Number of Arrests: Bob arrested 4 times in 11 mo's; Sally arrested 2 times in 19 mo's

[Kreya]

Hi,

Trying to figure out what I think is a simple problem but my math skills are rusty and I need some help .

Bob was arrested 4 times in 11 months. Sally was arrested 2 times in 19 months. Is there a way to calculate/estimate how many times they will each be arrested in a total of 24 months?

 

[JeffM]

Hi,

Trying to figure out what I think is a simple problem but my math skills are rusty and I need some help .

Bob was arrested 4 times in 11 months. Sally was arrested 2 times in 19 months. Is there a way to calculate/estimate how many times they will each be arrested in a total of 24 months?

Yes, but it is not a statistically robust estimate.

Arrests per month for Bob\(\displaystyle = \dfrac{4}{11} \approx 0.36.\)

Expected number of arrests for Bob over 24 months = \(\displaystyle 24 * \dfrac{4}{11} \approx 9.\)

You give it a try for Sally.

 

[Kreya]

Makes sense - thank you! So, for Sally, ((2/19)*24) = 2.526.... or 3

Yes, I figured this is a rough estimate that has some flaws... do you have any suggestions as to how I could get to a more robust estimate in the future? If I had the count broken down month by month or something like that?

 

[JeffM]

Makes sense - thank you! So, for Sally, ((2/19)*24) = 2.526.... or 3 You got it.

Yes, I figured this is a rough estimate that has some flaws... do you have any suggestions as to how I could get to a more robust estimate in the future? If I had the count broken down month by month or something like that?

The problem here is twofold.

Predictive statistics work best with large data sets gathered under relatively stable conditions. Bob is a single individual. If Bob is 23 years old and you had data for all 23 years of his life, that would be a lot of data, but his situation would not have been stable. It is unlikely that he was arrested at all while he was under 10 years of age. Moreover, if he keeps getting arrested approximately every 3 months, he is going to be spending all sorts of time in jail, where his arrest statistics will necessarily drop.

Lesson to learn: there are a lot of statistics out there that are worthless for predictive purposes. The data may have been gathered with great care, and the computations may have been done perfectly, but the results have little predictive value. Quantitative data are superior to qualitative data only in certain special circumstances.

If I were asked to think quantitatively about Bob's future, I'd be gathering data about a large group of men with frequent arrests in a short period of time and distinguishing between those who were incarcerated and those who were not. It is a lot easier, however, to think about him individually in a qualitative way: unless he changes his ways, he is probably going to be incarcerated in the not too distant future.

 

[Kreya]

The problem here is twofold.

Predictive statistics work best with large data sets gathered under relatively stable conditions. Bob is a single individual. If Bob is 23 years old and you had data for all 23 years of his life, that would be a lot of data, but his situation would not have been stable. It is unlikely that he was arrested at all while he was under 10 years of age. Moreover, if he keeps getting arrested approximately every 3 months, he is going to be spending all sorts of time in jail, where his arrest statistics will necessarily drop.

Lesson to learn: there are a lot of statistics out there that are worthless for predictive purposes. The data may have been gathered with great care, and the computations may have been done perfectly, but the results have little predictive value. Quantitative data are superior to qualitative data only in certain special circumstances.

If I were asked to think quantitatively about Bob's future, I'd be gathering data about a large group of men with frequent arrests in a short period of time and distinguishing between those who were incarcerated and those who were not. It is a lot easier, however, to think about him individually in a qualitative way: unless he changes his ways, he is probably going to be incarcerated in the not too distant future.

Thanks Jeff! I appreciate you taking the time to teach me and also for providing me with a detailed response!