Estimating variance with limited data?


Hello,

I am a real beginner in stats, so sorry for the potentially naïev
question (and badterminology)!

I have a series of 'experiments' each with a few observations within the
range of discreet values...

experiment A, results 1, 2, 1, 4, 3, 1, 4
experiment B, results 5, 2, 4, 4, 3, 6, 4, 5, 6, 7
experiment C, results 1, 9, 3, 4

Each 'experiment' has a ranking, and when I plot the mean value for each
set of results for each experiment, I think I can see a clear trend.

What I think I want to do is to estimate the variance of the results in
each experiment, so I can see what trends 'fit' the data. I think if I
give each point (mean) some error bars, I can see if my trend is supported
or not.


I used bootstrapping to estimate the variance of the mean value for each
experiment. However, I have a problem, some experiments have results that
only take one value. How do I estimate the variance in these cases?

I want to do that to match my intuition that

experiment X, results 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1


has less variance than

experiment Y, results 1, 1, 1, 1, 1


How should I present the data, given that I want to show an average value
with a variance?

I think perhaps I can do something tricky like add the mean value for the
whole results set to each experiment and recalculate the estimated
variance, but can I do that?


If it helps I can send my real data.

Thanks for any clues for how to advance my analysis,

All the best,
Dan.

.

Relevant Pages

  • Re: Estimating variance with limited data?
    ... >> I am a real beginner in stats, so sorry for the potentially naïev ... >> I used bootstrapping to estimate the variance of the mean value for each ... >zero for X is smaller than the p-value of the zero for Y, ... >X-variance being lower than the upper limit of the Y-variance. ...
    (sci.stat.edu)
  • Re: Estimating variance with limited data?
    ... Dan Bolser wrote: ... > I am a real beginner in stats, so sorry for the potentially naïev ... > I used bootstrapping to estimate the variance of the mean value for each ... Both X and Y have exactly the same variance -- zero. ...
    (sci.stat.edu)
  • Re: test for trend
    ... > population on yearly basis and I want to test for a trend in my data. ... > I have plotted my estimates and done a simple regression and plotted ... > the same unknown variance. ... Depending on how long a time series you have, you might want to fit a time series model instead. ...
    (sci.stat.math)
  • Re: Need Advice on a Simple Stat Question
    ... I'm using VB to raise a warning if there is a significant difference ... If you are also assuming that the observations from the first 30 days have identical distributions (across days -- that implies mean as well as variance are stationary) and that the last two days are identical to each other, the a two-sample t-test should suffice. ... If, say, there is trend during the first 30 days and you think a jump occurred during the last two, or the trend changed meaningful, you would need to use something a bit more complicated. ...
    (sci.stat.math)