Jellyfish Compliance with SQIDEP · MCU15/0122

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                                                                                                            Technical Papers




Figure 3. Q-Q plots for the Concentration removal efficiency (CRE) % distribution for TSS, TP and TN against Z-Score
(distance from the mean).




Figure 4. Q-Q Plots of log-transformed inlet and outlet concentration paired samples for TSS, TP and TN. The linear plots
demonstrate the data is now normally distributed.
log-transformation on the data. If the        “bell” shape if it is normally distributed.      Table 2 presents the results of the
baseline data is not normally distributed,    It should be noted that skewed data           parametric tests on the CRE% removal
a log-transformation may be required,         and data with large kurtosis (high and        data from Table 1. The test statistic, W,
which will result in some minor variations    wide peak), even though it may have           is calculated using the following formula:
to the statistical processes, as described    the appearance of a “bell” shape, is
in Olsson (2005) regarding confidence         not considered normally distributed.
levels, and Singh et al. (1997) regarding     The Q-Q plot is the most common and
transformation back to original data.         effective method to graphically identify
                                                                                            where:
                                              if data is normally distributed (Razali and
LOG TRANSFORMATION OF DATA
                                              Wah, 2011). Using this method, normally
Lognormal distributions tend to be            distributed data will plot as a straight
common in environmental data sets, as                                                          The per cent removal data is
                                              line, with minimal variance.
results from contaminant concentration                                                      normally distributed as the p-value
data sets tend to follow a skewed                Figures 3 and 4 display how the data       from the Shapiro-Wilk Test in Table 2
probability distribution. In the case that    in Table 1 are distributed. The per cent      is greater than 0.05. This numeric
the raw data is not normally distributed,     removals of TSS, TP and TN can be seen        result supports the graphical analysis
but appears to be positively skewed,          to be normally distributed according to       of Figure 2. The influent and effluent
then a lognormal transformation may           the linear Q-Q plot (Figure 3). The inlet     results were also tested for normality
be applicable (Singh et al., 1997).           and outlet Q-Q plots in Figure 4 were         after being log transformed, and the
The log-transformed data is then run          constructed using a log transformation        results shown in Table 3.
through parametric tests as per normally      of the inlet and outlet data. These results
                                                                                               The p values in Table 3 show that
distributed data, albeit with slight          indicate that the percentage removal is
                                                                                            the influent and effluent data for all three
variations (Olsson, 2005; Singh et al.,       normally distributed, while the inlet and     water quality parameters are lognormally
1997). However, it should be noted that,      outlet EMCs are log normally distributed.     distributed. This is a critical step in
if this log-transformed dataset still fails   Visual inspection alone, however, usually     preparation for the subsequent paired
the normality test (graphical method and      does not provide conclusive evidence          t-test, as a valid test requires that data
Shapiro-Wilk Test (1965)), then a lognormal   that the data is normally distributed, and    be normally distributed (Shapiro and
distribution is not suitable and another      a numerical parametric analysis should be     Wilk, 1965).
transformation should be adopted              conducted (Razali and Wah, 2011).
(Limpert et al., 2001).                                                                        It should be noted that, while it
                                              PARAMETRIC ANALYSIS                           is crucial to prove that the influent
GRAPHICAL METHODS TO                          OF NORMALITY                                  and effluent data are lognormally
IDENTIFY NORMALITY                            A parametric statistical analysis involves    distributed in preparation for the
Graphical methods involve plotting data       using numerical statistical methods to        paired t-test, it is also important to
frequency on a histogram, a box-plot, a       test data against the null hypothesis         prove that the percentage removal
stem-and-leaf plot, or a quantile-quantile    that the data is normally distributed.        rates are also normally distributed.
plot (Q-Q plot), then visually inspecting     There are many such statistical methods       This is critical, as the confidence interval
it in order to conclude if the data is        available, however the Shapiro-Wilk           is constructed around the percentage
normally distributed. For histogram           Test (1965) is considered to be the           removal, which requires the data to
plots, the data will display a uniform        most powerful (Razali and Wah, 2011).         be normally distributed.



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