Hypothesis Testing with One-Way ANOVA - Personal Home Pages

64 Pages·2013·3.78 MB·English

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AANNOOVVAA
Statistics
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1. Standardized z distribution of scores and of means
can be represented as percentile rankings.
2. t distribution of means, mean differences, and
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allowing us to analyze differences between 2 means
33.. NNuummeerraattoorr ooff tteesstt ssttaattiissttiicc iiss aallwwaayyss ssoommee
difference (between scores, means, mean
differences, or differences between means)
4. Denominator represents some measure of
variability (or form of standard deviation).
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(cid:121) Test Statistics
(cid:121) Numerator = Differences between groups
(cid:121) Example: Men are taller than woman
(cid:121)(cid:121) DDeennoommiinnaattoorr == VVaarriiaabbiilliittyy wwiitthhiinn ggrroouuppss
(cid:121) Example: Not all men/women are the same height
* There is overlap between these distributions.
( )
− μ − μ
M (M )
z = M t = M
σσ ss
M M
⎡(M − M )−(μ − μ )⎤ (M − M )
⎣ ⎦
t = X Y X Y = X Y
s s
Difference Difference
AAnnaallyyssiiss ooff VVaarriiaannccee ((AANNOOVVAA))
(cid:121) Hypothesis test typically used with one or more nominal IV (with at least
3 groups overall) and an interval DV.
(cid:121) tTest: Distance between two distributions
(cid:121)(cid:121) FF rraattiioo:: UUsseess ttwwoo mmeeaassuurreess ooff vvaarriiaabbiilliittyy
FF RRaattiioo ((SSiirr RRoonnaalldd FFiisshheerr))
between - ggroupps variance
=
FF
within - groups variance
(cid:121) Between-Groups Variance: An estimate of the
population variance based on the differences
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(cid:121) WWiitthhiinn-GGrroouuppss VVaarriiaannccee:: AAnn eessttiimmaattee ooff tthhee
population variance based on the differences
within each of the three or more sample
ddiissttrriibbuuttiioonnss
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(cid:121)(cid:121) EExxaammppllee: SSppeeeecchh rraatteess iinn AAmmeerriiccaa, JJaappaann, && WWaalleess
t test?
Two Sources of
VVaarriiaannccee::
t test?
t test?
Between &
Within
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p(A) AND p(B) = p(A) x p(B)
p(A) OR p(B) = p(A) + p(B)
(cid:121) TThhee pprroobbaabbiilliitty ooff aa TTyppee II eerrrroorr ((rreejjeeccttiinngg tthhee nnullll whheenn tthhee nnullll iiss
true) greatly increases with the number of comparisons.
Fishing Expedition
“If you torture the data long enough,
the numbers will prove anything you want” (Bernstein, 1996)
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(cid:121) Always preceded by two adjectives
1. NNumbber off IInddependdentt VVariiabblles
2. Experimental Design
(cid:121) OOne-WWay AANNOOVVAA: HHypothhesiis test thhat iinclluddes one
nominal IV with more than two levels and an interval DV.
(cid:121) Within-Groups One -Way ANOVA: ANOVA where each
sample is composed of the same participants (AKA
rreeppeeaatteedd mmeeaassuurreess AANNOOVVAA))..
(cid:121) Between-Groups One-Way ANOVA: ANOVA where each
samplle iis composedd off ddiifffferent partiiciipants.
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from 1st edition of textbook