Covering all sciences: Economics, biology, engineering, etc... there is no value that is "high." In one application I might expect a standard deviation that is close to zero no matter what the mean is. I am looking at retention time of a chemical on a chromatography column within the limits of that columns capacity. I expect that the deviation in retention time will have almost no variability. This is in contrast to I am looking at the reproductive rate of a small fish in the lower Mississippi delta over 5 years. Here, I might be lucky if my standard deviation is less than five times my mean.

What I would be more concerned about is whether a sample size of 4 is capable of accurately estimating a standard deviation.

5% is reasonable. but if you are forecasting share prices or currency you need it in still smaller decimals for greater accuracy. (the stocks with lesser standard deviations always posted lesser margins!!) In the case of behavioral, scale data you may just present it in relative terms rather than considering it on absolute terms

if the SD is more then ONE THIRD OF Arithmetic mean then it is considered high

Covering all sciences: Economics, biology, engineering, etc... there is no value that is "high." In one application I might expect a standard deviation that is close to zero no matter what the mean is. I am looking at retention time of a chemical on a chromatography column within the limits of that columns capacity. I expect that the deviation in retention time will have almost no variability. This is in contrast to I am looking at the reproductive rate of a small fish in the lower Mississippi delta over 5 years. Here, I might be lucky if my standard deviation is less than five times my mean.

What I would be more concerned about is whether a sample size of 4 is capable of accurately estimating a standard deviation.

If your model has normal distribution, there is no relationship between mean an SD. Greater SD means you will need a lager sample size to find significance. However, if your model assumes normal distribution, you can consider the 68 - 95 - 99.7% rule, which means that 68% of the sample should be within one SD of the mean, 95% within 2 SD and 99,7% within 3 SD. The most import is that to make sure if your model fits your data, not if the variance is high or low.

Dear Mathilde

When you deal with means, it is preferred to use standard error S.E. ( standard deviation of the means ) because it takes the sample size consideration in the account. 

S.E. = SD/ square root of sample size 

Good Luck

I would suggest using SD, not SE. One problem is that there are two definitions for SE. The first is as Khalid states, the second is as an estimated value that goes with least squared means. I simply do not trust that everyone keeps the definitions straight. In general SE is a value that is unique to each manuscript. As such, it is less useful. SE is great if you are trying to prevent other scientist from recovering your data for use in future research. Of course this issue is mostly irrelevant if the raw data are provided with the manuscript.

Regardless of your choice, be sure to provide your sample size. This is the actual sample size, not the planned sample size. So you set out 10 plots for each of ten treatments. If flooding ruins three plots, then I need to be able to figure out which treatments are missing replicates. If replicates are deleted for other reasons, I need to be able to figure out what has been removed.

Like Prof. Timothy wrote, standard deviation by itself it is not high or low. Standard deviation is an estimator of variance and you need to compare with your media. If you have n responses (for a basic statistic model, that is, the n responses are replicates of the same situation), you can calculate the media (ym) and standard deviation (s). Your standard deviation is fundamental for to declare your results as significant: You must calculate

T=ym/(sqrt(s^2/n))

If your T is greater than t-student at 97.5% (0.025 tail) with (n-1) degrees of freedom your results are significant at 5% (p

it is more of a judgement based on the purpose, so the subject under consideration matters whether it is rocket launching are students evaluation. Unnecessarily we mine too much in this.  It is like for an ordinary bowler, person use reaction needed for a  bouncer, in swinger, out swinger, leg break off break, yarker....finally get bowled by a straight ball.

Many thanks to you all for the answers. Anyway, I think my samples are too small to be statistically reliable so I will just stick with the means. 

Kind regards, 

Mathilde Callari

That is alright.but biased judgement will be there

Well, in comparing different groups' sample means by eyeballing, I'd also suggest doing that for SD, as similar groups should be comparable for both statistics. Or one could show the group ranges instead of SD.

-Bob

I am also more concerned about whether a sample size of 4 (or 9) is capable of accurately estimating a standard deviation. In this case, It could be better to show the group ranges.

Initially I wanted to apply a two sample t-test but my samples were way too small to be statistically reliable (none but two of the comparisons showed a significant difference statistically).  I ultimately decided to work with the means and the group ranges, which should give the least biased judgement possible, I think.. 

2.0% RSD is common for assay quantitation  in pharmaceuticals and biopharmaceuticals.  5.0% RSD is used for low concentration (~ug/mL) related substances.  The statistical LOQ has a 10.0% RSD.  See the requirements in USP section .

when the data concentration of mean ± SD way far than %68 (due to the empirical rule), the standard deviation is high. As we realised this, we developed a new approach for "deviation" which is less sensitive to skewness rather than standard deviation

Article TO DETERMINE SKEWNESS, MEAN AND DEVIATION WITH A NEW APPROAC...

Hi,

I suggest to present it as COV or  Relative SD with respect to its mean, to standardize your Sds. You could set limits to +/- 5% which is normally used.  If you are dealing with analytical data, you can use the AOAC Methods Limits Table for the % RSD.