Math 151 , Spring 2006, Day 42 Friday May 12 Hit reload.

Check here for any changes or updates.  (current as of 1pm Mon. May 15)

Help?   I'll be on campus: Find me in or around my office Tuesday 12-2, and Thursday 12-2; earlier or later on those days by prior email arrangement.  (Jury duty is "over").  I'll be checking email at least  once morning/ once evening each day, if you have short-answered questions..
Fay's sessions: Watch this space for updates.  Fay emails:

ON the in-class EXAM?
Computing standard deviation by hand   YES. (4 values, simple computations.)   Finding r from data by hand (pl. 119) No.
Doing a two-sample t procedure by hand (chapter 24) NO.   (Recognizing the difference between two-sample and paired sample (matched pairs), YES)
Figuring out SPSS output:  how to read, which output is appropriate  YES,  telling which menu commands, NO.

Homework questions? Day 41

The t-procedures:  "assume" normal populations, but turn out to be quite robust--results hold up against departures from normality.  (Not known until explored with computer simulations.)  Outliers, bi (or more) modality still a problem.

What we studied: (Overall: always questioning the source, context of data)
>>Data Analysis: description and exploration<<
          Normal distributions and "abnormal"--graphs, summary systems (mean/s.d., 5-number group)
          Categorical data, two way tables; marginal and conditional proportions
           Two related Quantitative variables; correlation, regression, how good (r, r-squared, residuals), predicting y from x
>>Data Production: Sampling, Designing Experiments<<
           Sample, Observational study, Experiment
           All the ways it can go wrong (biases, placebo effect, etc.)
 >>Statistical Inference: formal Estimating and Testing--
         quantifying our uncertainty and satisfying the skeptic<<
            Need: Language--Population/Sample, Parameter/ Statistic
                       Probability:  simple. Sampling Distributions of p-hats and y-bars. (Central Limit Theorem)
            Single proportion.  Single mean.  Paired Differences.  (Difference of means for two independent samples.)
            Confidence intervals  (For shoebox, on overhead)
            Hypothesis tests:  null and alternative (one and 2-sided), P-value, significance  and alpha

More about alphas, and testing as decision making (will not be on exam).

Anything you'll meet will fall into one of those big categories--
   --Fancy ways of torturing a data set to make it give up its secrets--"data mining," subtle and complex summary methods
   --Sophisticated experimental and sample designs
   --Estimations (usually intervals) , tests (P-values, "significant at") based on other parameters

 "If your only tool is a hammer, every problem looks like a nail."  Studies are often set up so that they can be analyzed using certain techniques.
  Conversely--if you want to do statistical inference, you'd better know what statistical processes you want to use, and design your study so those processes are appropriate.  Don't expect to just gather data and then figure out how to do statistics on it (not that this isn't done--all too often!)  If you've got nails, you need a hammer, if you have screws, you need a screwdriver.  It's not too hard to create data sets for which good inferential techniques don't exist!

Class stopped here: reading the rest is optional
What haven't we done?
--Chapter 22, comparing two proportions from independent samples.  Like comparing means, with niggling details in the SE computations.
--Chapter 26, testing whether categorical variables in two-way tables are dependent (the departures from equal proportions in all the columns are too much to attribute to sampling ("natural") variation, given independence) "Chi-Square" (Quantitative Research methods in Sociology)
--Chapter 27, testing if a correlation coefficient is really different from 0, making confidence interval-type fudge factors around our regression line. Chapter 29 on CD, Multiple correlation--relationships when there are more than 2 variables (Econometrics)
--Experiments with more than 2 treatments, and quantitative results ("Analysis of Variance" Ch. 28 on CD--take Quantitative Research Methods in Psychology)
--Methods that work when our normality assumptions aren't met.  ("Nonparametric" methods--"Mann-WhitneyU")
      Example (Optional): Tukey's Quick test (p. 465) for two independent samples. Doesn't need Normal!!
 (Not well known;  but worth knowing!)  Put data in order (back to back Stemplot?).  One group must have the highest value and the other group the lowest to use this.  How much do they not overlap?
Count the number of items in the "Higher" set that are bigger than all the items in the "Lower" set. Plus all the items in the "Lower" set that are smaller than all the items in the "Higher" set. (A tie at the edge = 1/2.)
"7, 10, 13"  7 or more? (2-sided) Sig. at .05.  10 or more? (2-sided)Sig. at .01.  13 or more? (2-sided)Sig. at .001.
Apply this to #17, p. 491

Thank you for a very interesting semester!