*Morphodynamics in a Tropical Shallow Lagoon: Observation and Inferences of Change DOI: http://dx.doi.org/10.5772/intechopen.90189*

0.05 (0.0000), there is a statistically significant difference between the means of the 12 variables of the six profile lines at the 95% confidence level.

To determine which means are significantly different from which others, a multiple range test (multiple comparisons of procedures that use the studentised range statistic to compare sets of means) was performed, and the summary results of which are shown in **Table 3**. Out of the 65 paired groups that were tested, an asterisk has been placed next to 35 pairs, indicating that these pairs show statistically significant differences at the 95% confidence level. It can be inferred from this that significant changes occurred on the lagoon water bed between 2008 and 2014 going from the direction west-east of the lagoon water bed.

To further ascertain the change within and between the 12 pairs of profile lines, a variance check test was carried out using Levene's method [76]. This statistic tests the null hypothesis that the standard deviations within each of the 12 columns are the same. Of particular interest are the generated p-values. A summary of the statistical test results (**Tables 5** and **6**) shows that there is a statistically significant difference among 47 out of 65 paired groups with the standard deviations at the 95% confidence level. **Table 6** shows a comparison of the standard deviations for each pair of samples. P-values less than 0.05, of which there are 47, indicate a statistically significant difference between the two sigmas at 95% significance level.

As part of these analyses, a least significant difference (LSD) assessment was carried out on the 12 pairs using Fisher's LSD; it gives the opportunity to deduce which group is significantly different from another; this is not possible using ANOVA. The LSD calculates the smallest significance between two means as if a test had been run on those two means. It makes direct comparisons between two means from two individual groups and any differences larger than the LSD is considered a significant result. The test takes the square root of the residual mean square from ANOVA and considers that to be the pooled significant difference (SD), taking into account the sample sizes of the groups being compared; it computes a standard error of the difference between the means. It also computes a *t* ratio by dividing the difference between means by the standard error of that difference. The various results exhibited by each groups is displayed in the graph of **Figure 10**. Comparing the results of **Figure 10** and the summary results (**Table 6**), it can be concluded that significant change exists between 2008 and 2014 on the Lagos Lagoon water bed from the northern region to the southern region of the lagoon.

Finally, of particular interest is the p-value of profile A-A<sup>0</sup> at the northern-most region very close to the inlets, and this has a p-value of 6.19 � <sup>10</sup>�<sup>4</sup> , which is less than 0.05. The error bar of the A<sup>0</sup> transect (2014 transect dataset) does not overlap

**Figure 10.** *Multiple comparisons means plot with 95.0% LSD intervals.*

**Contrast Sig Difference Limits** C 2008-D 2014 0.486667 0.955106 C 2008-E 2008 0.4415 0.755078 C 2008-E 2014 0.392 0.755078 C 2008-F 2008 \* **1.12122** 0.914445 C 2008-F 2014 \* **1.94511** 0.914445 C 2014-D 2008 0.250667 0.955106 C 2014-D 2014 0.492 0.955106 C 2014-E 2008 0.446833 0.755078 C 2014-E 2014 0.397333 0.755078 C 2014-F 2008 \* **1.12656** 0.914445 C 2014-F 2014 \* **1.95044** 0.914445 D 2008-D2014 0.742667 0.955106 D 2008-E 2008 0.6975 0.755078 D 2008-E 2014 0.648 0.755078 D 2008-F 2008 \* **1.37722** 0.914445 D 2008-F 2014 \* **2.20111** 0.914445 D 2014-E 2008 0.045166 0.755078 D 2014-E 2014 0.094666 0.755078 D 2014-F 2008 0.634556 0.914445 D 2014-F 2014 \* **1.45844** 0.914445 E 2008-E 2014 0.0495 0.477553 E 2008-F 2008 0.679722 0.702939 E 2008-F 2014 \* **1.50361** 0.702939 E 2014-F 2008 \* **0.729222** 0.702939 E 2014-F 2014 \* **1.55311** 0.702939 F 2008-F 2014 0.823889 0.871889

*Lagoon Environments Around the World - A Scientific Perspective*

**Test P-Value**

Levene's 6.69373 **4.51871E-10**

**Number of paired profile Range of P-value Significant status** 47 Less than 0.05 Statistically significant 19 Greater than 0.05 Statistically not significant

*\*denotes a statistically significant difference.*

*Summary of the statistical test variance check.*

**Table 4.** *Multiple range test.*

**Table 5.** *Variance check.*

**Table 6.**

**94**

with all the transect lines of C to F0 , so also does transect A. This indicates that there is a statistically significant difference in the depth values of transect lines AA<sup>0</sup> and those of C to F0 . However, transect CC0 shows no difference at all but does show significant variation with transects AA<sup>0</sup> and FF<sup>0</sup> . It can be concluded that significant changes have taken place between and within the transect line at varying degrees. Interestingly, it is evident in the results of **Figures 4**–**9** that erosion, shoaling, channel migration, channel movement and accretion take place along a west-east direction at different spatial location.
