problems a few days before the final. Basic Statistics Review Students are strongly encouraged to take a course in basic statistics (STA 120 or equivalent) prior to taking Biometrics. A basic statistics course not only covers fundamental material critical for success in Biometrics, but also provides an extensive introduction to topics such as probability, which are important in the biological sciences. You will find review material for the parts of basic statistics critical to BIO 211 on the course Blackboard site.BIO 211 Test Pac Version 12.0 Page 2 Table of Contents A GENERAL METHOD OF HYPOTHESIS TESTING............................................ 3 GOODNESS-OF-FIT................................................................... 5 GOODNESS-OF-FIT TEST - Example.................................................... 6 CONTINGENCY TABLE ANALYSIS........................................................ 8 CONTINGENCY TABLE ANALYSIS - Example.............................................. 9 ONE-SAMPLE t-TEST................................................................ 11 One-sample t-test - Example...................................................... 12 ONE-TAILED VS. TWO TAILED TESTS.................................................. 13 VARIANCE RATIO TEST.............................................................. 16 TWO-SAMPLE t-TEST................................................................ 17 Variance Ratio & Two-sample t-test - Example..................................... 18 MANN-WHITNEY U TEST.............................................................. 20 Mann-Whitney U Test - Example.................................................... 21 PAIRED-SAMPLE t-TEST............................................................. 22 Paired-sample t-test - Example................................................... 23 WILCOXON PAIRED-SAMPLE TEST...................................................... 24 Wilcoxon Paired-sample Test - Example............................................ 25 BARTLETT'S TEST.................................................................. 26 ONE-FACTOR (ONE-WAY) ANALYSIS OF VARIANCE (ANOVA)................................ 27 ONE-FACTOR (ONE-WAY) ANOVA - Example............................................. 28 Sources of Variation in a One-factor ANOVA....................................... 29 A Graphical Approach to Sources of Variation..................................... 33 MULTIPLE COMPARISONS............................................................. 36 KRUSKAL - WALLIS TEST............................................................ 37 TWO-FACTOR (TWO-WAY) ANALYSIS OF VARIANCE........................................ 38 Two-factor (Two-way) ANOVA - Example: randomized block........................... 39 Interaction...................................................................... 41 Two-factor (Two-way) ANOVA - Example: with replications.......................... 42 Experimental Design - Important Safety Tips...................................... 47 REGRESSION....................................................................... 48 Regression - Example............................................................. 49 Regression - Example - Scatter Plot.............................................. 51 CORRELATION...................................................................... 53 SPEARMAN RANK CORRELATION........................................................ 54 Spearman Rank Correlation – Example.............................................. 55 ANALYSIS OF COVARIANCE (ANCOVA).................................................. 56 ANCOVA (Analysis of Covariance) - Example........................................ 57 ANCOVA - Example plot............................................................ 58 THE CENTRAL LIMIT THEOREM - INTRODUCTION......................................... 61 Illustration for the Central Limit