4 ms·

Under a standard bell curve, what percentile would a 20 year marriage be then?

by tus89 6y ago

exporectomy 6y ago
If it was normally distributed, it would be 100% - the percentile of a -12 year marriage. So it's surely very much not a normal distribution.
- dahart 6y ago
  Normal distributions are used all the time to model strictly positive phenomena. https://math.stackexchange.com/a/1335872 https://math.stackexchange.com/a/1335872
  - exporectomy 6y ago
    That's alright when the negative values are way off the end of the tail, but a 20 year marriage is way more common than a 3.4 meter tall woman (same distance from the mean as a 0 meter tall woman).
    - dahart 6y ago
      That the marriage distribution by age and the height distribution of women might have different decay rates is very unsurprising. That does not demonstrate that using a normal distribution to model either one is inadequate. In order to actually demonstrate that a Gaussian curve is not a good fit for the distribution of marriage lengths, you’d need to show that the falloff on both sides of the “mean” is asymmetric, or that there are multiple peaks, or that the falloff does not trend exponentially, etc. Even a truncated normal distribution might fit the distribution of marriage lengths adequately. Figure 5 in the more recent data shows the CDF of the distribution of marriage lengths: https://www.census.gov/prod/2011pubs/p70-125.pdf https://www.census.gov/prod/2011pubs/p70-125.pdf You can compare that CDF to plots of the CDF of a normal distribution: https://en.wikipedia.org/wiki/Cumulative_distribution_function#/media/File:Normal_Distribution_CDF.svg https://en.wikipedia.org/wiki/Cumulative_distribution_functi... If you can translate & scale any lines from either graph to roughly match, then you can use a normal distribution to roughly model marriage lengths. BTW, we are both being pedantic. The grandparent didn’t claim it was a bell curve, they asked what the standard deviation would be assuming it was normally distributed. That’s something we can calculate, regardless of how normally distributed the data actually is. It’s a strawman to say the answer won’t be exact because the question assumed it won’t be exact. Also, I do not think marriages are exactly normally distributed. We could calculate some stats about how close they are or how far away they are. There is a single lump shape to the distribution, but there’s also some asymmetry, and the distribution is truncated on the left. My point is just that the two reasons you’ve brought so far aren’t showing that marriage rates are not a bell curve, you need better reasons that are more specific to the shape of the data in order to make that conclusion.
mkl 6y ago
I don't see any reason to think it follows a bell curve; it has to be skewed way to the right, as it can't be negative. The question you're asking is more-or-less answered in eric4smith's link, on page 6. The answer depends on the year of marriage, and the data is from 2001, so for 20 years of marriage, it can only go up to 1980. The percentage of men whose marriage had lasted at least 20 or 25 years, by year of marriage, was: 20yrs 25yrs 1955 to 1959 76.2 72.3 1960 to 1964 66.1 62.3 1965 to 1969 62.1 58.0 1970 to 1974 55.8 52.9 1975 to 1979 58.4

Under a standard bell curve, what percentile would a 20 year marriage be then?

by tus89 6y ago

Under a standard bell curve, what percentile would a 20 year marriage be then?

If it was normally distributed, it would be 100% - the percentile of a -12 year marriage. So it's surely very much not a normal distribution.

dahart 6y ago
Normal distributions are used all the time to model strictly positive phenomena. https://math.stackexchange.com/a/1335872 https://math.stackexchange.com/a/1335872
- exporectomy 6y ago
  That's alright when the negative values are way off the end of the tail, but a 20 year marriage is way more common than a 3.4 meter tall woman (same distance from the mean as a 0 meter tall woman).
  - dahart 6y ago
    That the marriage distribution by age and the height distribution of women might have different decay rates is very unsurprising. That does not demonstrate that using a normal distribution to model either one is inadequate. In order to actually demonstrate that a Gaussian curve is not a good fit for the distribution of marriage lengths, you’d need to show that the falloff on both sides of the “mean” is asymmetric, or that there are multiple peaks, or that the falloff does not trend exponentially, etc. Even a truncated normal distribution might fit the distribution of marriage lengths adequately. Figure 5 in the more recent data shows the CDF of the distribution of marriage lengths: https://www.census.gov/prod/2011pubs/p70-125.pdf https://www.census.gov/prod/2011pubs/p70-125.pdf You can compare that CDF to plots of the CDF of a normal distribution: https://en.wikipedia.org/wiki/Cumulative_distribution_function#/media/File:Normal_Distribution_CDF.svg https://en.wikipedia.org/wiki/Cumulative_distribution_functi... If you can translate & scale any lines from either graph to roughly match, then you can use a normal distribution to roughly model marriage lengths. BTW, we are both being pedantic. The grandparent didn’t claim it was a bell curve, they asked what the standard deviation would be assuming it was normally distributed. That’s something we can calculate, regardless of how normally distributed the data actually is. It’s a strawman to say the answer won’t be exact because the question assumed it won’t be exact. Also, I do not think marriages are exactly normally distributed. We could calculate some stats about how close they are or how far away they are. There is a single lump shape to the distribution, but there’s also some asymmetry, and the distribution is truncated on the left. My point is just that the two reasons you’ve brought so far aren’t showing that marriage rates are not a bell curve, you need better reasons that are more specific to the shape of the data in order to make that conclusion.

mkl 6y ago

I don't see any reason to think it follows a bell curve; it has to be skewed way to the right, as it can't be negative. The question you're asking is more-or-less answered in eric4smith's link, on page 6. The answer depends on the year of marriage, and the data is from 2001, so for 20 years of marriage, it can only go up to 1980. The percentage of men whose marriage had lasted at least 20 or 25 years, by year of marriage, was: 20yrs 25yrs 1955 to 1959 76.2 72.3 1960 to 1964 66.1 62.3 1965 to 1969 62.1 58.0 1970 to 1974 55.8 52.9 1975 to 1979 58.4