Appendix 4: Data analysis methods
Index of concentration (IC)
For each demographic variable (e.g. gender), an IC was calculated for each demographic group within that variable (e.g. men and women).47
For each demographic group, the IC was calculated by dividing the proportion of inquiries from that demographic group by the proportion of that group in the NSW population according to the 2001 census,48
and multiplying the result by 100. The following example illustrates the calculation process.
IC for men and IC for women for inquiries to the NSW Legal Aid Information/Advice Service
Proportion of inquiries from men ÷ Proportion of men in NSW * 100 = Index of concentration for men
45.6 / 49.4 * 100 = 92
Proportion of inquiries from women ÷ Proportion of women in NSW * 100 = Index of concentration for women
54.4 / 50.6 * 100 = 107
The IC for women (107), which is greater than 100, indicates that women accounted for a higher proportion of inquiries than would be expected given their proportion in the NSW population. The corresponding IC for men (92), which is under 100, indicates that men made fewer inquiries than would be expected based on their proportion of the NSW population.
The chi-square test is a non-parametric test that examines whether there is a significant relationship between two or more categorical variables with data in terms of frequencies. The chi-square test is based on a cross-tabulation of the relevant variables and compares the observed frequencies in each cell of the cross-tabulation with the frequencies expected on the basis of the null hypothesis.49
All of the chi-square tests in the present report were two-way, that is, conducted between two variables.
The chi-square test determines whether the relationship between the variables is significant. To determine which cells in the cross-tabulation had higher than expected frequencies, the standard residual for each cell was examined. The standard residual is the difference between the observed and expected frequency, adjusted for the scale effect of the frequencies. Cells with a standard residual greater than or equal to two were deemed to be significantly ‘higher than expected’, and are reported in the text.
Adjusting for missing values
For any variable (for a given service) with missing values for more than 10 per cent of inquiries, the following process was undertaken to decide whether to use a weighting process before presenting descriptive statistics (e.g. percentages) and conducting the chi-square tests involving that variable.
The distribution of missing values for the variable in question was compared to the distribution of valid values for the variable across both years and broad areas of law. If the distribution of missing values was similar to the distribution of valid values across both years and broad areas of law,50
the original frequencies for the variable were used in all analyses. If, however, these distributions differed,51
adjusted frequencies for the variable were used in all relevant analyses (e.g. percentages and chi-square tests).
The adjusted frequency in each case (e.g. in each cell of the chi-square cross-tabulation) was calculated as follows:
Adjusted frequency = original frequency * total no. of inquiries / no. of inquiries with valid values
Adjusted frequencies were used in the analyses for NSW Community Legal Centres involving age, income, country of birth or Indigenous Australian status, and for Legal Aid NSW involving source of income. In all other cases, original frequencies were used in the analyses. Note that, even in the cases where adjusted frequencies were used, the number of inquiries with valid values is still shown at the bottom of the relevant tables/figures.