Sexual identity proportions were calculated from the weighted number of adults in each sexual identity category in all three datasets. The proportions were calculated by sex for individual sexual identity categories (gay, lesbian, bisexual, and other), and for the total sexual minority population—defined as the sum of those four categories. Proportions were also calculated for the total sexual minority population by broad age group and sex. We do not present proportions by sex, age group and individual sexual identity categories as the variability around the point estimates increases significantly. The don’t know, not stated/refused responses were included in the denominators of the proportions.
Population estimates by sexual identity were calculated by taking the proportion of the population in each sexual identity category derived from the surveys and multiplying them by the published ERPs of Australia for 2011 and 2016. They were prepared in three steps. First, an estimate of the total sexual minority population aged 18 + by sex was calculated. Given a lack of information to suggest that any one survey dataset was more reliable than the others, we weighted all proportions equally. Thus, the sexual minority (\(M\)) population (\(P\)) aged 18 + by sex (\(s\)) was calculated as:
$${P}_{s,18+}^{M} ={ P}_{s,18+}^{ERP} \frac{1}{3}\left({p}_{s,18+}^{M,GSS}+{p}_{s,18+}^{M,HILDA-12}+{p}_{s,18+}^{M,HILDA-16}\right),$$
where \(ERP\) is the official estimated resident population, \(p\) denotes the proportion of the population, and \(GSS\), \(HILDA-12\), and \(HILDA-16\) refer to the three survey datasets with the HILDA labels including the survey wave number.
Second, estimates of the total sexual minority population by age groups 18–24, 25–34, 35–44, 45–54, 55–64 and 65 + were calculated. Preliminary (\(pr\)) estimates were calculated as:
$${P}_{s,a}^{M}\left[pr\right]={ P}_{s,a}^{ERP} \frac{1}{3}\left({p}_{s,a}^{M,GSS}+{p}_{s,a}^{M,HILDA-12}+{p}_{s,a}^{M,HILDA-16}\right),$$
where \(a\) refers to age group. Then a small constraining adjustment was made to ensure these age-specific estimates summed to the overall 18 + estimate:
$${P}_{s,a}^{M} ={P}_{s,a}^{M}\left[pr\right] \frac{{P}_{s,18+}^{M}}{\sum_{a}{P}_{s,a}^{M}\left[pr\right]}$$
Third, estimates of the 18 + population by sex by individual sexual identity category were calculated:
$${P}_{s,18+}^{m}\left[pr\right]={ P}_{s,18+}^{ERP} \frac{1}{3}\left({p}_{s,18+}^{m,GSS}+{p}_{s,18+}^{m,HILDA-12}+{p}_{s,18+}^{m,HILDA-16}\right),$$
where \(m\) refers to gay/lesbian, bisexual or other. As before, a slight adjustment was required to ensure consistency with the overall sexual minority estimate:
$${P}_{s,18+}^{m} ={P}_{s,18+}^{m}\left[pr\right] \frac{{P}_{s,18+}^{M}}{\sum_{m}{P}_{s,18+}^{m}\left[pr\right]}.$$