It is a great idea to test a hypothesis experimentally. I did your experiment too, and the result is:
hours in a day: when I saw your post it was 1 AM in the morning, estimating 2 hours in a day. ❌
months in a year: I’m born in Juni, so twelve months. ✅ Though, we could also have taken the current month as a base and then it would have been 8 months.
Earth size: I don’t know latitude but probably like yours—I’m in Hamburg. ✅ But I do know that the longitude here is pretty exactly 10. If I go by that the circumference should be 20 - instead of 360. ❌
human life expectancy: I’m 51. ✅
Several experiments show that I can extract useful information just by treating myself as a random sample, and thus a view that I can’t use myself as a random sample is false.
I think there are some problems here. I think be more accurate claim would be:
You can do experiments that extract useful information about whether you can treat yourself as a random sample (i.e., a representative or “typical” sample) by comparing the result of the experiment to the baserate.
Or at the very least, based on my experiments, for me, the claim seems to be false. I’m not representative enough. But I can’t know that without comparing my results to a baserate. I can’t use the observations to establish a baserate or make estimations such as expected lifetime.
From a statistical perspective, a random sample means:
Drawn randomly from the population of interest—but you are not randomly selected.
Having an equal and independent chance of being selected—but you are subject to bias.
The sample size is sufficient to capture variance—but you are n=1, thus variance is undefined.
You may not be representative in any observable or unobservable dimension for your purpose. And to know if you are representative, you have to look at other samples and then you are back so some kind of baserate.
Using oneself as a random sample is a very rough way to get an idea about what order of magnitude some variable is. If you determine that the day duration is 2 hours, it is still useful information as you know almost for sure now that it is not 1 millisecond or 10 years. (And if I perform 10 experiments like this, one on average will be an order of magnitude off). We can also adjust the experiment by taking into account that people are sleeping at night, so they read LW only during the day, evening, or early morning. So times above 12 or below 2 are more likely.
You are right that the point of the experiments here is not to learn the real time of the day, but to prove that I can treat myself as a random sample in general and after that use this idea in domains where I do not have any information.
I think the basis to treat myself as a random sample is the following:
I am (or better to say my properties are) randomly selected from the LW-readers population.
There is some bias in that selection but I assume that it is not large and I still can get the order of magnitude right even if I do not calculate the exact bias.
The sample size is sufficient if I want to learn the order of magnitude of some variable or if the difference between two hypotheses is sufficiently large. (If I take only one ball from a vase with 1000 balls, of which only one is green and 999 red, or from an alternative vase with 999 green and one red, I can identify the vase with high credence.)
It is a great idea to test a hypothesis experimentally. I did your experiment too, and the result is:
hours in a day: when I saw your post it was 1 AM in the morning, estimating 2 hours in a day. ❌
months in a year: I’m born in Juni, so twelve months. ✅ Though, we could also have taken the current month as a base and then it would have been 8 months.
Earth size: I don’t know latitude but probably like yours—I’m in Hamburg. ✅ But I do know that the longitude here is pretty exactly 10. If I go by that the circumference should be 20 - instead of 360. ❌
human life expectancy: I’m 51. ✅
I think there are some problems here. I think be more accurate claim would be:
Or at the very least, based on my experiments, for me, the claim seems to be false. I’m not representative enough. But I can’t know that without comparing my results to a baserate. I can’t use the observations to establish a baserate or make estimations such as expected lifetime.
From a statistical perspective, a random sample means:
Drawn randomly from the population of interest—but you are not randomly selected.
Having an equal and independent chance of being selected—but you are subject to bias.
The sample size is sufficient to capture variance—but you are n=1, thus variance is undefined.
You may not be representative in any observable or unobservable dimension for your purpose. And to know if you are representative, you have to look at other samples and then you are back so some kind of baserate.
Using oneself as a random sample is a very rough way to get an idea about what order of magnitude some variable is. If you determine that the day duration is 2 hours, it is still useful information as you know almost for sure now that it is not 1 millisecond or 10 years. (And if I perform 10 experiments like this, one on average will be an order of magnitude off). We can also adjust the experiment by taking into account that people are sleeping at night, so they read LW only during the day, evening, or early morning. So times above 12 or below 2 are more likely.
You are right that the point of the experiments here is not to learn the real time of the day, but to prove that I can treat myself as a random sample in general and after that use this idea in domains where I do not have any information.
I think the basis to treat myself as a random sample is the following:
I am (or better to say my properties are) randomly selected from the LW-readers population.
There is some bias in that selection but I assume that it is not large and I still can get the order of magnitude right even if I do not calculate the exact bias.
The sample size is sufficient if I want to learn the order of magnitude of some variable or if the difference between two hypotheses is sufficiently large. (If I take only one ball from a vase with 1000 balls, of which only one is green and 999 red, or from an alternative vase with 999 green and one red, I can identify the vase with high credence.)