Mokhtar -

I am not clear on your question. Are you saying that you need to judge a sample size to take, or are you saying you have a random sample and you want to know how good the results are for estimation of mean or total for a given variable? Do you have continuous data? To give you relevant answers, more details of your application are likely required.

As for statistical 'significance,' that is one of statistics most misleading terms that many practitioners and statisticians overuse and misuse very frequently. (Please see the link below.)

I think that whatever your question might be here, it is likely to best be answered using something to do with a standard error. If you are not already familiar with these terms, you could start with an Internet search of these terms: variance, standard deviation, standard error, bias, mean square error, sampling error, nonsampling error (such as measurement error), and depending on your application you might also want to search for ignorable nonresponse (which is not really "ignorable" at all), and nonignorable nonresponse.

Cheers - Jim

PS -  You could also look up (search on the Internet for) continuous data, and confidence intervals.  A confidence interval is technically a little complicated to interpret, but from a practical point of view, it is not really misleading and can be very straightforwardly helpful.   

Article Practical Interpretation of Hypothesis Tests - letter to the...

Hello Jim,

By measuring the length of incisors of sheep, I find that there are wide variations (from 11 to 22mm). Then, I should like to know if there is a statistical interpretation to this question, particularly knowing that the sheep with short incisors are the most desired.

Thanks a lot,

Mokhtar

Hi. - You might want to know about a specific group of sheep, say all the sheep in a certain district, and take a random sample. If it is a smaller group of sheep, you may be able to obtain a census, but if you try to collect too much, then your data quality may suffer in the form of more measurement error.

You could do descriptive statistics on whatever data you have, but be sure to note what group you are representing and how you collected the data.

A good sampling book would be Cochran, W.G.(1977), Sampling Techniques, 3rd ed., John Wiley & Sons. You could consult the first few chapters. Or perhaps this would help:

Applied Survey Sampling, 2015, Edward Blair and Johnny Blair, Sage Publications, Inc.

But first you need to be sure you understand descriptive statistics. There should be a great deal online about that. Beware of errors/typos though. Checking multiple sources should help.

You could start with some descriptive statistics to get a sample (or census) distribution. Plotting your points in a histogram may help see if the data have more than one mode ("peak" in the graph), which might indicate you have two or more distinct things going on. Best to try more than one histogram as it can make a big difference as to how you break up your 'bins,' such that some people really do not like them. I think it a good idea to try different kinds if graphs, including histograms perhaps, to learn more about your data.

Likely it is just a one-mode, perhaps somewhat symmetric distribution. You may not be able to assume normality for the standard deviation, but you likely can for the standard error of the mean, and obtain a confidence interval around that mean.

You could compare groups of sheep that way.

You could possibly do a scatterplot of incisor length as a function of some other continuous variable, and perhaps a regression with estimates of variance of the prediction error. (FYI, the square root of the estimated variance of the prediction error in SAS PROC REG is STDI.)

Anyway, I think you want to start with graphs and descriptive statistics.

Cheers - Jim

Mokhtar -

You said that a smaller incisor is more sought after?

Suppose you wanted to know what proportion of sheep in a given group/population/sub population had incisors of a given length or less. Call that p. then q could be the proportion with longer incisors. Thus p+q = 1. You could do a random sample and get an estimate and a standard error for p. There is information on that on the Internet and survey statistics books. (See "proportions.") You can find calculators for determining sample size needs on the Internet, but they will assume the worst case of p = q = 1/2 in an infinite population. That may well overestimate the sample size you need.

Jim

Salam,

Thanks Jim,

Indeed I have followed the steps that you have described for sampling (breed,district, age), and I will do as you indicated for analyses.

Thank you for pertinent clarification.