MATH 251, Probability and Statistics I, Fall 2005, Sept. 23, Day 13After class

Reading: Sec. 2.6: 1 copy outside my door, 1 on reserve.  Was Sec. 2.6 in IPS 4th ed. (pp. 187-203 for text.  Figures are -2 from download--fig. 2.30 in 4th ed is 2.32 in 5th)  or Download Acrobat file (Website, or it may be on your CD; "Supplemental Material".  Mine was missing all the figures and tables).  We want pp. 2-18 for the text.  I'm giving you the HW problems I'm asking for, in the Handout.
Two-way Tables for Categorical Variables (used to be in Ch. 2): Sec. 9.1, pp. 582-591, 9.2 pp. 591-93 (examples 9.12, 13, 14 only), and 9.3 pp. 601-3 only.
Hand in: 
Sec. 2.6: Transforming:  For the following you may need to Transform your x or y-data to a new variable in SPSS.  Use Transform>compute:  Use the function LG10( ) for the log base 10, LN( ) for natural log,  x^3 for x cubed.  Use  log base 10  unless told otherwise; but it really doesn't matter much. 

Problems are on handout. SPSS files will be linked to from here when I get them tracked down and relabeled, this afternoon.  Solutions
(You'll need to download them, then open with SPSS) 2.118 (not spss)  b, d Monotonic
2.123 (SPSS) fish weight
2.124 (SPSS) fish width (above file)
2.129 (SPSS) American population
2.121 (SPSS)  isotope decay
2.136 heart rate
2.131 tree biomass
2.138 (SPSS) tree seeds
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Two-way  tables Today, all by hand.  pp. 612ff.
For 9.1, 9.2, 9.3 students, do the following parts by hand.  KEEP your results for the next assignment, when you will use SPSS to do this and the rest of the parts. 
   9.1 Compute joint distribution (a),  and marginal distribution of age. (No graph.)
   9.2  Of 15-19 year olds, what is the proportion  who are full-time?
   9.3  Of full-time students, what is the proportion who are 15-19? Of part-time students, what is the proportion who are 15-19? 

9.9 a, b, c, d nonresponse
9.11 cocaine
9.7   Also, do the same for a 2 by 3 table.
9.23 gambling  Only this:  Turn the table here into a two-way table of Division vs. "wager/not wager" by doing the appropriate calculations
9.13 volunteer  Only this:  Can you extract from this table the proportions--or the counts--of men and women studied?
9.10 b only   career plans

Read, discuss 

2.134, 2.135 strength, weight. 

Optional 
 

2.120 transistors , Moore's law

HW Questions?
First midterm: two parts: in-class exam Monday, Day 17 (Oct. 3), plus data analysis project, in pairs.  Will randomly assign you to a pair. Email me if you want to work alone.  * Handout: * More Monday.
Exam will cover chapters 1, 2, and the first part of 9.  ("Exploratory" data analysis).

2.5 Causation:  The rooster believes the sun will not rise if he doesn't crow...
A silly website spoofs statistical obfuscation in general, especially mindless data crunching.
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Transforming variables (handout, plus Sec. 2.6)  See Day 12
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Relationships:  We know how to analyze/summarize quantitative vs. quantitative (scatterplot), and categorical  vs. quantitative (side-by -side histograms, stemplots, boxplots) .  Now
Categorical vs. Categorical  Sec. 9.1 "Two way tables"

 "Two way table"   "Contingency table"   "Crosstab(ulation)"  Hair color vs. Class year.
A thousand people are interviewed by the census bureau, and the results tabulated in this two way table.
Working Status vs. Sex.
Women Men Total
In Labor Force 350 450 800
Not in Labor Force 150 50 200
Total 500 500 1000

What is the "Percent of women in the labor force" ?
Calculate it Now. Write your answer down on a scrap of paper.
When you write or see percents, be clear what is on the  bottom of the fraction (even if it takes longer to say)!!.
From the New Yorker magazine, traditionally the most literary and error-free of all, Feb.14/21, '05:

CORRECTION: The Mail of January 3rd contained the incorrect statistic that four-fifths of Bush voters identified moral values as the most important factor in their decision.  In fact, four-fifths of those identifying moral values as the most important factor of their decision were Bush voters.
Marginal distribution:  Distribution of one variable, ignoring/summingover the other.

Working Status 
In Labor Force 800 80%
Not in Labor Force 200 20%
Total 1000 100%

Sex 
Women Men Total
500 500 1000
50% 50% 100%

Conditional distribution:  Distribution of one variable, with the individuals being only those which satisfy a condition in the other variable.
For women, their conditional distribution as to working status  For men, their distribution as to working status.
            "Column %s"--columns add to 100%:  "conditional distributions of working status by sex ".
Women Men Total
In Labor Force 350/500 = 70% 450/500 = 90% 80%
Not in Labor Force 150/500 = 30% 50/500 = 10% 20%
Total 500/500=100% 500/500=100% 100%

For those in the labor force, conditional distribution as to sex.
    For those not in the labor force, conditional distribution as to sex.
           "Row %s"--rows add to 100%:  "conditional distributions of sex by working status."
Women Men Total
In Labor Force 350/800 = 43.8% 450/800 = 56.2% 800/800=100%
Not in Labor Force 150/200 = 75% 50/200 = 25% 200/200=100%
Total 50% 50% 100%

Graphs to compare proportions:  parallel sets of bar graphs, see text, p. 603,.
  Segmented (stacked) bar charts,  of  % (so total length the same)   (Redundant if there are only 2 segments)
 % Women O            % Men X
OOOOOOOOOOOOOOXXXXXXXXXXXXXXXXXX  In Labor Force
OOOOOOOOOOOOOOOOOOOOOOOOXXXXXXXX  Not in Labor Force

Can do segmented bars of raw numbers, conveys different info:
 25 Women O            25 Men X
OOOOOOOOOOOOOOXXXXXXXXXXXXXXXXXX  In Labor Force
OOOOOOOOXX                     Not in Labor Force
Next:  SPSS (first handout, p. 6), Simpson's paradox.  Then back to Ch. 3


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Women Men Total
In Labor Force 350 450 800
Not in Labor Force 150 50 200
Total 500 500 1000
Of people in the labor force, what percent are women?  350/800=43.75%
Of women, what percent are in the labor force? 350/500 = 70%
Of people, what percent are women in the labor force? 350/1000 = 35% back