really exists. Methods have their prerequisites, strengths, and weaknesses, but when
coupled on a certain spectral range, they should reduce the number of wavelengths to
the most relevant for spectral discrimination of land covers compared without the loss
of important information related to the study objectives (Ben-Dor et al., 2009;
Thenkabail et al., 2004a,b). Decreasing the dimensionality of both field and satellite
hyperspectral data is of special importance and it still remains a challenge. Statistical
approaches include analyses of variance (Adam and Mutanga, 2009; Manevski et al.,
2011, 2012; Vaiphasa et al., 2005), correlation analysis (Mariotti et al., 1996), linear
discriminant analysis (Abdel-Rahman et al., 2010; Clark et al., 2005), and canonical
discriminant analysis (van Aardt and Wynne, 2001). Based on the number of variables
used in the explanation of certain phenomena, the statistical methods can be grouped
as univariate and multivariate techniques. Those are elaborated on next.
15.2.3.2 Univariate Statistical Techniques Statistical techniques that utilize only
one dependent variable, that is, factor (e.g., vegetation type or plant species), in
explanations of one or more independent variables (e.g., reflectance) are referred to as
univariate statistical techniques. The most common is the single-factor analysis of
variance (commonly known as one-way ANOVA), a parametric test that works well
even if the distribution is approximately Gaussian, especially when large samples
(usually more than 20) are used. The concept of ANOVA in the determination of
spectral regions where different land covers are most likely to be discriminated lies in
maximizing the spectral variability between the covers, at the same time minimizing
the spectral variability within them, for every wavelength in a certain spectral domain.
ANOVA explores the variability between the groups as a deviation of each group’s
mean from the “grand mean”— the mean of the means of all groups. Details on the
computation of variance and ANOVA can be found in traditional statistics textbooks
(Robson, 1994).
Similar univariate parametric statistical vegetation discrimination methods based
on the parametric ANOVA include t-tests (Jacobsen et al., 1995; Vaiphasa, 2006) or
Duncan’s multiple-range test (Jurado-Exposito et al., 2003). Even though statistical
tests such as ANOVA are practical data exploration tools used to find spectral
windows for statistical discrimination of different vegetation types, the results may
still not be independently interpreted without additional data analyses. This is because
the possibility of making a type I error, that is, rejection of the null hypothesis when it
is actually true, is increased due to the high number of variables, that is, wavelengths
(Vaiphasa et al., 2005).
An alternative approach that makes no assumptions about population distribution
is a nonparametric test. For example, one or more reflectance values are off scale, that
is, too high or too low, which is often true. This could cause variance homogeneity—
the most important requirement in parametric ANOVA—to not be achieved.
Although not completely free from the assumption of homogeneity of variance,
nonparametric analysis is an alternative which ranks the reflectance values from low
to high and the variance analysis is based on the distribution of the ranks (Artigas and
Yang, 2006). To this end, the Kruskal–Wallis nonparametric ANOVA compares the
medians of reflectance spectra from the land cover sensed in a similar manner to the
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297
coupled on a certain spectral range, they should reduce the number of wavelengths to
the most relevant for spectral discrimination of land covers compared without the loss
of important information related to the study objectives (Ben-Dor et al., 2009;
Thenkabail et al., 2004a,b). Decreasing the dimensionality of both field and satellite
hyperspectral data is of special importance and it still remains a challenge. Statistical
approaches include analyses of variance (Adam and Mutanga, 2009; Manevski et al.,
2011, 2012; Vaiphasa et al., 2005), correlation analysis (Mariotti et al., 1996), linear
discriminant analysis (Abdel-Rahman et al., 2010; Clark et al., 2005), and canonical
discriminant analysis (van Aardt and Wynne, 2001). Based on the number of variables
used in the explanation of certain phenomena, the statistical methods can be grouped
as univariate and multivariate techniques. Those are elaborated on next.
15.2.3.2 Univariate Statistical Techniques Statistical techniques that utilize only
one dependent variable, that is, factor (e.g., vegetation type or plant species), in
explanations of one or more independent variables (e.g., reflectance) are referred to as
univariate statistical techniques. The most common is the single-factor analysis of
variance (commonly known as one-way ANOVA), a parametric test that works well
even if the distribution is approximately Gaussian, especially when large samples
(usually more than 20) are used. The concept of ANOVA in the determination of
spectral regions where different land covers are most likely to be discriminated lies in
maximizing the spectral variability between the covers, at the same time minimizing
the spectral variability within them, for every wavelength in a certain spectral domain.
ANOVA explores the variability between the groups as a deviation of each group’s
mean from the “grand mean”— the mean of the means of all groups. Details on the
computation of variance and ANOVA can be found in traditional statistics textbooks
(Robson, 1994).
Similar univariate parametric statistical vegetation discrimination methods based
on the parametric ANOVA include t-tests (Jacobsen et al., 1995; Vaiphasa, 2006) or
Duncan’s multiple-range test (Jurado-Exposito et al., 2003). Even though statistical
tests such as ANOVA are practical data exploration tools used to find spectral
windows for statistical discrimination of different vegetation types, the results may
still not be independently interpreted without additional data analyses. This is because
the possibility of making a type I error, that is, rejection of the null hypothesis when it
is actually true, is increased due to the high number of variables, that is, wavelengths
(Vaiphasa et al., 2005).
An alternative approach that makes no assumptions about population distribution
is a nonparametric test. For example, one or more reflectance values are off scale, that
is, too high or too low, which is often true. This could cause variance homogeneity—
the most important requirement in parametric ANOVA—to not be achieved.
Although not completely free from the assumption of homogeneity of variance,
nonparametric analysis is an alternative which ranks the reflectance values from low
to high and the variance analysis is based on the distribution of the ranks (Artigas and
Yang, 2006). To this end, the Kruskal–Wallis nonparametric ANOVA compares the
medians of reflectance spectra from the land cover sensed in a similar manner to the
FIELD SPECTRORADIOMETRY
297