STATISTICAL METHODS FOR STUDYING THE EFFECT OF MULTIPLE OUTLIERS IN DESIGNED EXPERIMENTS
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Date
2013-08-05
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University of Agricultural Sciences, GKVK
Abstract
Design of experiments is the backbone of agricultural research
experiments. Adopting RCBD, with an aim to statistically test the
significance of several treatments, a given treatment is replicated ‘r’ times
to assess its power of repeatability for a trait. However, it so happens
that replicated values may not follow a normal pattern but have some
outliers/aberrant data, leading to non-significant results in ANOVA. It is
also not advised to delete them as the basic principle of randomization
will be violated and every observation may carry some useful information
for crop scientists to exploit. This calls for employing a robust analysis
approach, which gives suitable weights to those outliers based on
observed pattern of replications, extracts some information and ensures
statistical adequacy. Foregoing thoughts were elucidated by adopting
robust ANOVA techniques for comparing various pollination methods
(treatments) on seed yield and related traits of Brinjal crop. Cook’s
distance measure was computed to identify the outliers in the
experimental data.
Robust analysis, across eight traits, based on Huber’s and
Andrew’s M-estimation methods resulted decreased error mean square
as high as 90.03 per cent coupled with 97.17 per cent decrease in
Probability of Type 1 error and 85.02 per cent decrease in error mean
square coupled with 86.01 per cent decrease in Probability of Type 1
error, respectively. It was observed that by adopting suitable Mestimation
procedure, a researcher, without removing an outlier could
arrive at required inference about the treatmental differences without
violating basic principles of experimental designs.
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Keywords
statistical methods, sowing, fruits, sets, research methods, replication, developmental stages, yields, hybrids, crossing over