I am planing to report my data as Mean plus or minus contingencies. I know standard deviations are the ones that are most commonly used. But I have standard errors instead from a JMP analysis. Can I use Standard Errors in stead of deviations with my means? Thank you!
standard error is the standard deviation of sample means. i.e the deviation of the sample means from the population mean. while standard deviation is the deviation of the mean from the observed values. you can use the standard error if your data is samples from the same population.
These two mathematical concepts are not the same
Standard deviation (SD) This describes the spread of values in the sample. The sample standard deviation, s, is a random quantity -- it varies from sample to sample -- but it stays the same on average when the sample size increases.
Standard error of the mean (SE) This is the standard deviation of the sample mean, xBar, and describes its accuracy as an estimate of the population mean, mu. When the sample size increases, the estimator is based on more information and becomes more accurate, so its standard error decreases.
Tadesse -
I will basically agree with the above definitions.
The standard deviation of a population is estimated by the standard deviation of a sample, and that population distribution is described by various statistics in addition to the mean and standard deviation. There are shape parameters to consider. But the distribution of possible estimated sample means, with a larger sample size, becomes closer and closer to a "normal" distribution, as well as having smaller variance, with a larger sample size.
That is, if you are looking at the distribution of estimated mean values that could have been obtained by repeated sampling, that distribution has a smaller variability with a larger sample size for the one sample that you did collect. (The Central Limit Theorem explains this. It also explains that the distribution shape for those hypothetically estimated mean values becomes closer to a "normal" distribution with a larger actual sample.)
When estimating sample size needs, it is important to have some guess as to a population's standard deviation (an estimate of a fixed value), to then estimate a standard deviation of a mean, which is then called an estimated standard error, because you often want to sample until you can say you have a desired level of accuracy for the estimated mean. Confidence intervals (or in regression, 'prediction' intervals) can then be made. (Bias can be another concern.)
So to answer your question, is to know whether you want to present the estimated mean and estimated standard deviation of a population (estimates of particular values for a given population), or do you want to present the estimated mean of a population, and the estimated standard error of that mean.
So what are you trying to present? If your project goal is to describe a population, you likely want an estimated mean of the population, an estimated standard deviation of the population, and perhaps estimates of skewness and kurtosis, and/or ideas for the general type of distribution: gamma, beta, cauchy, whatever. A graph of the distribution would be nice. - However, if you are trying to describe the parameter, mean of the population, then you want the estimated mean, and the estimated standard error of that mean.
So think about the goal of the experiment. I think that usually you want to know the mean, so you estimate the mean and estimate the standard error of the mean, and that standard error gets smaller with increased (good) information.
Best wishes - Jim
I did not read above comments wholly, but I can say that if your aim is to describe the sample you have then you could use standard deviation. But if you wish to talk about the underlying population then you can use standard error.
To simply answer your question, yes, they are similar in that they both estimate variation. The standard deviation (SD) is an estimate of the variability in the population from which you sampled. The standard error (SE or SEM) is an estimate of variability in the theoretical population of means. The SD is useful in describing the variability of sampled data assuming normality. Are your data normally distributed? The SE is used to calculated confidence intervals (CI) and differences between means (again assuming normality).
Your never mentioned the sample size or the type of analysis. This is crucial information. If the sample sizes are small (n
In my view there is a bit difference between the two,the standard deviation is a measure of the dispersion, or scatter, of the data. In contrast, the standard error provides an estimate of the precision of a parameter (such as a mean, proportion, odds ratio, survival probability, etc) and is used when one wants to make inferences about data from a sample (eg, the sort of sample in a given study) to some relevant population. When the standard error relates to a mean it is called the standard error of the mean; otherwise only the term standard error is used. We can take the sample mean as our best estimate of what is true in that relevant population but we know that if we collect data on another sample, the mean will vary according to what is called the “sampling distribution.” Ideally we would like to have a measure of the uncertainty surrounding our estimate.
Dear
The standard deviation (often SD) is a measure of variability. When we calculate the standard deviation of a sample, we are using it as an estimate of the variability of the population from which the sample was drawn.The standard error of the sample mean depends on both the standard deviation and the sample size, by the simple relation SE = SD/√(sample size).
Regards
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