1. Stat 217 – Week 10

2. Outline Exam 2 Lab 7 Questions on Chi-square, ANOVA, Regression  HW 7  Lab 8 Notes for Thursday’s lab Notes for final exam Notes for final project report

3. Exam 2 Average around.78 Most common errors very easy to fix!  evaluation vs. interpretation of p-value Reject/Fail to reject Ho – make a decision What is it the probability of?  Interpretation of confidence interval vs. level I’m 95% confidence that – make parameter clear, context If I were to take thousands of intervals, what would be true roughly 95% of the time  What conclusions would you draw from this analysis? Be sure to address significance, causation, and generalizability with brief justifications in each case.

4. Lab 3 Very good model for final project report  Attention grabbing introduction Purpose, predictions, why reader should continue  Lots of data collection details (lots!)  Full discussion of descriptive statistics, relate to context, expectations  Include output, tie inferential results back to descriptive statistics, justify all statements  Critique your study at end  Proofreading, page breaks, organization, lead-ins, formatting advice (see BB page)

5. Lab 3 Now  Ho:  =0 where  represents the average price difference in the population of all textbooks at the two stores (El Corral – Aida’s)  Ha:  >0  t-statistic: 4.14, p-value =.000 (Minitab) Strong evidence is a genuine difference on average As long as believe random sample, normal population  95% confidence interval for  : (3.77, 11.35) I’m 95% confident that the average price difference is between $3.77 and $11.35 per book Meaningful difference?

6. Two categorical variables Compare observed counts to expected counts (under null model) for every cell of table Test statistic: How to find test-statistic: Minitab  Expected counts, cell contributions, test statistic, p- value  Small p-value  reject H 0  at least one  differs Technical conditions  All expected counts at least 5, randomness

7. Minitab output

8. Last Time – Chi-square Tests Whenever have a two-way table:  Independent random samples, binary response Ho:  1 =  2 =  3 = =  I  Independent random samples, categorical response Ho: population distributions are the same  Randomized experiment, categorical response Ho: No treatment effect  Random sample, two categorical variables Ho: No association between variable 1 and variable 2

9. One quantitative and one categorical When? Want to compare more than 2 means  Ho:  1 =… =  I  Ha: not all the population means are equal How? Compare variability between groups to variability within groups (sampling variability)  F-statistic (larger than expect to get under Ho?) One-sided p-value  Minitab

10. Minitab output

11. Two quantitative variables Creating and describing scatterplots  Direction, form, strength  Correlation coefficient r measures strength of linear association Modeling a linear relationship  Using Minitab to determine the equation  Using equation to make (reasonable) predictions about response variable from explanatory variable  Interpretation of slope and intercept in context

12. Last Time – Two quantitative variables Ho: no association or  =0 Ha: is an/positive/negative association Minitab output  t test statistic from “coefficient of x” row  two-sided p-value  SE(b) = amount of random variation of slopes from sample to sample Strength of evidence (p-value) vs. strength of association P. 605

13. Example: Gesell data Can we predict later intelligence based on when the child first speaks?

14. Removing the one child has a pretty big impact on the regression line, significance Example: Gesell data

15. Best conclusion?  Some evidence that children who take a particularly long time to speak may have lower IQ scores, but otherwise no relationship between age of first words and later IQ.  For children who take between 5 and 20 months, no relationship…

16. This week HW 7 due tomorrow Lab 8 due Thursday Course evaluations Thursday in lab  Mandatory!  Time in lab: review questions (Rebecca), finish Lab 8, finish final project report

17. Finals Week Final Exam Wednesday 10:10-1  Library Lab (35-111B)  Rebecca, Dr. McGaughy Final Project Report “due” Monday or before  With individual evaluation form Graded HW 7, Lab 8 available Monday? Review Sheet (with problems) online Final review Discussion Board forum Tuesday evening office hour?

18. Format of Final Exam Multiple choice (~30-40 min, ~20%)  Big ideas, not memorization, little calculation (calculator) Short, long written answers  Like midterms, partial credit  Open 3 pages of notes (to be turned in), Minitab, TOS Calculator applet  Cumulative though some emphasis on more recent material Some very familiar questions Recognizing which procedure to use Sampling distributions!

19. Food for thought Simulation vs. (CLT) analysis Descriptive statistics vs. inferential statistics Confidence intervals Other study aids:  Multiple choice review projects in BB (emphasizing terminology, earlier material)  Jeopardy  Email in evenings!

20. Submitting final project Either hard copy to Stat Department office or email  Make sure you email your data file to me  See notes and reminders in Blackboard

21. Thanks!!