Statistical Assessment of the Difference between the Height Differences Obtained by Spirit and Trigonometric Leveling Techniques

Due to the limitations associated with the use of trigonometric leveling, it seems that height differences obtained by methods of spirit and trigonometric leveling cannot be compared. Thus, it becomes necessary to identify the extent of the relationship between the height differences obtained by these two leveling techniques. Using statistical tests, it is possible to examine such a relationship. Hence, this paper aims to investigate this relationship by subjecting the difference in the height differences, to a statistical test of hypothesis, based on the field observed data in the study area located in Southeastern Nigeria. To achieve this aim, leveling was performed for each of the two methods, on two different leveling routes. Difference obtained from the height differences computed between consecutive test points for each of spirit and trigonometric leveling were further subjected to statistical tests. Under some statistical assumptions, the results obtained show that the calculated t-values; |t|, for the two separate leveling routes, are 0.003 and 0.001 for route-1 and route-2, respectively. Using the degree of freedom (df) as 78, and a 5% level of significance (alpha=0.05), in conjunction with t-value distribution table, gives a t-critical value (tcritical), of 1.994. Comparison of this value against the computed values of 0.003 and 0.001 indicates that the computed t-value is less than the table value, at a significance level of 5%, leading to the acceptance of the null hypothesis (H0), and rejection of the alternative hypothesis (Ha). The computed p-values, corresponding to the t-values, are 0.998 and 0.999, for routes 1 and 2 respectively. Therefore, since the P-value > 0.05 it is safe to accept the (H0); that there is no significant difference between the height differences obtained using spirit and trigonometric methods of leveling, provided strict leveling procedures are observed. This study will assist project managers and policy makers in deriving the data from finished level survey which is used to design roads, highways and airfields.