### Statistics error

The dual dimension of error statistics is philosophy and methodology. It is a perspective that includes both a group of statistical tools and their interpretation and justification. A general philosophy of science and the role of probability in inductive inference also refers to it. Comparing error statistical approaches to other philosophies in statistics requires an understanding of the intricate interconnections between philosophical and methodological dimensions. This chapter is about error statistical philosophy. It examines the interplay of the philosophical, methodological and statistical issues to clarify long-standing conceptual, technical and epistemological disputes surrounding both dimensions. The standard explanations of statistical methods only focus on the formal mathematical tools, without considering the general philosophy of science and induction that these tools are best suited for. This chapter also addresses statistical methods for testing and estimation, while simultaneously highlighting common misunderstandings.

**Sampling Error**

Sampling error is the difference between an estimate from a sample survey, and the “true” value that would be obtained if all the survey population was enumerated. Although it is possible to measure it from the population values (which are not known, otherwise there would be no need to survey), it can also been estimated from the sample data. When publishing survey results, it is important to account for sampling statistics error. This gives an indication about the accuracy of the estimate, and therefore the importance that can go into interpretations. Sampling error can be measured accurately if the principles of sampling are used within the limitations of available resources.

**Factors Affecting Sampling statistics error**

There are many factors that can affect sampling error, including sample size, sample design, and variability within the population. Although a decrease in sampling error in statistics is generally associated with larger sample sizes, it does not necessarily correlate. To reduce the sampling error by half, increase the sample size fourfold. The sampling fraction, which is the percentage of the population included in the sample, has a lesser impact. However, as the sample size increases relative to the population, the sampling error should decrease.

Sampling error is also affected by population variability. Higher errors are caused by more variable populations. The estimates or samples that were calculated from different samples will have greater variability. To reduce the effect of variability in the population, you can increase the sample size to make the sample more representative of the actual population. There are many sample design options that can affect the size and shape of the sampling error. The size of the sampling error can be reduced by stratification, while cluster sampling can increase it. (These designs are discussed in Sample Design ).

**Standard Error**

The standard error (SE) is the most common measure of sampling statistics error. The standard error measures the spread of estimates within the “true value”. The standard error is a measure of the spread of estimates around the “true value”. In practice, there is only one estimate, so it cannot be directly calculated. If the population variance is known, the standard error can still be calculated mathematically. The variance of the sample units can be used to estimate the standard error even if the population variance cannot be determined. A probability-based sample survey will produce an estimate with a standard error. This is known as the standard error of estimate (written se(y), where y represents the estimate of the variable). You should also note that:

- The standard error indicates how close the sample survey estimate was to the result that could have been obtained using the same operating conditions (an equal full coverage).
- The standard error in statistics is a measure of variation in values from repeated samples. It doesn’t measure the exact precision of the sample from which it is calculated.
- A small standard error is a small variation in the values from repeated samples. This means that there is less chance of a bad’ sample. Therefore, it is more likely that the estimate of the sample will be close to an equal coverage.
- The standard errors can be used for determining upper and lower limits (the ‘confidence interval’). This will include the result of an equal coverage with a certain probability.
- Any of the random samples can be used to estimate the standard error.
- The standard error from a sample is an estimate. It is also subject to sampling error.
- Statements about the standard error of estimates should be included when publishing survey results.
- Standard errors should be considered when comparing survey estimates.
- The square of the standard error is called the sampling variance.