Comparative Techniques

As expressed by Rowland (2003: 120), ‘Concepts and theories, such as the demographic transition, provide a general comparative setting for research, but

empirical comparisons are needed to substantiate conclusions and improve research’. In other words, it is essential to employ quantitative measures that will draw comparisons between populations with a view of seeking in-depth explanations of population and social change. Demographic summary measures refer to simple averages, such as the ‘crude rate’ or the total percentage doing X or Y. For a summary measure to be compared appropriately – and provide an explanation for the population and social change to which Rowland (2003) refers – it needs to be refined. This involves a process of controlling for differences in compositional attributes (such as population age structures) so that the populations being compared are, in the statistical context, the same. Consequently, refining a summary measure provides a possible explanation as to how compositional differences between populations, or within the same population over time, may have contributed differences in the experience of the phenomenon of interest (such as apprehension ratios).

One specific method for refining demographic summary measures is standardisation (Carmichael 1995; Rowland 2003; Jackson 2006; see Kitagawa (1955, 1964) for the earliest exponents of standardisation). The rationale of standardisation is to demonstrate the influence of compositional variance, and involves ‘removing’ compositional effects (such as age) that compromise the measurement of trends in the variable of interest (offence trends, for example). Such a method is useful because trends in any summary variable (like the total apprehension ratio) are compromised by at least two factors: changes in the underlying variable (such as the actual apprehension rate), and changes in the composition (or size) of the population for which the summary measure is being examined.

In sum, standardisation involves making populations ‘mathematically comparable’ – or the same – by applying a singular, standard set of compositional attributes (such as population age structure). This may involve controlling for differences in compositional attributes between multiple populations at the same point in time, or within a single population at multiple points in time. The attribute may relate to one of the populations being compared, or to a completely different population (although it makes more sense to use the former approach). The attribute is then held constant

over time, applying to it the observed age-specific ratios of the variable of interest across the period being examined. The summed results for each year in the analysis indicate what the total ratio or number of the variable of interest would have been

had the compositional attribute not changed over time, with the difference between the actual and standardised level taken to indicate the extent to which changes in the compositional attribute have either reduced or increased the variable of interest. For example, the 1987 age structure could be held constant across each year between 1987 and 1997, and applied to the actual offence ratios for each year, to indicate what offence numbers would have been had the population not aged structurally.

This process can be expressed as the following equation:

Ms(i) = ∑cmi(c).pi(c)

Where: Ms(i) = the actual population composition standardised to that of the standard population composition;

c = the compositional categories for the comparative variable; mi(c) = the specific measure for the standardised population for the compositional categories; and

ps(c) = the proportion of the standard population across the compositional categories.

This form of standardisation is direct standardisation. In the example of age- standardisation, this means that observed age-specific offence rates are applied to population numbers at each age. It differs from another form of standardisation, one which is often utilised in the existing studies of the association between structural ageing and crime trends: indirect standardisation. In the absence of known local age- specific offence rates, the known rates for elsewhere – or estimated rates calculated from known age-crime trends (as per Steffensmeier and Harer (1987 and 1991), for example) – are applied to the total offence numbers on a pro-rata basis, thereby generating an approximation of crime by age.

Decomposition analysis is a ‘variation’ of standardisation analysis (Carmichael 1995: 51). Here, the objective is to decompose the difference between two summary measures (say the difference between the 1987 and 1997 total offence ratios) into the components that are due to differences in the population composition (such as age structure), and differences in a specific measure (such as all factors that influence apprehension rates, including changes in surveillance and reporting levels), to determine the ‘real’ change in a measure over time. It does not, however, account for change in population size, because the analysis works with rates.

Retrospective Analysis: In this thesis, three applications of direct standardisation are used to investigate the prior impact of the age composition expression of the age structure-crime pattern: age, size, and apprehension (in Chapters 11 and 12). Age- standardised numbers indicate what apprehension numbers would have been over time had the population age composition (at the beginning of the period) remained constant, but actual population size and apprehension levels unfolded. Size- standardised numbers indicate what apprehension numbers would have been over time had population size (at the beginning of the period) remained constant, but actual age composition and apprehension levels unfolded. Apprehension- standardised numbers indicate what apprehension numbers would have been over time had age-specific levels (at the beginning of the period) remained constant, but actual age composition and population size unfolded. In addition, decomposition analysis refines the standardisation analyses, calculating the component of change in the crude apprehension ratio over time that changing age composition and apprehension levels account for. The processes used are explained further in Appendix A (section A.2).

Prospective Analysis: In order to ascertain the future impact of the age composition expression of the age structure-crime pattern, I also use a technique I call ‘simple decomposition’ (in Chapters 13 and 14). This two-step process holds apprehension levels constant at their 2004 level and variously applies them to changing population size (crude projection), changing age composition (resulting in an age-weighted projection which allows for both changing age composition and population size) and constant population size (resulting in a size-standardised projection where size is

held constant but age composition changes as projected). The difference between the various sets of results is then determined. The processes used are explained further in Appendix A (section A.3), but summarised, the approach is as follows:

Step A

Crude projection = effect of changing population size only

Age-weighted projection = effect of changing size and age composition

Difference = effect of changing age composition

Step B

Age-weighted projection = effect of changing size and age composition

Size-standardised projection = effect of changing age composition only

Difference = effect of changing population size

5.4 Summary and Conclusions

This chapter has outlined how the three analytical techniques that are used in this thesis to investigate the age structure-crime pattern (and the associated nature of the underlying relationship between age and crime) work, and what they achieve.

The first analytical technique, being correlation analysis, measures the direction and strength of a relationship between two variables. Such an analysis will provide a preliminary indication of whether there has been a change in age-crime trends, and whether these trends have occurred concurrently with change in the age composition of the general population, by offence and region. This analysis, which forms Chapter 7, thus provides insight into whether the age-crime pattern is variant or invariant, and as to whether cohort and/or age composition effects are likely to be identified in the ensuing analyses.

The second analytical technique, being cohort analysis, reorganises cross-sectional age-specific apprehension data to examine the longitudinal apprehension trends of birth cohorts. This technique is used to examine the cohort density expression of the

age structure-crime pattern (i.e. the classic expression of the Easterlin hypothesis) because it allows for the easy identification of birth cohorts that have experienced criminal trajectories which depart from the age-crime pattern (i.e. which cohort(s) has experienced an increase, rather than a decline, in its apprehension ratios as it has aged, and thus extended its participation in crime beyond the young crime-prone ages). These findings can, subsequently, be related to the size and relative disadvantage (in this case, unemployment rates) of cohorts to determine which findings are reflecting a cohort effect, and which are more likely to be reflecting a (common) period effect. Accordingly, cohort analyses permit for an assessment of whether birth cohorts are a potential source of variance in the association between age and crime, and whether large birth cohort size (and thus high levels of relative disadvantage) is more likely to result in such cohorts offending (or at least being apprehended) at a higher than anticipated level. Conducting such analyses by gender, offence, and state/territory would allow for a further assessment of potential variance in the age-crime pattern and impact of cohort density.

These analyses are refined in Chapter 6, once data availability has been determined, but are conducted in three stages, each using a slightly different approach. Total apprehensions are investigated in two stages (in Chapter 8). First, changes in age- specific apprehension ratios are identified over time (a cross-sectional analysis), and second, the same age-specific apprehension ratios are reorganised via the Lexis diagram to reflect the offending trajectories of birth cohorts (a longitudinal analysis). Offence-specific apprehensions are only investigated longitudinally (in Chapter 9), followed by a comparison of the sets of cohort-specific apprehension trends (in Chapter 10).

Finally, comparative techniques, which control for the impact of change in comparative measures (specifically population age composition, population size, and apprehension levels), are used to examine the age composition expression of the age structure-crime pattern (i.e. the atypical expression of the Easterlin hypothesis). Standardisation indicates what total apprehension levels would have been had there been no change in comparative measures, while decomposition indicates the contribution of changing age composition and apprehension levels to the difference

in crude apprehension ratios over time. Hence, such analyses indicate whether structural ageing has had a negative (i.e. reducing or containing) impact on total apprehension levels over time, and whether this impact (if any) has been higher or lesser than that of population growth or change in apprehension levels. Like the cohort analyses, conducting the comparative analyses by gender, offence, and state/territory would provide insight with regard to the potential variance in the association between age and crime and impact of age composition effects.

This aspect of the analysis is also refined in Chapter 6, but is conducted in two stages, again taking a slightly different approach in each. Using standardisation and decomposition analyses, the impact of past change in apprehension levels, population size, and age composition are calculated in relation to total apprehension levels (Chapter 11), and offence-specific apprehension levels (Chapter 12). The same approach is subsequently taken in calculating the impact of prospective change in comparative measures, which in this instance, are calculated from ‘simple decomposition’ analyses (Chapters 13 and 14).

Having established the appropriate analytical techniques and their application for this thesis, the following chapter discusses the complimentary data requirements, and how the availability (or otherwise) of such data shapes the central analytical framework.