Lecture 31: more Chapter 11, Section 3 Categorical & Quantitative Variable More About ANOVA ANOVA: Hypotheses, Table, Test Stat, P-value  1st Step in Practice: Displays, Summaries  ANOVA Output  Guidelines for Use of ANOVA  ©2011 Brooks/Cole, Cengage Elementary Statistics: Looking at the Big Picture 1 Learning Looking Back: Review 4 Stages of Statistics  Data Production (discussed in Lectures 1-4)  Displaying and Summarizing (Lectures 5-12)  Probability (discussed in Lectures 13-20)  Statistical Inference  1 categorical (discussed in Lectures 21-23)  1 quantitative (discussed in Lectures 24-27)  cat and quan: paired, 2-sample, several-sample  2 categorical  2 quantitative  ©2011 Brooks/Cole, Elementary Statistics: Looking at the Big Picture L31.2 Cengage Learning ANOVA Null and Alternative Hypotheses : explanatory C & response Q not related Equivalently,  (difference among sample means just chance) : explanatory C & response Q are related Equivalently, : not all the are equal  (difference too extreme to be due to chance) Depending on formulation, the word “not” appears in H or H . o a ©2011 Brooks/Cole, Elementary Statistics: Looking at the Big Picture L31.5 Cengage Learning Example: How to Refute a Claim about “All” Background: Reader asked medical advice  columnist: “Dear Doctor, does everyone with Parkinson’s disease shake?” and doctor replied: All patients with Parkinson’s disease do not shake. Question: Is this what the doctor meant to say?  Response:  ©2011 Brooks/Cole, Elementary Statistics: Looking at the Big Picture L31.7 Cengage Learning Example: ANOVA Alternative Hypothesis Background: Null hypothesis to test for  relationship between race (3 groups) and earnings: Question: Is this the correct alternative?  Response:  Words are better: say “_________________________”. ©2011 Brooks/Cole, Elementary Statistics: Looking at the Big Picture L31.9 Cengage Learning The F Statistic (Review) Numerator: variation among groups  How different are from one another?  Denominator: variation within groups  How spread out are samples? (sds )  ©2011 Brooks/Cole, Elementary Statistics: Looking at the Big Picture L31.10 Cengage Learning Role of Variations on Conclusion (Review) Boxplots with same variation among groups (3, 4, 5) but different variation within: sds large (left) or small (right) var among Scenario on right: smaller s.d.s  larger F = var within smaller P-value likelier to reject Ho conclude pop means differ ©2011 Brooks/Cole, Elementary Statistics: Looking at the Big Picture L31.11 Cengage Learning ANOVA Table Organizes calculations  “Source” refers to source of variation  DF: use I = no. of groups, N = total sample size  SSG measures overall variation among groups  SSE measures overall variation within groups  Mean Sums: Divide Sums by DFs  F: Take quotient of MSG and MSE  P-value: Found with software or tables  ©2011 Brooks/Cole, Elementary Statistics: Looking at the Big Picture L31.15 Cengage Learning Example: Key ANOVA Values Background: Compare mileages for 8 sedans, 8  minivans, 12 SUVs; find SSG=42.0, SSE=181.4. Question: What are the following values for table:  DFG? DFE? MSG? MSE? F?  Response:  DFG = 3 – 1 = 2  DFE = N – I = (8+8+12) – 3 = 25  MSG = SSG/DFG = 42/2 = 21   MSE= SSE/DFE = 181.4/25 = 7.256 F= MSG/MSE = 21/7.256 = 2.89  ©2011 Brooks/Cole, Elementary Statistics: Looking at the Big Picture L31.16 Cengage Learning Example: Completing ANOVA Table Background: Found these values for ANOVA:  DFG=3-1= 2  DFE=N-I=(8+8+12)-3= 25  MSG=SSG/DFG=42/2= 21  MSE=SSE/DFE=181.4/25= 7.256  F=MSG/MSE=21/7.256= 2.89  Question: Complete ANOVA table?  Response:  SoftwareP-val=0.0743marginally significant ©2011 Brooks/Cole, Elementary Statistics: Looking at the Big Picture L31.18 Cengage Learning