RESULTADOS ESPERADOS 1 INSTRUMENTO 1 (ver anexo)

Several basic statistical techniques including correlation tests and univariate analysis of variance (Oneway-ANOVA) were used to study the relationships between contributing factors, and relationships between structural/hydraulic conditions and contributing factors. One important aspect in most statistical techniques is the classification of variables into scale variables and categorical variables. Some techniques such as correlation test can only be applied to the scale variables, whilst others such as the cross table analysis can only be applied to the categorical variables.

Scale variables represent ordered categories with a meaningful metric, so that distance comparisons between values are appropriate. Examples of scale variables include age in years and income in thousands of dollars. In this study, scale factors are pipe size, pipe age, pipe depth, pipe slope and tree-count.

Categorical variables are classified as nominal variables and ordinal variables. Nominal variables represent categories with no intrinsic ranking. Examples of nominal variables include region, zip code, or religious affiliation. Ordinal variables represent categories with some intrinsic ranking. Examples of ordinal variables include attitude scores representing degree of satisfaction or confidence and preference rating scores. In this study nominal factors are pipe location, soil type and TMI. Ordinal factors are the structural and hydraulic conditions.

The SPSS software package can be used to perform the analysis and was used in this study.

4.3.1 Correlation Tests

The correlation test measures show how two variables are linearly related (Dasu and Johnson 2003). The Pearson's correlation coefficient is a measure of linear association between two scale variables (Johnson and Wichern 2002). The correlation coefficient takes values between [0, 1]. Generally, strong and weak linear relationships would take values between [0.85-1] and [0-0.5] respectively; the mild or moderate linear relationships would take values between 0.5 and 0.85. The t-test (Montgomery et al.

statistically significant by considering the P-value. If the P-value of the t-statistic is

smaller than a critical value of 0.05 for 95% confidence level, the linear relationship is considered statistically significant (Montgomery et al. 2004).

The correlation test was applied only to scale factors including pipe size, age, depth, slope and tree-count. The results are given in Table 4-3, which shows that there is a statistically significant correlation between pipe size and pipe depth. This correlation was mild since the correlation coefficient of 0.517 was between 0.5 and 0.85. In short description, this correlation was called statistically significant and mild. In a similar description, there are statistically significant and weak correlations between pipe size and age, pipe size and slope, pipe age and depth, and depth and slope. However, the ‘tree-count’ factor has no statistically significant correlation with other scale factors. The positive (+) correlation indicates a value of one variable increases with increase in the value of the other variable. Similarly, the negative (-) correlation indicates a value of one variable increases with decrease in the value of the other variable. The positive correlation between pipe size and depth is reasonable since the large size pipes are often used as the main pipes which must be buried deeper because of cover requirements. Similarly, the positive correlation between pipe size and age can be viewed in a sense that larger size pipes are often laid first followed by smaller size pipes which are often added later with urban development. On the other hand, the negative correlation between pipe size and slope could relate to design or construction practices in which large pipes can have smaller slopes (to reduce cost) because they typically are designed for larger minimum flows, which can provide the minimal required flow velocity (typically 0.75 m/s) to avoid settling of solids.

Table 4-3: Results of Pearson‘s correlation tests

Pipe Size Pipe Age Pipe Depth Pipe Slope Tree-count Pipe Size 1 0.106(*) 0.517(**) -0.165(**) 0.058

Pipe Age 1 0.102(*) 0.034 0.024

Pipe Depth 1 -0.101(*) 0.079

Pipe Slope 1 -0.008

Tree-count 1

(**): Correlation is statistically significant at the 0.01 level from t-test.

4.3.2 One-way ANOVA and Cross-Table analysis

Besides the correlation tests, the analysis of variance (one-way ANOVA) and cross- table analysis (Hair et al. 1998) can be used to detect associations between two variables.

The one-way ANOVA technique compares a scale variable across two or more groups of a categorical variable with a hypothesis of equality of group means. If the hypothesis is rejected, the scale variable has different effects on each group. For stormwater pipes, the common hypothesis is whether scale factors (i.e. pipe size, age, depth, slope, tree- count) have significantly different effects on three groups of pipes corresponding to three pipe (structural and hydraulic) conditions. On the other hand, the cross-table analysis technique assesses whether a category factor has an association with another category factor using the hypothesis of equality of cell counts across the table of two factors. If the hypothesis is rejected, the association or effect exists. For stormwater pipes, this test is carried out for categorical factors (i.e. pipe location, soil and TMI) on the pipe (structural and hydraulic) conditions.

The symmetric measure (Hair et al. 1998) is a statistical indicator that can be used to determine the degree of association in the cross-table analysis. The symmetric measure ranges between 0 and 1, with 0 indicating no association between the row and column variables and values close to 1 indicating a high degree of association between the variables.

Similar to the t-test in the correlation tests in Section 4.3.1, the F-test can be used for the

oneway-ANOVA and the Pearson Chi-square test can be used for the cross-table analysis in order to test whether the association is statistically significant by considering the P-values (Hair et al. 1998). If the P-value is smaller than a critical value of 0.05 for

95% confidence level, the hypothesis is rejected (Hair et al. 1998). 4.3.2.1 Structural Condition versus Contributing Factors

The results of performing one-way ANOVA and cross-table analysis on structural condition are given in Table 4-4 and Table 4-5 respectively. It can be seen From Table 4-4, all P-values are larger than the critical value which means that the structural

be seen from Table 4-5, only the hydraulic condition was found to have statistically significant effect on the structural condition as substantiated by its P-value of 0.002.

However, the symmetric measure shows a low degree of association between them. Table 4-4: One-way ANOVA on structural condition

Factors Mean Square F-statistic P-value Pipe Size 247200.9 2.205 0.112

Pipe Age 18.6 0.286 0.751

Pipe Depth 0.086 0.157 0.855

Pipe Slope 6.8 1.277 0.280

Tree-count 3.9 0.584 0.558

Table 4-5: Cross-table analysis on structural condition Factors Pearson Chi-

square Symmetric measure P-value Pipe Location 5.099 0.084 0.531 Soil Type 3.925 0.01 0.416 TMI 10.638 0.04 0.386 Hydraulic Condition 17.075 0.132 0.002*

*statistically significant at 0.05 significance level

4.3.2.2 Hydraulic Condition versus Contributing Factors

Similar to Section 4.3.2.1, the results of performing one-way ANOVA and cross-table analysis on the hydraulic condition are given in Tables 4-6 and 4-7 respectively. It can be seen that the pipe age and pipe slope were found to have statistically significant effect on the hydraulic condition. The structural condition and pipe location were found to have statistically significant effects on the hydraulic condition as substantiated by the

P-values in Tables 4-6 and 4-7 respectively. However, the symmetric measure using

contingency coefficient provides weak association between the pipe location and the hydraulic condition.

Table 4-6: One-way ANOVA on hydraulic condition Factors Mean Square F-statistic P-value Pipe Size 124129.042 1.102 0.333 Pipe Age 518.017 8.261 0.000* Pipe Depth .734 1.349 0.261 Pipe Slope 34.704 6.597 0.002*

Tree-count 13.412 2.020 0.134

*statistically significant at 0.05 significance level

Table 4-7: Cross-table analysis on hydraulic condition Factors Pearson Chi-

square Symmetric measure P-value Pipe Location 16.012 0.196 0.014* Soil Type 5.521 -0.034 0.238 TMI 17.510 -0.034 0.064

*statistically significant at 0.05 significance level