So you fuzz your data into the error ranges, e.g. your datum says 1500AD with
standard age error of 150 years, so you write 1000 records into the range 1350AD - 1650AD — taa daa, your data now includes the standard error.
Not exact matches
Mean and
standard errors of monthly weight gain after adjusting for maternal
age; race / ethnicity; education; household income; marital status; parity; postpartum Special Supplemental Nutrition Program for Women, Infants, and Children program participation; prepregnancy body mass index (calculated as weight in kilograms divided by height in meters squared); infant sex; gestational
age; birth weight;
age at solid food introduction; and sweet drinks consumption.
By taking the
age of patients» blood cells into account, the researchers» model, when tested in more than 200 diabetic patients, reduced the
error rate from one in three patients with the
standard blood test to an
error rate of one in 10.
Fig. 2 Median
age (and
standard error) at reported diagnosis for genetic conditions and vehicular injury for intact (dark bars) and neutered (light bars) females (a) and males (b).
The distribution for the measurement of carbon - 14
age has (we're assuming) the same
standard deviation for every calendar year, so it's always that case that we get some particular carbon - 14 measurement that was «unlikely», since any particular value for the measurement
error is unlikely.
take a horizontal ruler on fig1 and put it half a
standard deviation of the measurement
error (50y) higher up than the C14
age mean (the maximum of the red curve).
P (Obs calendar -
age = y) does not change much when y changes by a small amount, small enough that the carbon - 14
age changes by much less than the
standard deviation of the measurement
error.
This integral is over the same region for any hypothesized calendar
age, and therefore can be ignored when the amount of rounding is small compared to the
standard deviation of the
error.
If the measurement for carbon - 14
age has Gaussian
error with
standard deviation 100 (as seems about right for Nic's Fig. 2), and the measurement is rounded to one decimal place, and the calibration curve maps calendar
age 750 to carbon - 14
age 1000, then the probability of the observation being 1000.0 given that the calendar
age is 750 is 0.1 (for one decimal place) times the probability density at 1000 of a Gaussian distribution with mean 1000 and
standard deviation 100, which works out to 0.0004.
The
age profile is very similar to that I've already posted only with narrower
standard errors.
As well, since different numbers of trees contribute at different
ages, both the raw averages and the standardized averages (by subtracting the number one and then dividing by the
standard error) were calculated.
The volatility is just a reflection of the fact that there aren't many such trees — this is reflected in the width of the
standard errors through this portion of the
age curve.
Standard errors blow out massively from that point on and the point estimate for
age ~ 400 is (approximately) zero in any case.
How easy is it to report
standard errors around your LOESS
age function?
Suppose I generate a graph of the
age and year coefficients with
standard error bands (it's quickest if I do this in Excel of all things)-- how do I post it here?
Then, we conducted sensitivity analysis comparing the mean scale scores across
age and gender among the complete cases, all of the available cases, and the imputed cases (coefficients and
standard errors from 5 data sets were adjusted for the variability between imputations according to Rubin's rule).