What is statistical test _ statistics

Establishing hypotheses   Statistical tests is the work of judging the sampling results and the sampling distribution relative to the photograph. The method of descriptive statistics is sufficient to obtain the sampling results. Sampling distribution is not, it can not be obtained from the data, not the use of probability theory. This work will not be possible without the assumption of some necessary assumptions about the general population and the sampling procedures used.   Sampling distribution   After making the necessary assumptions, we can use the mathematical inference process to find the sampling distribution. As a result of the mathematics has been achieved, in fact, the statistical workers to do this work is often not really to seek the mathematical form of sampling distribution, but according to specific needs, to determine the specific problem of the statistical test should be used in which distribution of the mathematical table. Select the significant level and the negative domain   have a sampling distribution related to the problem, we can divide all possible results into two categories: one is unlikely; the other is expected to happen. That being the case, if the results we get in an actual sample are exactly the first category, we have reason to doubt the assumptions of the probability distributions. In statistical tests, these improbable results are called negative fields. If such a result does occur, we will negate the hypothesis, and the contrary will not negate the hypothesis. The specific form of the probability distribution is determined by the hypothesis, and there must be more than one. In statistical testing, the hypothesis that is tested is usually referred to as the 0 hypothesis (or the original hypothesis, expressed in symbolic H0) and is contrasted with other alternative hypotheses (represented by symbolic H1). It is noteworthy that the hypothesis can only be tested and never proved. Statistical testing can help us negate a hypothesis, but it does not help us to affirm a hypothesis. In order to make the test more rigorous and more scientific, more things are needed. First, we must determine the extent of the risk of offending the first and second categories of errors, and secondly, determine whether the negative field should include both ends of the sampling distribution. The first type of error is that 0 assumes that H0 is actually correct, but is denied. The second type of error is that H0 is actually wrong, but not denied. The second type of error is that 0 assumes that H0 is actually wrong, but not denied. Unfortunately, no matter how we choose the negative domain, it is not possible to completely avoid the first category of errors and the second type of error, and it is not possible to simultaneously reduce the risk of committing two types of errors to the minimum. For any given test, the smaller the risk of the first type of error, the greater the probability of the second type of error, and vice versa. Generally speaking, it is not possible to estimate the probability of the second type of error in detail. The first type of error otherwise, the probability of committing the first type of error is the sum of the probabilities of the various results in the domain. Since the risk of committing the first type of error is contrary to the risk of committing the second type of error, we must weigh the risks of the first type of error and the risk of the second type of error in the statistical examination. The probability that we have chosen to make the first type of error, called the level of significance of the test (expressed in alpha), determines the negationThe size of the field. If the sampling distribution is continuous, the negative domain can be established at any level that it wants to establish, and the magnitude of the negative field can be consistent with the requirement of a significant level (as in the subsequent normal test). If the sampling distribution is discontinuous, we should use the cumulative probability method to find a group of results that constitute a negative field. That is, on the known probability distribution table, the probability of the least probability at both ends begins to accumulate to the center until the sum of the probabilities is slightly smaller than the selected significant level. On many occasions, we can predict the direction of deviation, or only interested in one direction of deviation. When the direction can be predicted, at the same significant level of the condition, unilateral test is more appropriate than the bilateral test. Because the negative field is concentrated to the more appropriate side of the sampling distribution, a relatively large tail end can be obtained. This would reduce the risk of committing a second type of error in the same way as the risk of committing the first type of error is unchanged. Calculation of the test statistics   after the above work, the next step is to do the same as possible to the ideal test of the actual sample (such as the actual do a repeat toss coin test), and from the sample data obtained to calculate the test statistics. The test statistics are a comprehensive indicator of the sample, but differ from the statistics to be discussed in the Nineth parameter estimate, which is not used as an estimate, but only as a test. The Judgment   hypothesis test refers to the refusal or retention of the 0 hypothesis, also known as the significance of verification. After selecting the negative field and calculating the test statistic, the last procedure is completed, that is, the hypothesis of the taking and the shed is determined according to the test or sample result. If the result falls within the negative field, the 0 hypothesis will be negated under the condition that the first class error probability is known to be committed. Conversely, if the result falls in the negative extraterritorial, then does not negate the 0 hypothesis, at the same time, has the risk of committing the second kind of mistake.
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