Dear Colleagues,
For environmental monitoring and water quality data analysis, what are the possible statistical mistakes can happen?
Yes, definitely the standard deviation can be higher than the mean, because they measure different things (location and spread, and spread may be larger than the location value). As for the second question, it is very general: all kinds of mistakes can happen, from wrong sampling method to wrong interpretation of an inferential test correctly applied.
Of course! as mentioned in the earlier answer! Your mean is the mid point of your data values and standard deviation is a measure of the deviation in those values. the two are completely different from each other one is the measure of central tendency other measures variability.
Easy, I am sampling from a Gaussian distribution that I know is Standard Normal (mean=0, sd=1). I take three values from this distribution. I manage to get two values that are within 1 sd of the mean and one value that is 14 sd from the mean. I calculate the sample mean and standard deviation and find sd>mean in my sample. Since we mostly do not know the true mean and standard deviation, we will never know that we have by chance found an unusual observation.
Someone else tries to repeat my experiment and will (probably) get a different result.
The problem diminishes as sample size increases but never goes away. I could take 100 values and 68% could be within 1 standard deviation of the mean. I could also get one value that was 30+ standard deviations from the mean. The chance that this happens is low. To reliably find values so extreme should take many thousands of values, but there is always the chance of finding them with fewer samples.
There are also times when some process is highly variable and the standard deviation will naturally be larger than the mean.
Here are four sets of four numbers each and showing mean and standard deviation.
(20, 24, 27, 45) mean=29 sd=11.05
(1, 10, 14, 91) mean=29 sd=41.70: an extreme value
(1, 2, 44, 45) mean=29 sd=24.83: values shifted to the "tails" or possibly bimodal.
(-2, 24, 27, 67) mean=29 sd=28.48: tails moved further out, the two middle values remained the same as original set of values.
- Badges
- Science topic