By mentioning racial bias, I was making the wider point of how the statistics rely on data that is inherently biased due to how it was collected; Inequality in policing and the judicial system leads to different outcomes.
A concrete example from the UK is that in the year ending March 2024, under the "stop and search" procedures, "there were 59,549 searches of women, [...] and 447,952 searches of men [...]" (Elided parts of the quote are because the article compares stats to the year prior, which isn't relevant to our discussion)
That's a ratio of men and women being searched of around 15:2 . I'm going to treat that as if it were 7:1, because I want to set up a hypothetical. Now obviously this doesn't include any of the downstream stuff like rates of actually getting arrested, or later found guilty, because that would be far too complex to consider here. Let's treat stop and search rates as a proxy for crime rates, and consider two different scenarios that could explain these data.
In scenario 1, we would assume that for each gender, the number of people stopped and searched is proportional to the number of people who commit crimes, I.e. that:
the gendered ratio of stop and search (7:1) ≈ the gendered ratio of crimes committed (7:1)
Now for scenarios 2, let's assume that this isn't the case, and that actual ratio of crimes committed is 𝒳 :1, where 𝒳 is unknown; although my belief is that 𝒳 lies somewhere between 1 and 7 (i.e. that women commit more crimes than is recorded in the stats, but likely not significantly more than men do), 𝒳 could even be larger than 7.
There's a lot of possible reasons why we might find that 𝒳 ≠ 7. Police may actually use stop and search as a tactic to harass women (depressingly common based on what we've seen of police abusing their power against women), leading to women being over counted in the stats compared to their actual crime rates; or maybe police are less likely to stop and search women because they've found that to find contraband like drugs, a more invasive search would be necessary (I, and many women I have known have occasionally hid small, secret items in their bras, and I imagine many criminals would have had the same idea); or maybe police officers are worried about being accused of abusing their power to harass women, so their personal sense of professional risk leads them to be less likely to stop women. I'm not trying to make the case for any of these in particular, merely assert that there are many plausible reasons why the ratio of stop and searches might be different to the ratio of crimes committed.
In both scenario 1 and 2, our data shows us the same thing: that men commit more crimes than women at a roughly 7:1 ratio. However, in scenario 2, this conclusion is an incorrect one, due to bias in how the data was collected. The crux of my point is that we don't know whether reality is closer to scenario 1 or 2, and we don't have a way of knowing because we have no way of counting true rates of crime; anything that tries to study crime is inevitably going to have a heckton of false negatives — that is, criminals who get away with it. And every innocent person who has been imprisoned is a false positive. False positives and false negatives are a problem in any statistical study, but I am arguing that this is especially significant in this case due to well documented inequalities in policing, affecting multiple axes of oppression. That's why I brought up racial bias — to highlight the many flaws of policing as a method of data collection.
Often when we run into the problems of false positives and false negatives in statistics, we are able to estimate how accurate our proxy measurements are by comparing them to a reference gold standard. During COVID, for instance, when Lateral Flow Tests (LFTs) were being tested, we were able to test them against PCR tests, which were known to be extremely accurate. We have no such reference standard when it comes to crime stats — all we have is the proxy. What I am advocating for is that we keep this in mind, and take any crime statistics with a hefty dose of salt