2      175      325      500
		        208.33   291.67
		
		Total      625      875     1500
		
		Chi-Sq =  2.667 +  1.905 +
		          5.333 +  3.810 = 13.714
		DF = 1, P-Value = 0.000
		------------------------------------------------	
	Simpson's Parodox
	    If we divide by programs applied to, we see a different story
		------------------------------------------------	
		Expected counts are printed below observed counts
		
		       acceptA  rejectA    Total
		    1      400      250      650
		        403.45   246.55
		
		    2       50       25       75
		         46.55    28.45
		
		Total      450      275      725
		
		Chi-Sq =  0.029 +  0.048 +
		          0.255 +  0.418 = 0.751
		DF = 1, P-Value = 0.386
		------------------------------------------------	
		Expected counts are printed below observed counts
		
		       acceptB  rejectB    Total
		    1       50      300      350
		         79.03   270.97
		
		    2      125      300      425
		         95.97   329.03
		
		Total      175      600      775
		
		Chi-Sq = 10.665 +  3.111 +
		          8.783 +  2.562 = 25.120
		DF = 1, P-Value = 0.000
		------------------------------------------------	
		
	    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) ??

	    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

	Probability
	    random: long-term predictability vs short-term unpredictability
		law of large numbers / "law" of small numbers

	    scale: 0 to 1 (0% to 100%)
	    personal vs. mathematical (relative frequency)

	4 Rules and applications
		axiomatic method
	    four rules "overhead"
	    examples
		probability of losing luggage is 1/176 (Krantz)
		
		P(heart attack kills) = .33, P(cancer kills) = .2 
			[assuming death]
		estimated probability of grades
		
		probability of two girls (P(boy) about .512)

		probability of winning 2 of 3, 3 of 5 given an estimate
			for each game
		
	video -- Life By the Numbers (#4 Prob) 
		02:00 (or 08:20) - 27:00: intro to prob., Graunt, casinos
		27:00 - 42:25: polling, polio, prob assesses results

	







		note that (p)(1-p) < .25, so use .25	
		note that p-hat is usually very close to p, especially if
			the sample is large

		example: sample 1600 people and 500 people say yes
		
	 	example: Reeses' pieces

	Testing a hypothesis
		1) determine null and alternative hypotheses
		2) collect data 
		3) compute test statistic
			test stat is a measure of how true the 
			null hypothesis seems to be
		4) determine likelihood of such an extreme test 
			statistic if null hypothesis is true (p-value)
		5) make a decision

	Testing Hypotheses for Proportions
		test statistic is z-score

	    example: predicting election outcomes 


==

Tuesday, January 25
	Topic: Time Series
	Topic: Wrap-Up
	Due: HW #10 @ hw06.shtml
	Vocab: time series, long-term trend, seasonal variation,%%
	seasonal adjustment, cycle 

	A look at Calvin Tuition Data

	Time series
	    plot Calvin Tuition Data
	    plot CPI (with Calvin Price Index?)
	    births
	    Dow Jones
	    postage?

	Things to watch for
	    cherry picking data
	    choice of units ($ vs inflation adjustments, etc)
	    vertical axis doesn't start at zero (magnifies steepness)