MATH 251, Probability and Statistics I, Fall 2007 Sept. 21, Day 13.After class.**Mentioned in class:*HW Downloads fixed(?)*

Reading: Handout (log transformation, 1-variable). + IPS 5th ed. pp. 143-5
 + 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. 
Next: 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:  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.  A. (SPSS)  Table 1.5 (tornado damage) and Table 1.8 (guinea pig survival) gave histograms highly skewed right.  For each of these data sets:  Make a histogram, take the log of the data and make a new histogram.  Tell if this transformation makes a "nicer" (more symmetric) graph. Problems are on handout. SPSS files are  linked to from here. .Solutions (The .sav files are now on the website. They don't seem to want to open directly into SPSS, at least on my office machine, though they should..You'll probably need to download them, then open with SPSS..The .por files are still there on the website, but not directly linked to any more..) 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

Read, discuss  On handout: 2.118 a, d 2.119 sin   2.134, 2.135 strength, weight.

Optional For problem A, if the log transformation didn't do a good job, work through the ladder of powers and look for one that does better.   2.120 transistors , Moore's law

HW Questions? Day 12
Some leftovers, 2.4:  On overhead projector:

Summary numbers are likely to be more highly correlated than "raw" numbers.
"Anscombe's quartet:"  summary numbers are not sufficient to describe relationship! (Data p. 169, ex. 2.80)
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**Mentioned in class:** Probable quiz Wednesday: Possible items: Matching Normal quantile plot with histogram. Scatterplot stuff: description, regression line: finding a residual, r² as proportion of explained variability, calculating a and b from means, s.d.'s and r; facts and cautions. Transformations.

Project ("is" first prelim): Analyzing a data set, finding all its secrets. To be done in pairs, which I will assign. Email me any concerns about potential partners; I will try to achieve the greatest good for the greatest number.
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Transforming variables (handout, plus Sec. 2.6) Notes Day 12

The article I mentioned "Life on the Scales; Simple mathematical relationships underpin much of biology and ecology," is hanging on my door. Also another copy is in a folder in the box outside my door, so you don't have to stand and read. Encouraged, not required.