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# Categorical Variables

A categorical variable is a variable that can take on one of a limited, and usually fixed, number of possible values, thus assigning each individual to a particular group or “category.” In order to examine the relationship between each categorical variable and “Gauge Value Change per Month”, this study adopts an ANalysis Of VAriance (ANOVA) which statistically compares the average “Gauge Value Change per Month” in different categories of each variable. In our dataset, the following variables are categorical variables:

• • Rail Profile which is associated with the type of rail profile at the inspection point (i.e. 41 kg, 57 kg, 60 kg, 80 lb, 96 lb).
• • Rail Type which is associated with the inspection point (i.e. GP, TT, G or T).
• • Route which is a categorical variable to indicate the route number (i.e. 57, 59, 70, or 75). In this study four different tram routes are used.

Table 5 shows the results of the ANOVA, including F-Value and significance value. Higher values of F-value indicate greater difference between average values of “Gauge Value Change per Month” in different categories of variables. Significance value (if less than 0.05) suggests the differences are statistically significant. According to Table 5, all categorical variables are important for modelling “Gauge Value Change per Month”. However, based on F-Values, “Rail Profile” has the greatest impact.

To visually inspect the impact of “Rail Profile” on “Gauge Value Change per Month”, Figure 4 shows average “Gauge Value Change per Month” in different

Table 5. ANOVA between “Gauge Value Change per Month ” and categorical variables

 Variable F-Value Significance Rail Profile 84.3 0 Rail Type 51.5 0 Route 55.3 0

Figure 4. Impact of repair on degradation of curves: Relationship between “Gauge Value Change per Month ” and “Rail Type ”

categories of rail profile. Accordingly, “Gauge Value Change per Month” varies noticeably in various rail profile types. This shows that type of rail profile is an influencing factor on degradation of tram tracks and significant in rail maintenance. Figure 5 presents the relationship between different categories of “Rail Type” and average “Gauge Value Change per Month”. Figure 6 also depicts average “Gauge Value Change per Month” in different tram routes. Accordingly, route 59 has the highest “Gauge Value Change per Month” and route 70 has the lowest. This shows that for valid analysis of the degradation and maintenance of tram tracks, each route has to be individually assessed.

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