Statistical significance addresses whether an observed difference between groups is likely to reflect a real difference rather than random chance. It is a function of both the size of the effect and the sample size.
For the numbers that you contested the effect size here is enormous. Transwomen137 times the female rate for imprisonment for sexual offences. You need very few observations to be statistically significant.
Don’t believe me? Run the chi-squared or Fischer tests and tell me what you come back with.
Nope. Small sample sizes matter.
"A statistically insignificant result means the observed differences, patterns, or trends in your data are likely due to random chance. This is typically indicated by a p-value greater than 0.05 (meaning there is more than a 5% probability the outcome happened accidentally). 1, 2, 3,
Key Characteristics & Thresholds
The P-value: If a p-value is greater than 0.05, scientists usually fail to reject the null hypothesis. This means the test cannot confidently prove the variable being studied caused the observed effect. 1, 2, 3, 4]
Small Sample Sizes: One of the most common causes for insignificance. If you only survey 10 people, it is much harder to prove a trend compared to surveying 1,000 people. 1, 2]
Practical vs. Statistical: Something can be "statistically significant" but lack real-world value. Conversely, an insignificant finding doesn't mean your study is a failure; it simply means the evidence isn't strong enough to make a definitive claim. 1, 2, 3]
Common Reasons for Insignificant Results
Low Statistical Power: There are not enough participants or observations to detect an actual effect.
Weak Effect Size: The actual difference between your test groups (e.g., control vs. experimental) is incredibly small.
High Variance: The data is too noisy, spread out, or inconsistent to isolate a clear trend. 1, 2, 3, 4, 5]"
"Cass did not look at offending. She complained about the paucity and poor quality of clinical research."
I never said Cass was about offending. The point was a lot of research wasn't included based on small sample sizes.
"Did you read the judge’s quote you pasted? It supports the idea that transwomen are a greater risk than females."
Did you? Or don't you understand the the implication of the words "unconditional" or "risk assessment"
“I can accept, at any rate for present purposes, that the unconditional introduction of a transgender woman into the general population of a women’s prison carries a statistically greater risk "
As the judge goes on to say:
"But that statistical conclusion takes no account of the risk assessment which the policies require.”
In other words its the unconditional introduction that raises the risk like it would for any prisoner not being trans that did. Prison policy requires risk assessment for housing for this reason. For example their policies requires not housing prisoners who have committed violent crimes with the non violent.
And if its still not obvious to you why do you think the Judge ruled it was lawful to imprison trans women in women's prisons if the risk was increased?