What Are the Different Types of Trend Analysis Statistics?

Univariate statistical analysis is the description and inference of the quantitative characteristics of a variable. It is the simplest and most basic statistic. It includes two major aspects, namely descriptive statistics and inferential statistics .

Univariate statistical analysis can be divided into two major aspects, namely descriptive statistics and inferential statistics . The main purpose of descriptive statistics is to reflect the basic information contained in a large amount of data in the simplest general form. Its basic methods include centralized trend analysis and discrete trend analysis . Inferential statistics use the data obtained from the sample to infer the overall situation. It mainly includes interval estimation and hypothesis testing ^[1]

Simply put, inferential statistics is a method of estimating the overall parameter value using the statistical value of the sample. The content of inference statistics mainly includes two aspects: one is interval estimation; the other is hypothesis testing.

Univariate Statistical Analysis Interval Estimation

The essence of interval estimation is to use a certain range (confidence interval) of sample statistical values to estimate the overall parameter value under a certain degree of confidence (confidence). The size of the range reflects the accuracy of this estimate, and the level of confidence reflects the reliability or certainty of this estimate. The results of interval estimation can usually be expressed in the following way: "We are 95% sure that the monthly wage income of employees in the city is between 182-218 yuan." Or "the probability of females accounting for 50% to 52% of the province's population is 99%."

The reliability or certainty in interval estimation refers to the probability of success when using a certain interval to estimate the overall parameters. It can be explained as follows: if the sampling is repeated 100 times from the population, about 95 times the statistical value of the sampled samples will include the parameter values of the population, then the reliability of the estimation of this interval is 95% For the same population and the same sampling size, the size of the given interval is directly proportional to the certainty with which such an estimate is made, that is, the larger the estimated interval, the greater the certainty of the success of this estimate; Conversely, the less certainty it is. In fact, the size of the interval reflects the accuracy of the estimation. The former is inversely proportional, that is, the larger the interval, the lower the accuracy; the smaller the interval, the higher the accuracy. For accuracy, the smaller the estimated interval is, the better; but for accuracy, the larger the estimated interval is, the better. Therefore, people always need to balance and choose between the two. In social statistical analysis, the commonly used confidence levels are 90%, 95%, and 99%, and the corresponding allowable errors (a) are 10%, 5%, and 1%, respectively. Confidence is commonly used in calculations

To represent. Below we introduce the interval estimation methods for the population mean and population percentage respectively.

(1) Interval estimation of the population mean

The interval estimation formula for the population mean is:

among them,

Is the sample average; S is the sample standard deviation;

Called confidence is

of

value;

Is the sample size.

(2) Interval estimation of overall percentage

The interval estimation formula for the overall percentage is:

Here,

Is the percentage in the sample.

Univariate statistical analysis hypothesis test

Hypothesis testing problems are another type in inferential statistics. First of all, it should be noted that the hypothesis here does not refer to the theoretical hypothesis at the abstract level, but refers to the empirical level hypothesis connected with the sampling method and relying on the sampling data for verification, that is, statistical hypothesis.

Hypothesis testing is actually making a hypothesis on a certain parameter of the population and then verifying it with sample statistics to determine whether the hypothesis is acceptable to the population. Hypothesis testing is based on the principle of small probability in probability theory, that is, the principle that "small probability events cannot occur in one observation". However, if the actual situation happens to be a small-probability event in an observation, how to judge it? One is that the probability of the event is still small, but it happens to be encountered; the other-it is The probability of doubting and denying the event is not necessarily small, that is, the event itself is not considered to be a small probability event, but a high probability event. The latter judgment is more reasonable, and it represents the basic idea of hypothesis testing. To summarize, the steps for hypothesis testing are:

(1) Establish nothingness hypothesis and research hypothesis. The null hypothesis is usually taken as the null hypothesis.

(2) Choose an appropriate significance level a (ie, the size of the probability) according to the needs, usually a = 0.05, a = 0.01, etc.

(3) Calculate the statistical value according to the sample data, and find the corresponding critical value according to the significance level.

(4) Compare the critical value with the statistical value. If the critical value is greater than the absolute value of the statistical value, accept the null hypothesis; otherwise, accept the research hypothesis ^[1] .