In the sampling survey, the general average is often inferred from the sample average. Sample standard deviation is suitable for data with normal or near-normal distribution. It is a statistic that mainly describes the degree of variation between the mean values of multiple homogeneous samples with the same sample size in small sample test. That is, if the same experiment is repeated many times, the degree of change between them is used. Obviously, the smaller it is, the smaller and more stable the variation of the sample average is, and the more reliable it is to estimate the overall average with the sample average. Therefore, in order to illustrate its stability, reliability or compare several groups of data (which is the most common in scientific research papers), descriptive data should be used. In practical application, it should be written as "mean standard error" or expressed as "Mean SE" in English.
2. Standard deviation can also be used for interval estimation and point estimation (confidence interval) of population average.
According to the principle of normal distribution, the average sample? There is a standard error? The combination can also give the confidence interval estimation of the normal population average, that is, infer the confidence interval of the population average, such as the commonly used "average T 0.05 (n- 1) * standard deviation"? (where t0.05 (n- 1) is the t-bound value with a sample size of n) represents the 95% confidence interval of the overall average, which means that the overall average is within a given range with 95% confidence.
3. Standard deviation can also be used to test the significance between averages, so as to judge whether the difference between averages is caused by sampling error.
For example, the 1000-grain weight of a local wheat variety =34 grams, and now a new variety is introduced from other places. The average 1000-grain weight was 35.2 grams through multi-point field experiments. Is there any significant difference in 1000-grain weight between newly introduced varieties and local varieties?
Whether there is a significant difference in 1000-grain weight between newly introduced varieties and local improved varieties is essentially to judge whether the difference between and is caused by field test or sampling error, so it is necessary to carry out significance test. T test is used here, so it is considered that the difference in 1000-grain weight between newly introduced varieties and local improved varieties is caused by sampling error, so there is no significant difference between them. Therefore, it is necessary to use the significance test between means.