Stat 217 – Day 7 Quantitative data (Topic 7) Preliminary question #1: What do you think is a typical weight for a male Olympic rower? Handout

Notes on HW 1/Lab 1 See me with grading concerns  Check mark, “OK”, squiggle underline, ?, !  It, proof,…  HW Solutions/model lab (soon) available online HW 1: Good job  Blackboard reminders  Act 1-7: Injury rate per 1000 participants  Direction of bias and why suspect  Describing a confounding variable – connect to both EV and RV Lab 1: Good job  A bit holistic… What to pay attention to…  See comments online  A bit more on “reasoning” (beyond “it’s a small p-value” at end) Could it have been a “coincidence”? “By chance?” Later will want to be more formal in this interpretation

Last Time – Comparing groups (Categorical response) Organize data: Two-way table Numerical summary: Conditional proportions Graphical summary: Segmented bar graph  Comparing conditional distributions across groups  Variables are independent if conditional distributions don’t vary P. 98 “Watch Out”

Activity 6-2: AZT vs. HIV Explanatory variable  Good: whether received AZT  Bad: whether AZT works  Bad: those who received AZT  Bad: AZT Response variable  Good: whether baby was HIV+  Bad: whether fewer HIV+ babies with AZT/whether AZT has an effect  Bad: number of HIV+ babies

Activity 6-2 (p. 98) Experiment – was explanatory variable (identify) imposed by researchers? Conditional proportion with HIV in each group  40/183 =.219 vs. 13/180 =.072  Difference: =.1464  Can be difficult to interpret size of this difference (f) Relative risk =.2186/.0722 = 3.03  Those in the placebo group were more than 3 times more likely to HIV-positive baby. placeboAZT HIV + Not HIV +.52 vs..37

A bit more on relative risk…

Lessons It is incorrect when interpreting the difference in two conditional proportions/percentages (.1464) to say “the decrease is X%.”  Percentage change implies multiplication not subtraction Make sure the interpretation is consistent with how you did the calculation

Activity 6-2 (g) With a randomized, placebo-controlled experiment, can attribute this to AZT!  Make sure consider “design issues”  What population are you willing to generalize the results to? Good: Don’t know if they were randomly selected… Good: HIV+ women, volunteers Good: HIV+ moms who have money… Bad: Yes since randomly assigned Bad: No since small sample Bad: No if believe no difference Why not diet? Age? Seriousness of condition beforehand?

Activity 6-2 cont. Still have to ask whether the difference (ratio) is statistically significant (Lab 2)  Could this difference in the groups (large relative risk) have arisen just by the random assignment process (by coincidence)?  Well, let’s mimic the random assignment process and see what types of results we get…

Assessing Significance…

Questions? Questions on Topic 6?  6-5, 6-12 Questions on Lab 2? Questions on HW 2?

Topic 7 (variation of Activity 7-1) Some variables from Blackboard survey  cost of last hair cut  number of siblings  number of states visited  your heights  rating value of statistics  number of heads in 100 coin tosses Type of variables? Graph?

Topic 7 ABCDEFABCDEF cost of your last hair cut number of siblings number of headsnumber of states you’ve visited your heights your rating values of statistics

Important features (p. 121) A big distinction in the behavior of the 3 graphs on the left? Shape is an important feature when describing the overall distribution

Topic 7 ABCDEFABCDEF cost of your last hair cut number of siblings number of headsnumber of states you’ve visited your heights your rating values of statistics Skewed to the right Symmetric Skewed to the leftslightly

Important features (p. 121) Center  Easy with symmetric distributions  How decide when skewed? Spread or variability  Consistency Outliers  Identify and consider explanations!  Other unusual features

To Turn in with partner  What is your guess of my age?  When I look at the distribution of everyone’s guesses, what shape do you think the distribution will have? For Wednesday  Activities 7-3, 7-4: stemplots  Finish HW 2, Continue Lab 2