What is a statistical hypothesis in hypothesis testing?

1. According to the degree of complexity:

1) Descriptive assumptions. is a description of the general outline and external appearance of an object. The aim is to provide people with speculations about certain external connections and approximate quantitative relationships of things, such as the study of the impact of educational development on changes in the birth rate of the population.

2) Explanatory assumptions. Reveal the internal connections of things to illustrate the reasons for things.

3) Hypotheses of sexuality. It is a scientific speculation about the future development trend of things. This kind of speculation cannot be made without a deeper and more comprehensive understanding of reality.

2. According to the direction of change in the relationship between the variables in the hypothesis

1) Conditional assumptions. It means that there is a conditional relationship between the two variables in the assumption, and the expression "if...... is usedThen ......2) Differential assumptions. It refers to the fact that there is a certain degree of difference between the two variables in the hypothesis.

3) Functional assumptions. It is a hypothetical causal covariance between two variables, and it is expressed mathematically, i.e., y=f(x).

3. According to the nature of the assumption:

1) General assumptions. It is a hypothesis that speculates on the relationship between general species, pointing to universal, abstract, generalizable examples.

2) Specific assumptions. It is a hypothesis that speculates on the relationship between specific objects, pointing to individual, specific, and specific cases.

3) Hypothesis of nothingness. Also known as a statistical hypothesis, it is a hypothesis that speculates about some non-existent, unbiased relationship, pointing to neutral, undifferentiated, and undifferentiated cases.

The original intention of the nihilistic hypothesis is to negate oneself through the test of facts, and if the nihilistic hypothesis is denied, the tendency of the result will be clearly revealed.

3. According to the tendency of the hypothesis to express the relationship between variables

1) Directional assumptions. Indicate the expected direction of the hypothetical outcome in the statement, indicating the characteristics and tendencies of the differences between the variables.

2) Non-directional assumptions. The expected direction of the hypothetical results is not indicated in the statement, but the differences between variables are expected to be revealed through the collection of data and the test results, which is often expressed by nihilistic assumptions.

<> In hypothesis testing, a statistical hypothesis refers to a set of assumptions about a parameter made about a set of data or a population, and it usually has two types: null hypothesis and alternative hypothesis. A null hypothesis usually means that the value of a parameter is equal to a given standard value, while an alternative hypothesis means that the value of a parameter is not equal to a given standard value.

In hypothesis testing, we need to perform statistical analysis of the sample data to determine whether to reject the null hypothesis and accept the alternative hypothesis, so as to make a conclusion to infer the population parameters.

A hypothesis that is pre-set for the needs of the research problem. In hypothesis testing, statistical hypotheses have null hypothesis h0 and alternative hypothesis h1For example, the impact of gender on academic achievement is to be studied.

Define xi and yi as the results of a certain subject for boys and girls, and the null hypothesis x=y can be set up and inferred by statistical methods. It may also be some assumptions that apply statistical methods, or assumptions that are often used statistically, such as normality. What are the types of statistical assumptions?

What do they mean.

In general, statistics has three meanings: statistical work, statistical information, and statistical science. The relationship between statistical work, statistical data, and statistical science is:

The results of statistical work are statistical data, and the basis of statistical data and statistical science is statistical work, which is not only a theoretical summary of statistical work experience, but also a principle, principle and method guiding statistical work. What are the statistical assumptions for an ideal gas.

There is no force between the ideal gases, and the gases understand that the mass of the particle has no interaction force, and try to point out which of the following statistical hypotheses are simple assumptions and which are recombination.

First empty!='\0'The second empty !=' 'The third null ==' 'But there is a problem with this algorithm, if you don't enter anything, it will definitely go wrong The main point of the algorithm is that a word is either at the beginning of the line It is not a space when it is not at the beginning of the line The character in front of it is a space What is a statistical hypothesis test?

What are the basic steps? What to look out for when doing hypothesis testing.

Statistical hypothesis testing is the testing of a proposition. Four steps: The first step is to formulate a hypothesis.

In the second step, the third step of calculating the statistic is to look up the table and obtain the critical value. Step 4: Draw conclusions: If the statistic falls into the acceptance domain, the null hypothesis is accepted.

To put it simply, it's the law of the opposite. For example, in the bilateral test, ask if there is any significant change, and you have to verify whether there is any, of course, the equal sign is placed in the original falsehood. For example, "a machine tool factory processes a part, according to experience, the ellipticism of the factory processing parts approximately obeys the normal distribution, and its overall mean is m0 = *** The overall standard deviation is s = ** Now change a new machine tool for processing, extract n = 200 parts for inspection, and the ovality obtained is *** Try to ask whether the average value of the ellipticity of the new machine tool processing parts is significantly different from before?

If it is a one-sided test, such as "According to a large amount of data in the past, the service life of the bulb produced by a factory obeys the normal distribution n (1020, 1002). Sixteen samples were randomly selected from a recently produced batch of products, and the average life of the samples was measured to be 1080 hours. Try to judge whether the service life of this batch of products has been significantly improved at the significance level.

The null hypothesis you're going to make is naturally not improving. Of course, there are other methods, but they are basically counter-proof.

The null hypothesis is based on the requirements of the question, and the equal sign must be placed in the null hypothesis.

Hypothesis testing is divided into two-sided hypothesis testing and one-sided hypothesis testing, the two-sided hypothesis test is aimed at proving whether a certain parameter of the population is equal to a specific value, while the one-sided hypothesis is to prove whether it is greater than or less than a fixed value, the basic principle is to first assume that a certain hypothesis of the population is true, if the phenomenon that leads to an unreasonable result is generated, the null hypothesis is rejected, if it does not lead to an unreasonable phenomenon, the null hypothesis is accepted.

The so-called "small probability event" in hypothesis testing is not an absolute contradiction in logic, but is based on the principle widely adopted in practice, that is, a small probability event almost does not occur in an experiment, but to what extent can the probability be counted as a "small probability event", obviously, the smaller the probability of a "small probability event", the more convincing it is to reject the null hypothesis h0, and this probability value is often remembered as (0< <1), which is called the significance level of the test.

For different problems, the significance level of the test is not necessarily the same, and it is generally believed that the probability of the event occurring is less than or equal, that is, the "small probability event".

The null hypothesis is a hypothesis that you want to prove or not, as opposed to the alternative hypothesis, which generally contains an equals sign.

The setting of the null hypothesis is the primary problem of the unit root test. By analyzing the shortcomings of the null hypothesis setting in the previous unit root test, and considering the credibility of the null hypothesis and the reliability of the test at the same time, Jin Tingliang proposed a reasonable setting strategy and improved test procedure for the unit root test null hypothesis.

The setting of the original hypothesis, the test formula and the determination of the critical value in the unit root test procedure are all based on the data generation process of the sample sequence, which is more scientific than the traditional unit root test procedure and improves the reliability of the test.

Therefore, it is undoubtedly of great significance to study the sensitivity of the test results of the new test procedure to the estimation of the data generation process model to further improve the unit root test theory.

The null hypothesis is "invalid" in a sense because it usually represents a "status quo". It is formalized by "asserting" that a population parameter or combination of population parameters has a certain value. In the example, the null hypothesis is that "the average gasoline ** for the entire state is the dollar".

The null hypothesis is written h0, then h0: =.

The basic steps of hypothesis testing are as follows:

1. Put forward a test hypothesis, also known as an invalid hypothesis, with the symbol h0; The symbol for the alternative hypothesis is h1.

h0: Sample-to-population or sample-to-sample variability is caused by sampling error;

h1: There are essential differences between samples and populations or samples from samples to samples;

The pre-set inspection levels are; When the test hypothesis is true, but the probability of being incorrectly rejected, is denoted as , usually taken = or =.

2. Select the statistical method, and calculate the size of the statistic according to the corresponding formula from the sample observation value, such as x2 value, t value, etc. According to the type of data and the empty point in Texas, the z-test, t-test, rank-sum test and chi-square test can be selected respectively.

3. According to the size of the statistics and their distribution, determine the size of the probability of equilibrium p that the test hypothesis is true and judge the results. If p> and the conclusion is that H0 is not rejected according to the level taken, it is considered that the difference is likely to be caused by sampling error, which is not statistically valid. If p is concluded to be significant according to the level taken, rejecting h0 and accepting h1, then it is considered that this difference is unlikely to be caused by sampling error alone, and is likely to be caused by different experimental factors, so it is statistically valid. The magnitude of the p-value can generally be obtained by consulting the corresponding cut-off table.

Statistical hypothesis testing, also known as statistical hypothesis testing, is a statistical inference method used to determine whether the differences between samples and samples and populations are caused by sampling errors or essential differences.

Significance testing is the most commonly used method of hypothesis testing, and it is also the most basic form of statistical inference, the basic principle of which is to make some kind of assumption about the Biki characteristics of the population, and then make inferences about whether the hypothesis should be rejected or accepted through statistical reasoning from sampling studies. Commonly used hypothesis testers include z-test, t-test, chi-square test, f-test, etc.

The basic idea of hypothesis testing is the principle of small probability events, and its statistical inference method is a counterproof method with a certain probabilistic nature. The idea of low probability is that a small probability event will not occur in a single trial.

The idea of the counter-evidence method is to first put forward a test hypothesis, and then use appropriate statistical methods to determine whether the hypothesis is true by using the principle of small probability. That is, in order to test whether a hypothesis h0 is correct, the hypothesis h0 is first assumed to be correct, and then a decision to accept or reject hypothesis h0 is made based on the sample.

If the sample observations lead to a small probability event, the hypothesis h0 should be rejected, otherwise the hypothesis h0 should be accepted. The so-called small probability event in hypothesis testing is not an absolute contradiction in logic, but is based on the principle widely adopted in practice, that is, a small probability event almost does not occur in an experiment, but the probability is small enough to be counted as a small probability event.

Hypothesis testing attention issues:

1. Before hypothesis testing, attention should be paid to whether the data itself is comparable.

2. When the difference is statistically significant, attention should be paid to whether the difference is meaningful in practical application.

3. Select the correct hypothesis testing method according to the type and characteristics of the data.

4. According to the profession and experience, determine whether to choose unilateral inspection or bilateral inspection.

5. When judging the conclusion, it should not be absolute, and it should be noted that there is a possibility of judgment error regardless of whether the hypothesis is accepted or rejected.

The basic principle of statistical hypothesis testing is hypothesis testing = significance level + small probability thinking + counterproof.

The so-called principle of small probability is that it is almost impossible for a small probability event to occur in a single experiment. That is, if a certain hypothesis about the population is true, it is almost impossible for an event that does not favor or support that hypothesis to occur in a single experiment; If an incident had happened in one experiment, we would have reason to doubt the veracity of this hypothesis and reject it.

Hypothesis testing is an important part of statistical inference, which is used to determine whether a hypothesis is correct. In data analysis, the parameters of a population are always unknowable, and the parameters of a population can only be inferred from statistics. In the process of statistical inference, certain hypotheses need to be made about the parameters, and then hypothesis testing is carried out on the proposed hypothesis.

Hypothesis testing and parameter estimation (including point estimation and interval estimation) are two important basic methods for inference statistics based on the central limit theorem and sampling distribution.

Directionality of the test:

One-sided test: A test that emphasizes a certain direction, with a percentage of significance being . Two-sided test: a test that emphasizes only difference and no directionality, with a significance percentage of 2.

For the same criterion of saliency argument, the critical region of the one-sided test is greater than that of the two-sided test in one direction, so if the difference occurs in that direction, the probability of a one-sided test being wrong is smaller, and we also say that it has a higher test power.

1. Hypothesis testing.

1) Basic idea.

Hypothesis testing: A hypothesis refers to a certain assumption about the characteristics of the population (such as parameters and distributions), and then uses probability to judge the consistency of the information provided by the sample search data and our conjecture about the characteristics of the population, so as to judge the correctness of the conjecture in combination with professional knowledge.

Using probability to represent the results of comparisons – the idea of small probability counter-proof.

1) The idea of low probability: small probability events (generally refer to the probability less than or equal to basically not occur in an experiment.)

2) Counter-argument idea: first put forward the hypothesis to be tested, and if the sample information does not support the hypothesis, reject the hypothesis.

2) Basic steps.

1.Establish test hypotheses and determine the level of testing.

h0 Null Hypothesis: In hypothesis testing, the hypothesis that is used to test is called the null hypothesis. It is usually expressed as "no difference" or "invalid", and is often represented by the symbol h0.

H1 Alternative Hypothesis: A "hypothesis" that is related to the null hypothesis and is opposed to each other, usually called an alternative hypothesis "alternative hypothesis", and is often represented by the symbol H1.

Level of a test: artificially prescribed, indicating the maximum allowable probability of h0 that the rejection is actually true, commonly expressed by symbols; the maximum error rate at which the hypothesis h0 is rejected in advance, which determines the criteria for low-probability events; It is often taken in practice, but it is not set in stone.

Bilateral test.