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33 Cards in this Set
- Front
- Back
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ANOVA
use to evaluate? useful? |
evulates diff. among 3 or more populations (k)
parametric very robust! |
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ANOVA variables
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1 independant discrete also called factor
has 2 or more levels ex gender/ race 1 dependant continous variable |
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ANOVA assumptions
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sample sizes ~ =
equal variances dependant variable continous and pop normally distributed samples random and independantly drawn |
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what about error with ANOVA
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gets rid of Type I error from t or z tests
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One way analysis of variance ANOVA aka
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univariate anova
simple anova etc F test |
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hypothesis 1 way anova
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Ho = u1 = u2 = uk
All pop means equal (no effect) H1 = ui = uk for sum i and k -at least one pop mean diff -doesnt mean all diff |
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Partition of Total Variation
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Total variation broken down into:
Variation from treatment SSb + Variation from Random Sampling (error) SSw |
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F-distribution
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skewed to right
only +ve 1 tailed # degress freedom increases looks more normal degrees of freedom: Column (K-1) Row (N-K) |
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Between variation
-known as -degress freedom calc -sum squares given -mean sum squares calc -F stat |
Factor
K-1 MSb= SSb / (K-1) F stat- MSb/MSw |
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within variance aka
degrees freedom mean square etc |
Error
N-k MSw = SSw / (n-k) |
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if F > than table ------>
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reject
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2 way anova
about and variables |
2 factors on dependant variable
interaction tween diff lvls of 2 factors each factor 2 or more lvls degrees of freedom for each factor is one less than # of lvls |
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Ho for 2 way anova
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pop mean of first factor =
pop of 2nd factor = no interaction tween factors |
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Homoscedacitiy
Heteroskedasiticity |
equal variance
unequal variance |
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Post Hoc /Multiple comparison tests
do what? |
procedures to find which means differ sign. after sign F value found in ANOVA
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Pairwise Comparisons vs Complex contrasts
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PC-
equal n- Tukey, Newmeus-Keuls unequal n - Tukey/ Kramer CC- Scheffe |
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how post hoc works
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maintain type I error rate
adjust size critical value up to compensate for more than 1 comparison |
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degree of adjustment in post hoc
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liberal- slight, less control type i error, more control type ii
conservative- opposite ex scheffe |
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Pairwise comparisons
non pairwise (complex compare) |
2 group at time
-3 or more groups mean scores of each subset compared |
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type i error post hoc
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comparisonwise error rate
-probability make type i error for any comparison experimentalwise error rate -probability at least 1 type i error for all possible comparisons |
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studentized range (q) distribution
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-determine min diff. tween largest and smallest means nessessary to reject hypothesis
-like t distribution -values depend on # group and degrees freedom |
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Tukey
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honestly significant diff. test (fuckers)
all pairwise comparisons while maintain alphaE at preestablished alpha lvl Ho: ui = uk for i not equal to K use q distribution |
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Newman-Keuls method
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based on layer approach
critical values change depending on range in set of means considered must rank means from low to high |
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Tukey vs Newman-Keuls
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TUkey less stat power
aplhaE greater in Newman-Keuls |
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Dunnett
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compare control group w/ treatments
for dose finding studies |
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Complex- Scheffe
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versitile for complex hypothesis
ex-are 2 experimental group diff than control hypothesis stated in terms of linear combination of coefficient and means, sum of coefficient = 0 only posthoc for PAIRWISE OR NONPAIRWISE tests stat is F but crit value found by multiplying that by table (K-1) |
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Others- Duncans Multiple Range test
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use Q, rank of means if farther mean less straight standard sig.
same as Newman-Keuls but critical value less stringent use special table |
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Others- Fishers
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like multiple t test
pooled estimates of variance |
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A Priori or Planned Comparisons
about when use stat power-weak/strong? |
bypass ANOVA for more specific tests (comparisons)
more stat power -Planned orthogonal contrasts -Trend analysis |
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Planned orthogonal contrasts
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special set of contrast before data collected
contrasts independant maintain alpha |
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Trend Analysis
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when independant variable in ANOVA is quantitative
examine function relation tween lvls of independants and group means of dependants |
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finally Bonferroni Technique
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for adjusting alpha lvl
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what tests applied to explain why ANOVA F test sig.?
which dont give a fuck about ANOVA |
DGF-the APriori (planned)
Planned orthogonal and Trend analysis can be done after anova but not really nessesary to do the anova cuz you know what your looking for |
