| Hand in: Moore, Sec. 7.1
p. 364 7.1, 7.2, 7.3 "Standard error" & t-distribution family p. 373, 7.4 CI t* p. 386, 7.19 Shrimp ATP CI A common calculational mistake is to divide the SE by square-root-of-n. But square-root-of-n is already IN SE! Don't divide by it again! (I.e. pay attention to the difference between "standard deviation" and "standard error.") 7.5, 7.6 test, one- & two-sided 7.7 DDT Find the mean and standard deviation by hand!(only 4 points) (or SPSS or calculator) and do the rest by hand. Make a note of your results; we will do this on SPSS too, check the results. (SPSS) A. Work through the handout
on SPSS for Ch. 7, first page.
Print and Hand in the tables shown on the handout.
Next:
(SPSS) p. 382, 7.11 caffeine
dependence
Again, watch out for the direction of your differences and what they
mean.
|
MATCHED PAIRS t
procedures--
"Paired samples"(SPSS),
"Paired comparisons"
before--after, left
hand--right
hand, Drug A vs. Drug B on the same person or on a matched pair.
For each pair, find the difference
in the observed values. Then treat these differences as if
they
are "the" data set, from a normal population, and do One-sample t
procedures.
Usually (always?) the null hypothesis
will be "
µ = 0", there is "no difference"
between the treatments.
Example: wax paper sandwich
bags:
Is the wax layer the same inside and out?
25 bags: measure (wax outside - wax inside)
for each. (pounds per square foot).
Differences: xbar
= .093, s = .723 n =
25
SEM = .723/5 = .1446
H0 : µ
= 0 (mean
difference
is
0)
t = (.093 - 0)/SEM
= .093/.1446
= .643.
Ha : µ
Not = 0 (there is a
difference)
t is less than .685 (d.f. = 24)
which is right-tail t* for probability .25
Because test is 2-sided, double the tail: .50. P value is greater
than .50.
No evidence for difference.
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ROBUST procedures: a confidence
interval or significance test is called robust if the
confidence
level or P-value doesn't change very much when the assumptions of the
procedure
are violated. pp. 379-80.
t-procedures are quite robust against
nonnormality.
But
sensitive
to outliers. Look at data. Need SRS!
Details: n <15
t ok unless data clearly not normal, or if there are outliers.
n > 15 t ok unless there is strong skewness, or
outliers.
n > 40 or so: t ok even if there is skewness.
(Outliers?
I suggest trying with and without them, see what changes).
Refer to chart of
possibilities,
Day
37
Matched-pairs data (differences) are often more normal in
shape than the separate variables ("oddness" is often the same for both
items in a pair, and disappears in subtraction. Another reason
why
this is a nice experimental design.
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SPSS for Matched Pairs (backside of 7.1 handout)
Go through handout (see HW):
You can let SPSS calculate the difference, or you can compute
the differences into a new variable, and work with that variable.
Note to the handout:
--You can click and drag borders of tables to make them
fit better
(as I did for the handouts).
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