18
P. Lazo et al.
2.4 Data Processing and Statistical Analysis
Statistical analysis was used to investigate the variability and spatial distribution of
TM atmospheric deposition, and to assess the most probable pollution sources of
the elements under investigation. The concentration data of the elements were interpreted on the basis of the results of descriptive and interfering statistic analysis. The
distribution type of the data of each element and their possible outlier concentrations
were examined through the frequency distribution, and the frequency plots confirmed
by the statistical significance levels at p > 0.05. Statistical method was applied to
evaluate the background level of metals in moss samples. Matschullat et al. (2000)
and Reimann et al. (2002) have used the upper concentration limits (UCL = median
+ 2 * SDEV) to identify the outliers of each element. The UCL values are referred
as the upper limit of geochemical variation that were suggested as “threshold levels”
for clean-up goals of the environmental legislation (Reimann et al. 2002). The values
lower than the lower concentration limits (LCL = median – 2 * SDEV) are referred
as the background content. For elements with high variation (CV % > 75%), the
UCL and LCL level of each element were calculated as (median ± SDEV). The
background level was calculated on the basis of the LCL level of each element that
was re-plotted after excluding the outlier points higher than the respective UCL levels
of the sorted original data (Qarri et al. 2015). EWMA charts were also used to detect
the linear trend of the univariate variables (Bissell 1984; Aerne et al. 1991) and the
potential shifts in location scale and shape parameters (Liu et al. 2013). The use
of univariate control charts in environmental study make it possible to investigate
the moving range of two successive observations of temporal and spatial distribution characterized by an irregular distribution of nonparametric data set (Qarri et al.
2015, Haridy and Wu 2009). Nonparametric control charts in multivariate spatial
rank have been discussed by Zou et al. (2012). In this case, the median values instead
of average values were used to characterize the central tendency towards the data
and the variability of the data could be estimated. The upper and lower control limits
(UCL and LCL) were computed for the median moving ranges by applying pooled
standard deviation, the proper values of λ (the weight of EWMA that ranges from 0
to 1) and the k value. The value of λ was carefully chosen to balance the robustness
to non-normality and the detection ability to various shift magnitudes (Stoumbos and
Sullivan 2002). Based on the median concentration of each element, the proper k
values (k = 1–3) are selected. For the elements with high values of standard deviation
compared to their median values, a small k value is used.
The relationship between the elements in moss was tested by Spearman correlation
analysis, confirmed by the statistical significance level, P < 0.01. Factor analysis
(FA) was applied as an extension of the correlation analysis to assess the relationship
between elements present in moss samples and to identify the most important factors
that probably affect the association of the elements in the same factor. FA may
explore the hidden multivariate structures of the data (Reimann et al. 2002; Astel
et al. 2008) and may clarify the link between the elements that tend to have similar
origins or to subsequently develop similar associations on the data matrix. Each
P. Lazo et al.
2.4 Data Processing and Statistical Analysis
Statistical analysis was used to investigate the variability and spatial distribution of
TM atmospheric deposition, and to assess the most probable pollution sources of
the elements under investigation. The concentration data of the elements were interpreted on the basis of the results of descriptive and interfering statistic analysis. The
distribution type of the data of each element and their possible outlier concentrations
were examined through the frequency distribution, and the frequency plots confirmed
by the statistical significance levels at p > 0.05. Statistical method was applied to
evaluate the background level of metals in moss samples. Matschullat et al. (2000)
and Reimann et al. (2002) have used the upper concentration limits (UCL = median
+ 2 * SDEV) to identify the outliers of each element. The UCL values are referred
as the upper limit of geochemical variation that were suggested as “threshold levels”
for clean-up goals of the environmental legislation (Reimann et al. 2002). The values
lower than the lower concentration limits (LCL = median – 2 * SDEV) are referred
as the background content. For elements with high variation (CV % > 75%), the
UCL and LCL level of each element were calculated as (median ± SDEV). The
background level was calculated on the basis of the LCL level of each element that
was re-plotted after excluding the outlier points higher than the respective UCL levels
of the sorted original data (Qarri et al. 2015). EWMA charts were also used to detect
the linear trend of the univariate variables (Bissell 1984; Aerne et al. 1991) and the
potential shifts in location scale and shape parameters (Liu et al. 2013). The use
of univariate control charts in environmental study make it possible to investigate
the moving range of two successive observations of temporal and spatial distribution characterized by an irregular distribution of nonparametric data set (Qarri et al.
2015, Haridy and Wu 2009). Nonparametric control charts in multivariate spatial
rank have been discussed by Zou et al. (2012). In this case, the median values instead
of average values were used to characterize the central tendency towards the data
and the variability of the data could be estimated. The upper and lower control limits
(UCL and LCL) were computed for the median moving ranges by applying pooled
standard deviation, the proper values of λ (the weight of EWMA that ranges from 0
to 1) and the k value. The value of λ was carefully chosen to balance the robustness
to non-normality and the detection ability to various shift magnitudes (Stoumbos and
Sullivan 2002). Based on the median concentration of each element, the proper k
values (k = 1–3) are selected. For the elements with high values of standard deviation
compared to their median values, a small k value is used.
The relationship between the elements in moss was tested by Spearman correlation
analysis, confirmed by the statistical significance level, P < 0.01. Factor analysis
(FA) was applied as an extension of the correlation analysis to assess the relationship
between elements present in moss samples and to identify the most important factors
that probably affect the association of the elements in the same factor. FA may
explore the hidden multivariate structures of the data (Reimann et al. 2002; Astel
et al. 2008) and may clarify the link between the elements that tend to have similar
origins or to subsequently develop similar associations on the data matrix. Each