height (male 11)	N(146cm,8cm) = 	N(57.5,3.15)
	   	 
		weight (male 18-24)	N(162,29.1) 
		weight (femail 18-24)	N(134,27) 
	   	 
		1994 SAT mean Verbal = 423, 7% above 600, 42% below 400
			approx s.d. 120
			now renormalized to N(500,100)
			what percent score 800?

		1987 CA women's salaries  mean=11,600; s.d.=10,500

Tuesday, January 11
	Topic: More Pictures of Data
	Topic: Relationships between Categorical Variables
	Topic: Chi-Squared
	Read: Utts 9 

	Due: HW #3 @ hw02.shtml

	Vocab: pie chart, bar chart, pictogram, line graph, scatter plot 

	    make some with survey 1 data

	Common problems with plots, graphs, and pictures
	    1) missing labels
	    2) scale doesn't start at 0
	    3) changes in labeling along an axis
	    4) misleading units
	    5) poor information

	Picture Checklist
	    overall impression
		1) is message clear?
		2) is purpose clear?
		10) is there any clutter?
	    source
		3) is source given?
		4) is source reliable? 
	    labeling
		5) is labeling clear?
		6) do axes start at 0?
		7) is scale constant?
		8) are there any breaks along axis? are they easy to spot?
	    	9) was inflation adjustment made?

	Banner chart and follow-up letters
	Utts, Figure 9.9 (page 149) and fixed version
	
	Read: Utts 12
	Act: Golf Balls in the Yard @ data/golfballs.shtml
	Vocab:  contingency table, cell, row, column, conditional percentage, %%
		rate, test statistic, chi-sqaured statistic, p-value, %%
		statistical significance, proportion, odds, relative risk, %%
		odds ratio, Simpson's paradox %%

	Physician's Health Study data

			attack	no att.	total	rate/1000
		Aspirin	104	10,933	11,037	9.4
		Placebo	189	10,845	11,034	17.1
		Total	293	21,778	22,071

	    Question of the day:  why is this data so compelling?
		significance: how unusual is this? (chi-squared)
		magnitude: how big is this?

	Golf ball distribution and test statistics
	    4-sided dice, computer simulation

	Chi-squared statistic (on golf ball data again)
	    what should we expect if there is no association?
	    how can we adjust our measurement to account for sample size?

	Hugo -- 4 times in 12 rolls; how unusual is that?
		have students roll 12 dice several times and count number of 
			6's rolled (work in pairs)

	
	Return to Physician's Health Survey
	    significance: do chi squared

		P-value:  interpretted the same for all statistical tests!
		chi-sqared table (degrees of freedom)

	    magnitude: relative risk 

		percentage having trait = (# with trait / total #) * (100%)
		proportion having trait = (# with trait / total #) 
		    i.e. probablility written as decimal
		risk of having trait = # with trait / total # 
		odds of having trait = # with / # without to 1
				     = # with to # without
		odds against trait   = # without / # with to 1
				     = # without to # with
		relative risk: 	     = one risk / other risk
		increased risk:      = change / original (* 100%)

	Misrepresenting risk
	    1) no baseline risk given
	    2) no time period given
	    3) unclear population (may not apply to you)

	Simpson's Parodox
	    hospital example (Utts chapter 12, pages 213-215)
		give combined results first, then separate

					survive	die	s rate 	d rate
			standard	  505	 595 	.46	.54
			new		  195	 905	.18	.82
			total		  700	1500	

	
	
			standard 	    5	  95	 .05	.95
			new		  100	 900	 .10	.90
			total		  105	 995	 

	    discrimination example (Utts, chapter 12, pages 215-217) ??

	    Berkeley admissions (Utts page 221, exercise 14)
		video clip -- FAPP #10 2:04:45 -- 2:08:40 [maybe longer]

	    death penalty

		326 cases, white defendant: 19/160 get death pen. (.119)
		           black defendant: 17/166 get death pen. (.102)

			when separated by victim's race, see different story
				[overhead from Moore 207]

	    point: statistically significant means that the effect is not 
			likely to be due to chance alone, but there may be
			some other factor than the obvious one that is
			reason