What is standard error: Definition and 23 Discussions

The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error of the mean (SEM).The sampling distribution of a mean is generated by repeated sampling from the same population and recording of the sample means obtained. This forms a distribution of different means, and this distribution has its own mean and variance. Mathematically, the variance of the sampling mean distribution obtained is equal to the variance of the population divided by the sample size. This is because as the sample size increases, sample means cluster more closely around the population mean.
Therefore, the relationship between the standard error of the mean and the standard deviation is such that, for a given sample size, the standard error of the mean equals the standard deviation divided by the square root of the sample size. In other words, the standard error of the mean is a measure of the dispersion of sample means around the population mean.
In regression analysis, the term "standard error" refers either to the square root of the reduced chi-squared statistic or the standard error for a particular regression coefficient (as used in, say, confidence intervals).

View More On Wikipedia.org
  1. A

    A Standard error of the coefficient of variation

    What is the standard error of the coefficient of variation in an exponential distribution?
  2. M

    How to interpret the Standard Error in this experiment?

    Does the S.E. of $38.72 mean, I sould expect to win or lose up to $77.4 (2x S.E), 95% of the time?
  3. I

    Standard deviation and standard error

    The mean of some data was 21.2°C, the standard deviation was 2, and the standard error was 0.8. My textbook says that using one standard deviation, we would report the temperature of the substance as 21.2 ± 2°C, while using the standard error, the temperature would be reported as 21.2 ± 0.8°C...
  4. Athenian

    Finding the Relative Uncertainty for the Standard Error of the Mean

    While I will not be showing the graph here, I am trying to dissect what the question even means. While I do understand that relative uncertainty can be found via the equation ##\frac{\sigma_A}{A}##, I do not understand how I can find the "relative uncertainty of SEM". Does anybody here have any...
  5. Vital

    I T-distribution, standard error - how to interpret

    Hello. Math is not my strongest part, yet, so I will be very grateful for your help and for giving the answer in sort of "plain" English, meaning that it will be great if you don't go too deep into the rabbit hole using difficult terminology, as these distribution issues are truly difficult for...
  6. Erenjaeger

    Please help, stuck -- Standard error in speed of sound wave....

    https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-xfa1/v/t34.0-12/13100972_1004336679646107_71786442_n.png?oh=c0e0ad9cf30125d301d2069c6402b621&oe=57222F24&__gda__=1461854936_dad2ac5d3bd3a844b9428cd47c7dc733 Not sure if this counts as "advanced physics homework" but can someone please help me...
  7. R

    How to calculate Standard Error for unequal sample sizes

    Gurus, can you help please? I've been given a set of samples, each has different sample size and mean (but not individual observations). I'm trying to figure out the population standard deviation so that I can estimate required sample size for certain confidence intervals. My question is how...
  8. U

    MHB OLS standard error that corrects for autocorrelation but not heteroskedasticity

    Question: By mapping the OLS regression into the GMM framework, write the formula for the standard error of the OLS regression coefficients that corrects for autocorrelation but *not* heteroskedasticity. Furthermore, show that in this case, the conventional standard errors are OK if the $x$'s...
  9. H

    Individual Measurement Uncertainty vs. Standard Error of Regression

    Let's say a student does a simple experiment where she conducts 10 trials at each x value (at each value of the independent variable). She collects data over 30 x values, giving her 300 total trials. For each of the 30 x values, she averages the 10 y values and she calculates the standard...
  10. M

    What is meant by standard error for linear and quaratic coefficients ?

    Dear Fellows, If we fit our data to a quadratic equation then What is meant by standard error for linear and quaratic coefficients ? I know that standard error is the standard deviation from the Sampling data. But for individual coefficients what is its interpretation ? Best Wishes Masood
  11. O

    Explain how do we get standard error.

    Homework Statement I know that standard error is to calculate how the sample deviate from the population. But standard deviation divide √n ,then will get it. And I don't understand why there is a T/n from the picture I uploaded. Please help Homework Equations Standard error x sqrt(n)...
  12. J

    Maybe a dumb question on standard error in equations

    Homework Statement I am using a value of change in y say 12.10 cm + or - .06cm. I am trying to find velocity using the formula v= sqrt(2*g*change in y) how do I evaluate this equation with my standard error? because I can't just add or subtract the .06cm after since I will have a...
  13. Z

    Calculating Standard Error of Mean for 2D Histogram Data

    Hey everyone, I'm not sure if there is an effective answer to my problem, but here goes: I am working on Ramachandran plots for short peptides (3 amino acids long). For every snapshot of the protein (this would be my data point) there are two angles being recorded, the phi and psi angles...
  14. L

    Statistics - Standard Deviation, Standard Error and Mean

    Hello, Just had a question regarding statistical analysis. I'm trying to calculate the average of 4 numbers from a data set of 6 numbers in excel without manually choosing to average only the 4 numbers. e.g. 85 20 32 45 27 3 (total mean = 35.3 desired mean = 31) 100 30 27 40 21 1...
  15. C

    Standard Error of Replicates, Each With Standard Error

    So I have a situation that I keep confusing myself with: I am running a computer simulation that, after a set number of iterations (a block) will output the running average (mean) of a property and the standard error based on the previous blocks. So, as the simulation runs, these standard...
  16. O

    Changing standard error to standard deviation.

    Hi all, I've done a regression and have the Standard Error of the X co-efficient (i.e. the slope). How do I change this figure to the standard deviation? Is the formula STD DEV = (STD ERROR)/(degrees of freedom)^0.5 Where degrees of freedom = N - number of X coefficients. ...
  17. H

    Calculating Average Error Uncertainty from a Large Set of Data

    Homework Statement Hi, I have this question that is bothering me. If I have a large set of data, each with its unique error uncertainty. How do I get the average error uncertainty from all the data points? Do I simply use the equation below: (∆ Z) ² = (∆A)² + (∆B)² And divide...
  18. G

    Calculating The Mean, Standard Error, and Standard Error of the Mean

    Hi, How do you calculate the Mean and standard error of a data set without having to crunch all the numbers? I have a set of data with 45 entries and numbers in the tens of thousands and was wondering if there was a way to calculate these without have to punch hundreds of number into a...
  19. A

    Standard error for marginal effect in regression?

    Hi, I have a regular OLS regression that includes a variable both by itself and squared (i.e. y=b0+b1*x+b2*x^2). I am interested in the marginal effect of the variable at the mean. I know how to get the point estimate, but does anyone know how to get standard errors for the marginal effect...
  20. N

    Understanding Standard Error for All Amigos

    Hello my hard rocking amigos!:smile: I have a question about standard error. If I had a single sample, I could infer the population mean by using the sample standard deviation (n-1 version of s.d.), and then dividing this by the square root of the sample size to get the standard error, which...
  21. V

    Calculating Standard Error for Sample Size

    hi, just wondering if there different ways to calculate the standard error for large and small sample size and if its so wats the formula we use? please give me a hand, hope this question makes sense. cheers
  22. N

    Calculating Average Wave Speed and Standard Error

    [SOLVED] Standard error Homework Statement A student determined the following values for the wave speed; calculate the average value of the wave speed and its standard error 50.8, 50.6, 51.8, 52.0, 50.9, 51.6, 51.3, 51.5 Homework Equations avg wave speed = 51.3 The Attempt at a...
  23. M

    Having trouble with Standard Error of the Mean

    Question 8 - From your results above, which would be the best estimate of the true mean height (170.18cm) of the population of Bioinformatics students? Explain! I am having a little trouble on this question and what exactly is it. It is asking me for which would be the best estimate of...