Biology Reference
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STEP 3: Calculate the form difference matrix based on these
Monte Carlo samples.
STEP 4: Repeat Steps 2 and 3 B number of times.
The Bootstrap sample based form difference matrices obtained in
this fashion can be collected in a matrix with K ( K
1)/2 rows and B
columns. In this matrix each column is a form difference matrix
obtained at the end of Step 3 and each row represents B form differ-
ence ratios for a linear distance between a specified pair of landmarks.
To obtain a confidence interval for each linear distance, the ratios
in each row are sorted in an increasing order. If a 90% confidence inter-
val is sought, then the first 5% and the last 5% of the total entries in
this sorted row are deleted. The minimum and the maximum entries
remaining in that row constitute the lower and upper confidence lim-
its for that particular linear distance. This is done separately for each
row to obtain a confidence interval for each linear distance ratio.
Monte Carlo-based EDMA-I testing procedure
STEP 1: Calculate the form difference matrix using the esti-
mated mean forms for the two populations. Calculate
ˆ
ˆ
max
FDM
(
M
,
M
)
ij
ij
1
2
T
.
ˆ
ˆ
obs
min
FDM
(
M
,
M
)
ij
ij
1
2
STEP 2: Assuming that the first population is the base sam-
ple, generate a new set of samples X 1 * , X 2 * ,…, X n *
from
ˆ
, ˆ
ˆ
, ˆ
NM
(
,)
I
and Y 1 * , Y 2 * ,…, Y m * from
NM
(
,)
I
.
1
K
,
1
1
K
,
1
STEP 3: Calculate
STEP 4: Repeat Steps 2 and 3 B times to obtain T 1 * , T 2 * ,…, T B * .
STEP 5: Arrange T 1 * , T 2 * ,…, T B * in an increasing order. Reject
the null hypothesis of equality of shapes if T obs is in the top α -th
percentile where α
is the size of the test. Search WWH ::

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