Standard Error of Mean (S.E.M.)

· Source: http://www.dxy.cn/bbs/thread/6492633#6492633

6 Floor:

"As far as I know, the SD reaction is the variability of the observed value, which represents the average representation, while the SEM is standard error of mean, is the average sampling error, the average sampling accuracy, because the real value is not known, the accuracy of the statistical estimates can not be measured, But statistical methods can be used to measure accuracy. The error source of the test is systematic error and sampling error (random error), the system error is easy to overcome, the sampling error is caused by many uncontrollable internal and external factors, with contingency, even if it is very careful in the experiment, it is difficult to eliminate, but can be reduced by increasing the number of repetitions. For small samples with few repetitions (n≤30) with MEAN±S.E.M, repeat a large sample (n>30) with MEAN±SD. ”

· Wiki:https://en.wikipedia.org/wiki/standard_error

The standard error in the mean (SEM) is the standard deviation of the Sample-mean ' s estimate of a population mean. (It can also is viewed as the standard deviation of the The "error in the" The sample mean with respect to the true mean, since the Sample mean is an unbiased estimator.) SEM is usually estimated by the sample estimate of the population standard deviation (sample standard deviation) divided B Y the square root of the sample size (assuming statistical independence of the values in the sample):

where

s is the sample standard deviation (i.e., the sample-based estimate of the standard deviation of the Popu lation), and N is the

Size (number of observations) of the sample.

· Differentiate between "standard deviation" (Std deviation) and "Standard Errer" (Error)

Standard deviation: Measure the degree of dispersion of a group of numbers, standard error: Standard deviation of sample statistics, which is an indicator of the error of sample sampling.

Source: http://www.zhihu.com/question/21925923

Standard deviation is the difference between a set of values, which represents the degree of dispersion
Calculation formula:

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In simple terms, each number of a set of data is compared with the average of the data in that group, and the amount of data is discrete. For example, the class of male students are almost 1.75m tall, then we can say that the class of boys height standard difference is very small, because everyone is close to the average data is very concentrated. However, five Yao Ming, 10 Panchangjiang form a group, well, this height data is very discrete, uneven, standard deviation is very big ....

Standard error is the standard deviation of the sample statistic.
in reality, we do not know the general situation, always with the distribution of samples to infer the overall. For example, the cost of monthly meals for college students in China is how much. For this problem, we can not nationwide statistics of the major colleges and universities each student's food, so, we use the sample to infer the overall situation to obtain the data we need. For example, the extraction of China are east some of the college students to study the food. At this point, the standard error has been generated. It is an indicator that measures the error of sample sampling.

give another example to clarify the problem.
For example, overall is 1 2 3 4 5 6 7 8 9 10 The overall average is: 5.5
and A to the overall sampling, may get 5 8 3 2 average is 4.5
b Sampling, get 3 7 9 2 average 5.25
c Sampling, get 4 6 9 2 4 1 average of 4.3
ding ..... ................... Average is x
So, 4.5, 5.25, 4.3.........x make up a new distribution, which is a sample of the average distribution, then what is the standard deviation of this distribution? Using the formula, we can draw the standard deviation of this distribution, which is standard error. (Of course, the distribution of statistics has an average, standard deviation, variance, correlation coefficient and so on.) And here we have an average of chestnuts. )

If you know the overall standard deviation,
if, without knowing the overall standard deviation, the standard deviation of the sample is used, its unbiased estimation
in short, it is the standard deviation of the statistic (sample).

Standard Error of Mean (S.E.M.)