The Effect of Age on Road Traffic Fatality Index in Ghana

In this paper, data on road traffic casualties by age groups, from 2009 to 2013, will be used. Using published road traffic casualty statistics from the National Road Safety Commission of Ghana, a 2  8 contingency table is used to determine whether road traffic casualty and age group are independent. A one factor analysis of variance tests shall be used to conduct a comparative analysis of the rate of road traffic fatalities per 100 casualties across the various age groups in Ghana. A multiple comparison test, using the Fisher least significance difference (LSD) method, shall be conducted to determine which pairs of age groups are significantly different. The study will show that road traffic casualty is not independent of age group. The analysis of variance will show that there are significant differences in road traffic fatality indices (fatality per 100 casualties) among various age groups in Ghana. The risks of dying in a road traffic accident among children under 6 years and older population who are over 65 years are both significantly higher than those of other age groups. This points to the fact that, although smaller number of children under 6 years and older population who are over 65 years die in road traffic accidents each year, more and more people as a proportion of the recorded number of casualties, are being killed through road traffic accidents among these two categories of age groups. Thus, the probability of being killed in a fatal road traffic accident is significantly high in each of these two age groups.


Introduction
The European Economic Commission (EEC) and the World Health Organization (1979) have recommended a definition for a road traffic accident fatality.This includes only deaths which occur within 30 days following a road traffic accident while road traffic casualties refer to road traffic accident victims injured or killed within 30 days of the accidents.A number of countries have not yet adopted this definition.For example, in some countries, a road traffic fatality is recorded only if the victim dies at the site or is dead upon arrival at a hospital.In order to make comparison of accident statistics between countries reasonable, figures obtained from countries which have not adopted the 30-day fatality definition, should be properly adjusted.No adjustment is required for figures from countries such as Ghana, U.S.A and Great Britain, which have adopted the standard fatality definition.
Casualties of road traffic accidents in Ghana by age groups, from 2009 -2013, are given in Table 1.Unlike many fatal diseases, road traffic accidents kill people from all age groups, including young and middle-aged people in their active years.A cumulative total of 10 555 fatalities is recorded over the 5-year period.The highest fatalities during the period were in the 26 -35 year old.Table 1 also shows that the active age group, 16 -45 years, was the most vulnerable in road traffic fatalities, representing 63.2% of the total fatalities in the 5-year period.
According to the National Road Safety Commission (NRSC) of Ghana 2013 annual report, one key national Road Traffic Fatality index (F.I.) required for characterization and comparison of the extent and risk of road traffic fatality is fatalities per 100 casualties (see Hesse and Ofosu, 2015).In Table 1, the distribution of the rate of road traffic fatalities per 100 accidents by age groups from 2009 -2013 are also computed.It can be seen, from Table 2, that the F. I. increased from 24.5 to 31.2 among children under 6 years from year 2009 to 2013, whilst that of the "over 65" age groups increased marginally from 30.7 to 36.9 over the same period.In very simple terms, these changes imply that the chance of at least one casualty dying as a result of road traffic accident has increased over the period.It can be observed that, over the 5 year period, the "over 65" continues to be the age group with the highest national fatality rate.For instance, in 2013, about 37% of all road traffic casualties who were over 65 years lost their lives while 31% of casualties who were 5 years old or less died as a result of road traffic accidents.In this study, we wish to know whether road traffic casualty and age group are independent.If they are independent, then we would expect to find the same proportion of fatalities across various age groups.We also propose the use of the completely randomized single factor experiment to determine if there are significant differences in road traffic fatality index rates among the various age groups.

Method
Table 4 shows an r  c contingency table where ij O is the observed frequency for level i of the first method of classification and level j of the second method of classification, where is the marginal total for row i and 1 is the marginal total for column j.Note that 11 , where n is the total sample size.
We are interested in testing the null hypothesis 0 : H the row-and-column methods of classification are independent against the alternative hypothesis 1 : H the row-and-column methods of classification are not independent.
were ij E is the expected cell frequency for the (ij) th cell.It can be shown that, if 0 H is true, then: It can also be shown that, for large n, the statistic H has an approximate chi-square distribution with (r -1)(c -1) degrees of freedom if 0 H is true (see Ofosu and Hesse (2011)).Therefore, we would reject the hypothesis of independence if the observed value of the test statistic H is greater than the critical value 2 , ( 1)( 1) , where  is the size of the test.An extensive treatment of the chi-square distribution can be found in the book by Lancaster (1969).
If we reject the null hypothesis, we conclude that there is some interaction between the two criteria of classification.

Test of Independence
The null and the alternative hypotheses are: 0 : H Casualty is independent of age group.Rows 1 : H Casualty is not independent of age group.
We first find the expected cell frequencies.These are calculated by using Equation (2).Table 5 shows the expected cell frequencies of Table 3  , obtain the cells in Table 6.

Completely Randomized Single Factor Experiment
Table 2 is a typical data of a single-factor experiment with 8 levels (age groups) of the factor, where the factor is the effect of age on F. I. We wish to determine if there are significant differences between the average F. I. across the 8 age groups.In The one-way analysis of variance model assumes that the observations are normally and independently distributed with the same variance for each region or factor level (see Ofosu et al. (2014)).

Validation of Normality and Homogeneity of Variances Assumptions
We check the normality assumption, using the Shapiro-Wilk W test.The null hypothesis is 0 : H observations under each region are normally distributed against the alternative hypothesis 1 : H observations under each region are not from a normally distributed population The value of the Shapiro-Wilk W test statistic for each of the eight age groups is given in Table 7 below.H is rejected at the 5% level of significance if the computed value of W is less than 0.762, the tabulated 5% point of the distribution of the Shapiro-Wilk test statistic.For each of the 8 age groups, we fail to reject 0 H and therefore conclude that there is not enough evidence of non-normality of these samples.
Levene's test (Levene 1960)  is greater than 0.05, 7, 32 2.33.F  Since the observed F-ratio, 1.332, is less than the critical F-value, 2.33, we fail to reject the null hypothesis at the 0.05 level of significance and conclude that there are no significant differences among the ten variances.

One-way Analysis of Variance
Since the normality and homogeneity of variances assumptions are validated, we can use the one-way analysis of variance to determine if the fatality indices across age groups vary significantly.We wish to test the hypothesis 0 : H The mean fatality indices are the same across the 8 categories of age groups, against the alternative hypothesis 1 : H The mean fatality indices are not the same for at least 2 of age groups.The total corrected sum of squares is given by 85 2 40 11 2 .. 2374.360.
The sum of squares among treatments is The within treatment sum of squares, , SSW can be obtained from the equation The analysis of variance results, based on the data in Table 2, are summarized in Table 8 below.H is true, F has the F-distribution with 7 and 32 degrees of freedom.We reject 0 H at significance level 0.05 when the observed value of F is greater than 0.05, 7, 32 2.33.F  From Table 8, the computed value of F is 55.513.Since the observed F-ratio, 55.513, is greater than the critical F-value, 2.33, we reject the null hypothesis at the 0.05 level of significance and conclude that there are significant differences among the fatality indices across the 8 age groups.

Multiple Comparison Method
Since the analysis of variance indicates that the null hypothesis should be rejected, it means that there are differences among the 8 treatment means.But as to which of the means are significantly different, the analysis does not specify.Obviously, in such a situation, we need a different method for comparing individual treatment means.One such methods is the multiple comparison test.
The oldest multiple comparison method, and perhaps the most widely used, is the least significant difference method of Fisher, who first discussed it in the 1935 edition of his book "The design of experiments" (see Ofosu et al. (2014)).To use this method, we first calculate the least significant difference, (LSD), for the given data.This is given by Over 65 30.9 For example, from Table 9, it can be seen that, the observed numerical difference between the mean fatality indices for the age groups "0 -5" and "26 -35" is 17.9.Since 17.9 is greater than 3.068, it follows that there is a significant difference between the two age groups with respect to F. I.It is obvious that the road traffic fatality index for "0 -5" age group is significantly higher than that of other age groups except for "Over 65".This means that, the risk of dying in a road traffic accident among "0 -5" and "Over 65" are both significantly higher than those of other age groups, recording an average rate of 29.0 and 30.9 deaths per 100 casualties, respectively.

Conclusion
We"ve shown that road traffic casualty level depends on age group of victims involved using a 2  8 contingency analysis.
The analysis of variance revealed that there are significant differences in road traffic fatality indices (fatality per 100 casualties) among various age groups in Ghana.The risks of dying in a road traffic accident among children under 6 years and older population who are over 65 years are both significantly higher than those of other age groups.This points to the fact that, although smaller number of children under 6 years and older population who are over 65 years die in road traffic accidents each year, more and more people as a proportion of the recorded number of casualties, are being killed through road traffic accidents among these two categories of age groups.Thus, the probability of being killed in a fatal road traffic accident is significantly high in each of these two age groups.This may be due to higher fragility of children and older population of road users.
These findings are consistent with a related study by Loughran et al. (2007), in which they reported that older drivers are more than twice as likely as middle-aged drivers to cause an accident.The research revealed that drivers and passengers riding in cars driven by older drivers are nearly seven times likelier to die in an auto accident than are passengers and drivers riding in cars driven by middle-aged drivers.This statistic suggests that older individuals are much likelier than middle-aged individuals to die in a car accident.Given these trends, the research suggests that public policy should focus more on improving the safety of automobile travel for older drivers and less on screening out older drivers whose driving abilities have deteriorated unacceptably.

Table 1 .
Age distributions of fatalities and injuries from road traffic accidents from 2010 to 2013

Table 4 .
An r × c contingency table

Table 5 .
using Equation (2).For example, Expected cell frequencies of Table3   H is true, H has the chi-square distribution with 7 [i.e.(2 -1)(8 -1)] degrees of freedom.We reject 0 H at 0.05 level of significance when the computed value of the test statistic is greater than

Table 6 .
Calculations of the observed test statistic Since.10856.5914.07  , we reject the hypothesis of independence and conclude that casualty is not independent of age group.
Table 2, let ij y represent the th i observation taken under the th j age group and

Table 7 .
Observed values of the W test statistic is used to test if 8 samples have equal variances.We wish to test ij H   for at least one pair (i, j).i n = number of observations from treatment (region) i Levene F has the F-distribution with 4 and 40 degrees of freedom.0H is rejected at significance level 0.05 when the observed value ofLeveneF

Table 8 .
Analysis of variance table

Table 10 .
LSDThe observed difference between each pair of means is compared to the LSD.If the observed numerical difference is greater than 3.068, then the road traffic fatality indices of the two age groups are significantly different.The values of the observed numerical differences between pairs of means of the 8 age groups are given in Table9.Pairs of age groups with fatality indices not significantly different are highlighted in Table9.Observed numerical differences between pair of means of road user classes