Jellyfish Compliance with SQIDEP · MCU15/0122

4
Technical Papers


 Table 2. Results of the Shapiro-Wilk            Table 3. Results of the Shapiro-Wilk Parametric Test for log-transformed influent
 Parametric Test for % removal to test           and effluent data.
 for normality of the data distribution.
                                                                                  TSS                         TP                           TN
                       %
                              % TP     % TN                              Influent       Effluent   Influent        Effluent     Influent        Effluent
                      TSS

                     0.039    0.511    0.449                              7.012          5.574      2.893           3.215          3.208         2.589


                     0.040    0.551    0.516                              8.054          5.724      3.032           3.234          2.979         2.835

 W (test statistic) 0.982     0.928    0.872     W (test statistic)       0.871          0.974      0.954           0.994          0.929         0.913

 p-value (>0.05)     0.974    0.441    0.116     p-value (>0.05)          0.111          0.708      0.693           0.996          0.448         0.357

NON-PARAMETRIC TESTING                          3. Calculate the mean of the differences           CONFIDENCE INTERVAL
If there are no transformations that can          (   )                                            After the data has been proven to be
be utilised to transform the raw data           4. Calculate the standard deviation of the         statistically significant, a 95% confidence
into a normal distribution, then non-             differences (    )                               interval can be constructed. The 95%
parametric tests need to be used to                                                                confidence interval is defined in Neyman
test for differences in populations. An         5. Calculate the Standard Error (SE) of the
                                                                                                   (1937) as follows:
example is the Wilcoxon Signed-Rank Test          mean difference:
instead of the paired t-test (McDonald,                                                              “There is a 95% probability that
2014). Confidence intervals can also be                                                            the calculated confidence interval
calculated non-parametrically, as described                                                        encompasses the true value of the
in Geyer (2003), or utilising methods such                                                         population mean.”
                                                6. Calculate the t-statistic, using a
as bootstrapping (Wang, 2001). However,           t-distribution with n – 1 degrees of               This involves calculating the standard
these methods can sometimes be complex            freedom:                                         error, then adding/subtracting the
in nature and require specialised statistical                                                      standard error to/from the mean to create
software to conduct statistical modelling.                                                         the upper and lower bounds. There is a
   A less mathematically intensive method       7. t-distribution tables can be referenced
                                                                                                   95% probability that the true population
would be to increase the sample size to           to find the corresponding p-value                mean exists within these bounds (Tan
larger than 30, as the Central Limit Theorem      (probability) with the t-statistic (T)           and Tan, 2010; Neyman, 1937).
states that, as sample size increases, the        and n – 1 degrees of freedom.
distribution of sample means approaches
a normal distribution, regardless of initial       For a 95% confidence level, if the p-value
distribution (Bonacci, 2012).                   is less than 0.05, the null hypothesis (there      where:
                                                is no difference between the sample set
STATISTICAL SIGNIFICANCE –                      means) is rejected, and the data sets are
PAIRED T-TEST                                   considered statistically different.
The paired t-test is used to assess the
                                                   The paired t-test was conducted on the
statistical difference (or significance)
                                                log transform of the influent and effluent
between two normally distributed data
                                                test data, and results are presented in              For the 95% confidence level, the Z
sets. In this case, it is used to compare the
                                                Table 4. The paired t-test results for TSS,        score equates to 1.96 for a two-tailed test.
influent and effluent data sets to establish
                                                TP and TN are significantly beyond the 95%
if their population means are statistically                                                           In this case, as the CRE percentage
                                                confidence level (p<0.05), therefore we can
different. If it can be confirmed that the                                                         defines the removal efficiency of the
                                                reject the null hypothesis and conclude that
two sets of data do not have the same                                                              stormwater treatment device, confidence
                                                the influent and effluent concentration data
population mean, then it can be concluded                                                          intervals were constructed around the
                                                sets are statistically different.
that there is a statistical significance
between them (Cramér, 1946).                     Table 4. Paired t-test results for the field test data reported in Table 1. The
                                                 log-transformed influent and effluent concentrations are being compared for
   The following steps describe the              statistical difference.
methodology used in conducting a paired
                                                 H0 = there is no difference between the
t-test (Shier, 2004):
                                                 concentration means of the influent &                      TSS                TP                TN
1. Construct a null hypothesis, i.e.             effluent populations
    that there is no statistical difference
                                                 Mean of Differences (µd) Loge(mg/L)                     2.267                1.011             0.672
    between the population means.
                                                 Std. dev. of Differences(σd)                            0.858                0.746             0.525
2. Calculate the difference for each pair.
    This is done by subtracting the effluent     Std Error (SE)                                          0.271                0.746             0.166
    concentration from the influent
                                                 T-Statistic                                             8.357                4.288             4.042
    concentration for each event (i.e.
                                  for each       Degrees of Freedom (n-1)                                     9                9                  9
    event pair of data, where i varies from
                                                 Paired t-test Result (Must be < 0.05)                  1.6x10      -5
                                                                                                                              0.002         0.0029
    1 to n).




WATER MAY 2015