Which stats test to use in this situation

[TrpnBils]

This is a two-fold statistical thing I want to pursue and I'm unsure of which test(s) to use. Using data of gender and age at time of death from a large, old cemetery in town I want to compare two things:

1. Average life expectancy of citizens of our town compared to the national average
2. Whether there is a noticeable difference in life expectancy after the development of major vaccines over the past 100 years.

I'm figuring I will lump ages into groups of 5 years (died at ages 0-5, 6-10, etc) so there will be multiple groups, not including separation of genders.

Thoughts?

 

[mfb]

To get the current life expectancy, I think you will need data about recent deaths, together with the age distribution* in your town.
You also need the assumption (or data) that "gets buried at the cemetery" is independent of the age at time of death.

2. Whether there is a noticeable difference in life expectancy after the development of major vaccines over the past 100 years.

Same issue, and there it is even harder to get the age distribution in the living population. It might be a reasonable assumption that moves in/out of town are independent of the age*, in that case you can just count how frequent different ages are.* a simple example why this is relevant: imagine a small town with a big old people's home. Many old people will move to that town and die there. Does this mean that all inhabitants there reach that age? Of course not.

 

[TrpnBils]

So is it even possible then to compare something like the average life expectancy of a male born in my town in 1930 to the national average for males in that year?

It doesn't seem like that should be that difficult

 

[mfb]

It is possible, but it is not easy. It is not sufficient to count gravestones for deaths in 1930 (or any other year).

 

[blue_raver22]

For the first question, comparing the average life expectancy of citizens in your town to the national average, you could use a two-sample t-test or a one-way ANOVA. This will allow you to determine if there is a significant difference between the two groups.

For the second question, whether there is a noticeable difference in life expectancy after the development of major vaccines, you could use a two-sample t-test or a one-way ANOVA as well. However, since you are planning to group the ages into 5-year intervals, you may also want to consider using a Chi-square test to compare the proportions of individuals who lived past a certain age (e.g. 80 years old) before and after the development of vaccines.

Overall, it is important to consider the assumptions and limitations of each statistical test and choose the most appropriate one based on your specific research question and data. It may also be helpful to consult with a statistician or conduct a power analysis to determine the appropriate sample size for your study.