Non-Parametric Statistical Methods And Data Transformations In Agricultural Pest Population Studies

440 CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(3) JULY-SEPTEMBER 2012
SCIENTIFIC NOTE
S
NON-PARAMETRIC STATISTICAL METHODS AND DATA
TRANSFORMATIONS IN AGRICULTURAL PEST POPULATION STUDIES
Alcides Cabrera Campos1*, Caridad W. Guerra Bustillo2, Magaly Herrera Villafranca3,
and Moraima Suris Campos4
Analyzing data from agricultural pest populations regularly detects that they do not fulfillthe theoretical requirements
to implement classical ANOVA. Box-Cox transformations and nonparametric statistical methods are commonly used as
alternatives to solve this problem. In this paper, we describe the results of applying these techniques to data from Thrips
palmi Karny sampled in potato (Solanum tuberosum L.) plantations. The χ2 test was used for the goodness-of-fit of negativebinomial distribution and as a test of independence to investigate the relationship between plant strata and insect stages.
Seven data transformations were also applied to meet the requirements of classical ANOVA, which failed to eliminate the
relationship between mean and variance. Given this negative result, comparisons between insect population densities were
made using the nonparametricKruskal-Wallis ANOVA test. Results from this analysis allowed selecting the insect larval
stage and plant middle stratum as keys to design pest sampling plans.
Key words: Kruskal-Wallis test, negative binomial distribution, Box-Cox transformations, Thrips palmi, Solanum
tuberosum.
1Universidad de las Ciencias Informáticas, Autopista Novia
del Mediodía, km 2½, Torrens, Boyeros, La Habana, Cuba.*Corresponding author (alcides@uci.cu).
2Centro Universitario Municipal de Güines, Calle 86, N° 7312, entre
73 y 77, Güines, Mayabeque, Cuba.
3Instituto de Ciencia Animal, Apartado Postal 24, San José de las
Lajas, Mayabeque, Cuba.
4Centro Nacional de Sanidad Agropecuaria, Autopista Nacional
y Carretera de Tapaste, San José de las Lajas, Apartado Postal 10,
Mayabeque, Cuba.
Received: 8 December2011.
Accepted: 23 May 2012.
tatistical management of data in population studies of
agricultural pests is one of the greatest challenges for
researchers dedicated to plant protection; this occurs when
they are faced with designing experiments, data analysis,
and drawing conclusions. The parametric statistical
methods are widespread and well-known and are the most
used in these studies.Nevertheless, many researchers do
not know that they are subjected to fulfilling theoretical
assumptions, such as normality, variance homogeneity,
and no correlation between errors. If these conditions
are not fulfilled, the statistical analysis of the results can
be invalidated (De Calzadilla et al., 2002; Santos et al.,
2005).
The lack of normality of errors is of little importance
inFisher’s F-test from ANOVA because it is a robust
technique in the presence of deviations of this assumption.
However, it may affect variance homogeneity mainly when
there is a great difference in the number of observations
in the groups or treatments. This heterogeneity is
usually accompanied by non-normal variables, so it is
recommended that transformations be applied to stabilize
variances andnormalize responses (Box and Cox, 1964;
Peña, 1994; Font et al., 2007).
Menchaca (1973) considered the parametric family of
transformations of Y in Yi(λ), where λ defines a particular
transformation, and it is assumed that for any unknown λ,
the transformed observations Yi(λ) (i = 1, 2, …, n) fulfill
the basic hypothesis, these elements are provided by Box
and Cox (1964). Transformations areperformed to search
for a new scale in the analyzed variables in such a way
that the errors are approximately normally distributed and
have homogeneous variances (Eisenhart, 1947; Steel and
Torrie, 1992).
Data of agricultural pest populations do not generally
fulfill the basic assumptions to apply parametric statistical
methods because they are essentially discrete. This
explains why...