The Multivariate Approach OneWay CrossSpeciesFostering House mice onto house mice prairie deer mice or domestic Norway rats After weaning tested in apparatus with access to tunnels scented like clean pine shavings house mouse deer mouse or rat ID: 756578
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Slide1
Correlated-Samples ANOVA
The
Multivariate
Approach
One-WaySlide2
Cross-Species-Fostering
House mice onto house mice, prairie deer mice, or domestic Norway rats.
After weaning, tested in apparatus with access to tunnels scented like clean pine shavings, house mouse, deer mouse, or rat.
House mice and deer mice were descendants of recently wild-trapped mice.
Reversed light cycle, red lightingSlide3
Mus musculusSlide4
Peromyscus maniculatusSlide5
Rattus norwegicus
domesticSlide6
Homo sapiensSlide7
data
Mus
;
infile
'C:\ ... \tunnel4b.dat'
;
INPUT
NURS V_clean V_Mus V_Pero
V_Rat
VT_clean
VT_Mus VT_Pero VT_Rat
T_clean
T_Mus
T_Pero
T_Rat
TT_clean
TT_Mus
TT_Pero
TT_Rat
L_clean
L_Mus
L_Pero
L_Rat
LT_clean
LT_Mus
LT_Pero
LT_Rat
;
Format
NURS rodent.
;
The TT_ variables have been transformed to normal.Slide8
The ANOVA
Proc
ANOVA
;
Model
TT_clean
TT_mus
TT_pero
TT_rat
= /
nouni
;
Repeated
scent
4
Contrast
(
1
)
/
summary
printe
;
run
;
“
nouni
” suppresses irrelevant output
“summary” and “
printe
” gives us ANOVA tables for contrasts and “
printe
” tests
sphericitySlide9
Contrasts
Contrast(1) – compare the first condition with all other conditions.
Profile – compare each condition with the next condition
Polynomial – trend analysis
Helmert
– contrast each condition with the mean of the following conditions
Mean(n) -- contrast
each level (except the n
th
) with the mean of all other levels.Slide10
Mauchly
Sphericity
Assumption Violated
Sphericity
Tests
Variables
DF
Mauchly's Criterion
Chi-Square
Pr > ChiSq
Orthogonal Components
5
0.6433986
14.87119
0.0109Slide11
MANOVA
MANOVA Test Criteria and Exact F Statistics for the Hypothesis of no scent Effect
Statistic
Value
F Value
Num DF
Den DF
Pr > F
Wilks
' Lambda
0.58343
7.85
3
33
0.0004
Pillai's Trace
0.41656
7.85
3
33
0.0004
Hotelling-Lawley Trace
0.71398
7.85
3
33
0.0004
Roy's Greatest Root
0.71398
7.85
3
33
0.0004Slide12
Univariate Approach
Source
DF
Anova SS
Mean Square
F Value
Pr > F
Adj Pr > F
G - G
H - F
scent
3
1467.267
489.089
7.01
0.0002
0.0009
0.0006
Error(scent)
105
7326.952
69.7804
Greenhouse-Geisser Epsilon0.7824Huynh-Feldt Epsilon0.8422
Both
the G-G and the H-F are near or above .75, it is probably best to use the
H-F
df
= 3(.8422), 105(.8422) = 2.53, 88.43Slide13
Contrasts: Clean Scent vs.
Mus
musculus
:
p
= .008
Peromyscus
maniculatus
:
p
= .29
Rattus
norvegicus
:
p
= .14Slide14
Untransformed Means
proc
means
;
var
T_clean
--
T_Rat
;Slide15
Randomized Blocks Data
data
multi;
input
block1-block3;
subj
= _N_;
B1vsB3 = block1-block3;
B1vsB2
= block1-block2;
B2vsB3=block2-block3
;
cards
;
10 9 7
8 6 3
7 6 4
5 6 3
And two more casesSlide16
Randomized Blocks ANOVA
Proc
ANOVA
;
Model
block1-block3 = /
nouni
;
Repeated
block
3
/
nom
;Slide17
Randomized Blocks Results
Source
DF
Anova SS
Mean Square
F Value
Pr > F
Adj Pr > F
G - G
H - F
block
2
39.00000
19.50000
39.00
<.0001
0.0004
0.0001
Error(block)
10
5.000000
0.500000
Greenhouse-Geisser Epsilon0.6579Huynh-Feldt Epsilon0.8000Slide18
Pairwise Comparisons
proc
means
t
prt
;
var
B1vsB3 B1vsB2 B2vsB3;
run
;Slide19
Want Pooled Error?
The comparisons on previous slide use individual error terms.
Get more power with pooled error.
First, unpack data from multivariate setup to
univariate
setup.
Then use ANOVA with desired procedure (LSD,
Tukey
, REGWQ, etc.)Slide20
Unpack the Data
data
univ
; set multi;
array b[
3
] block1-block3; do block =
1
to
3
;
errors = b[block]; output; end; drop block1-block3;Slide21
The Unpacked Data
subj
block
errors
1
1
10
1
2
9
1
3
7
2
1
8
2
2
6
2
3
3
3
17And so onSlide22
LSD with Pooled Error
Proc
ANOVA
;
Class
subj
block;
Model
errors =
subj
block;
Means
block /
lsd
lines
;
run
;Means with the same letter are not significantly different.t GroupingMeanNblockA9.333361 B8.333362 C
5.833363Slide23
SPSS
Want to use SPSS instead of SAS?
See my document
The Multivariate Approach to the One-Way Repeated Measures ANOVA