Help times: Me, Monday
10-12 (come to my office), Faherty Mon. Afternoon 2:30-4:30
Me, Tuesday morning (if taking later).
Amanda 3-7 Wednesday
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Textbook: Moore, 2nd ed., (yours) WILL be used next semester
(one more time.)
Homework: you may hand in late homework
up to the time you begin the exam. After now, to me directly,
or under my door. (Will get registered in but not carefully read.)
NO CAMPUS MAIL! Returned HW will be in usual yellow folder
outside my door.
~~~~~~~~~~~~~~~
Please fill out an evaluation,
return it to the ENVELOPE circulating
or on the projection cart.
Two sample: We use Equal variances
not assumed method;
Older method: "Equal variances assumed"--the
"pooled two-sample t-procedure ." (See
Moore p.406.) a different formula for
SEdiff , different df. If n1= n2,
the two SEdiff formulas give the same answer. But
the df's are still different). Safer to use "Equal variances NOT
assumed" as a rule. More...
"Pooled
two-sample t-procedure " == "Equal variances assumed" was
the only choice in many circumstances before the above good approximations
were developed, computing power increased, and robustness was explored.
Big problem: How do we know that we have
equal
variances? We don't. The usual test for equal variances
has these problems: (Read Moore pp. 413-14)
1) the Null hypothesis is that the variances
are equal, and we gather evidence only against a null hypothesis.
So we don't have a way of assessing evidence for equal variances
(the null hypothesis). Best we can say is we don't have strong evidence
against.
2) the usual test on variances is highly NONRobust
(highly sensitive) to departures from normality in the populations.
So don't bother.
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Robustness of two-sample t-procedures: p.
401:
very
good when distributions have similar shapes
(even if not normal.)
Equal sample sizes improve robustness
against non-normality (so that's one reason why we design that way.)
Questions on HW, others:???
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ON the EXAM?
Computing standard deviation by hand (like
#7.7, p. 374, like pp. 38-9). YES. (4 values, simple computations.)
Doing a two-sample t procedure by hand
(like p. 401, 7.34 beetles in oats (test), p. 412, 7.49 voice
onset time (test and CI) NO
Figuring out SPSS output: how to read,
which output is appropriate (including two-sample) YES,
telling which
menu commands, NO.
What we studied:
[Data Analysis: description and exploration]
[Data Production: Sampling, Designing
Experiments]
[Statistical Inference: formal Estimating and Testing--
quantifying our uncertainty and satisfying the skeptic]
Anything you'll meet will fall into one of those categories--
Fancy ways of torturing a data set to make it give up
its secrets--"data mining," subtle and complex summary methods
Sophisticated experimental 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!
More time? Look at these problems, with a neighbor.
Decide what to do. (These are a good addition to review problems)
p. 424, # 7.68
p. 424, # 7.69, part b.
p. 426, middle--problems 74, 75, 76.
The end! Thank you for the pleasure of
being your teacher.
Good luck!
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