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.)
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.)