# Forensic pathology probability question regarding perpetrator sex

#### billo

##### New Member
I am a forensic pathologist wondering about the best way to calculate the probability of the sex of a perpetrator based on statistics about wounding. I'll provide fake numbers, since I don't want to get into the weeds about the studies themselves.

Let's say I have the following:

If you look at number of wounds, males tend to cause 10 wounds or more, while females tend to cause 9 wounds or less, e.g.

10 wounds or more:

Males: 60% yes, 40% no
Females: 20% yes, 80% no

Males tend to attack at night, females during the day

Males: 80% night, 20% day
Females: 30% night, 70% day

Males tend to be strangers, females tend to be acquaintances

Males: 75% stranger, 25% known
Females: 35% stranger, 65% known

Note that none of the above are necessarily really true. It's just for illustration.

Given, all other things being equal, a victim, then who

1) Was attacked at night
2) Suffered 12 blows
3) Was attacked by a stranger

What is the probability that the attacker was male? What other information do I need -- do I need the absolute numbers of attacks, e.g. number of killings at night versus during the day, absolute numbers of killings by males versus killings by females, etc.?

Thanks!

billo

#### hlsmith

##### Less is more. Stay pure. Stay poor.
I am not a probability whiz, but you need to state whether these attributes are independent or not. If they are independent I believe you just need to do something simple like multiply them, but if they are conditional you need to control for this and use something like Bayesian network analyses. What you need to know is whether those numbers hold in subgroups. So probability attacker male given night controlling for #wounds;

P(male | night, # wounds) = P(male | night), is something like what you have to prove. Sorry if I am a little bit off in this remarks.

#### billo

##### New Member
Yes, I'm assuming they are independent. I'm hesitant just to multiply it out because I'm thinking that I have to include some prevalence data, e.g. number of male perpetrators vs number of woman perpetrators in the population. For instance, if there are 100 female perpetrators and 100 male perpetrators, then out of 200 killings, 110 will be at night, of which 80 will be by males and 30 by females, so that the probability that the perpetrator is male is 72%, based on that one criterion. In contrast, if there are 100 males and 50 females, there will be 95 killings at night, of which 80 will be by males and 15 by females, so that the probability that the perpetrator is male would be 84%.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
As noted, you get what you pay for here. I think your values about need to be for part of it like this:

Stabbed >9x:
Males 60%
Females 40%

At Night:
Males 60%
Females 40%

Stranger:
Males 70%
Females 30%

Some reason I felt compelled to make this, but unsure it helps...
Stab +, Night +, Stranger +: 25%
Stab -, Night +, Stranger +: 17%
Stab -, Night -, Stranger +: 11%
...
Stab -, Night -, Stranger -: 5%
____________________________________
100%

Now maybe repeat using this process, plus include your above number of percentages for attributes, or something like that??

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#### katxt

##### Member
This is one approach - Assume 100 M and 50 F perps and 10+ stabs, night and stranger all independent
From 100 M, we get 60% 10+, 80% night, 75% stranger = 100*60%*80%*75%= 36
From 50 F we get 20% 10+, 30% night, 35% stranger = 50*20%*30%*35% = 1.05 giving a total of 37.05 possibilities.
So males are 36/37.05 = 97.2% likely and females are 2.8% (This is effectively Bayes rule.)
Alternatively, quote the odds as 36 to 1.05