Response to characteristics of nursing homes associated with COVID-19 outbreaks and mortality among residents in Victoria, Australia.

We refute the contention of Lange1 that the stated findings in our recent article2 are not supported by the statistical analysis and rebut his claim that our conclusions ought to be altered. First, the p values highlighted by Lange were reported in our subgroup analyses (Tables S1–S3). These are separate to our primary analyses. The appropriate and correct p values should have been computed from Tables 1 to 3. The associations between variables with p < 0.05 are correctly annotated in those tables. Second, Lange's statistical interpretation is fundamentally flawed. The foundations of interpreting empirical research are frequently noted as differentiating what is statistically significant, what is real and what is clinically important,3(p119) and of appreciating the assumptions of statistical tests and the implications when these are violated.4 The Pearson χ2 test and associated p values assume that the finite data are sampled from an (effectively infinite) population.5(p308) This is to be distinguished from our research study, which did not sample but rather included the entire population of nursing homes in Victoria. The p values may be of interest in approximately quantifying the effect size relative to the population size but have no meaningful statistical interpretation when there is no sampling. We accordingly omitted numerical p values from Tables 1 to 3 for economy of space. We did not make any claims about χ2 statistics, p values or statistical significance in the discussion of our primary results. Our descriptive results are correctly stated for an entire study population. For example, it is true that the proportion of not-for-profit operators was highest among homes with a high case-fatality rate (50.0%) than those with medium (23.5%) or low (37.0%) case-fatality rates. This cannot be rendered untrue by a calculated p value (0.3) that is interpreted as being ‘not statistically significant’. We acknowledged our research is subject to other types of measurement error beyond the scope of significance testing; for example database incompleteness. We reviewed these limitations at length, and our conclusion is appropriately cautious. The descriptive results are presented accurately without embellishment, international studies are presented for comparison and associations are described without necessarily implying causation. No conflicts of interest declared. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.