MATCHED PAIRS t procedures:
before--after, left hand--right
hand, Drug A vs. Drug B on the same person or on a matched pair (pp.
246-7)
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 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
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 > .50.
No evidence for difference.
SPSS: Transform/Compute
"tables": CDF functions take value x, give Prob of being
less than or equal to x (like our book's Normal table)
IDF functions take probability p, give value x such that the probability
of being less than or equal to x is p. The help in SPSS on these
is sloppy, leaves off the "or equal to." Irrelevant for continuous distributions,
crucial for discrete ones.
Doing t-tests and CI's: see handout, SPSS manual. Note: SPSS gives "Sig. 2-tailed." We've been calling this "P-value: 2-tailed." Divide by 2 to get P-value for a one-tailed test.
References: SPSS book, pp. 53-54(Normal), 76-79(Binom,Norm), 91-2(t)
for tables. Ch. 7 for tests and CI's.
Handout covers IPS sections 7.1, 7.2, additions
and corrections to SPSS manual .
HW Day 35 *Still doing Sec. 7.1, thru top of 517.
Skim "power" for concept. Read ahead: 518-523. Sign test and log
transformation, I hope, Friday.
| Matched-pairs by hand: the points on p. 514 are
good.
Often the "differences" will be more normal than the "befores" or the "afters" by themselves. 7.17, 18 piano lessons -->reasoning? For a, do a dot plot. For b, look in the answers for the mean and standard deviation, then go on. For the P-value, give the approximations from the table. - - - - - - - - - - - - - - - - - - - - - - - - - - - Hand in: (using SPSS) Using SPSS in lieu of tables: You may use your calculator as an aid. Sketch the probabilities, and show your computations. If feasible, check with book table. A. 1)Find a) P(Z < 1.3) b) P(Z > 1.3) c) P (-1 <Z<1.3) (Z is standard normal) Find z* such that d) P(Z < z*) = .95 e) P(Z >z*) = .07 2) a) P(X < 1.3) b) P(X > 1.3) c) P (-1 <X<1.3) (X is N(1,2)) Find x* such that d) P(X < x*) = .95 e) P(X >x*) = .07 3) a) P(t(30) < 1.3) b) P(t(30) > 1.3) c) P(-1 <t(30) < 1.3) Find t* such that d) P(t(30) < t*) = .95 e) P(t(30) >t*) = .07 4) a) P(X < 14) b) P(X< 10) c) P ( 11 < X < 14) d) P(X> 10) (X is binomial, B(15, .8)) p. 523, 7.2 (using SPSS tables for t* and CI)
Matched Pairs (SPSS) You should make a variable containing the
differences, to check for normality, outliers. Then you can do the"one
sample" test on it, or do the "paired-samples" test on the original
variables. BE CAREFUL what gets subtracted, with one-sided alternatives.
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