Univariate analysis mainly focuses on the description of univariate and statistical inference. It uses the simplest general form to reflect the basic information contained in a large number of sample data and describe the centralized or discrete trend in sample data. Univariate statistical inference is It is to infer the overall situation from sample data, mainly including interval estimation and statistical hypothesis testing.
To describe the central tendency of a univariate sample, the commonly used statistical description methods include the mean, mode and median. Interval estimation refers to the estimation of the value interval of the population under a certain confidence range. A statistical hypothesis is to first make a hypothesis on a certain parameter of the population, and then use sample statistics to verify the hypothesis, thereby deciding whether to accept or reject the hypothesis.
Data analysis begins with univariate analysis. The purpose of univariate analysis is to characterize and describe the characteristics and laws of variable distribution by sorting, processing, organizing and displaying data, and calculating indicators that reflect the central tendency and degree of dispersion of the data. Different types of variables require different methods and indicators.
Univariate analysis, also known as "univariate statistical analysis", is the description and statistics of a variable at a point in time, so it can be divided into univariate descriptive statistics and univariate inference statistics.
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Univariate descriptive statistics
Univariate descriptive statistics means "reflect the basic information contained in a large amount of data in the simplest general form." When using univariate descriptive statistics for data analysis and research, it can be carried out from the following three aspects.
(1) Determine frequency distribution and frequency distribution
Frequency refers to the number of data distributed in each category, and each category and its corresponding frequency are listed one by one, which is the frequency distribution. Normally, the frequency distribution appears in the form of a frequency distribution table.
Frequency distribution is the ratio distribution of the frequency of different values to the total in a set of data, usually expressed as a percentage. Like the frequency distribution, the frequency distribution also appears in the form of a frequency distribution table.
The frequency distribution table is the relative proportion of different categories in the population, and the frequency distribution table is the absolute proportion of different categories in the population.
(2) Conduct analysis of central tendency
The so-called central tendency analysis is to use a representative value or typical value to reflect the general level of a set of data, or to reflect the concentration of this set of data to this representative value or typical value. Because central tendency analysis scientifically abstracts the commonality of a large amount of data and can explain the general level of the researched object under specific conditions, it is widely used in univariate descriptive statistics.
When analyzing central tendency, it can be realized by calculating mode, median and average.
(3) Conduct discrete trend analysis
Discrete trend analysis refers to the use of a special value to reflect the degree of dispersion between a set of data. Discrete trend analysis can be realized by calculating the total distance, the odds ratio, the standard deviation, and the dispersion coefficient.
Univariate inferential statistics
In actual social surveys, censuses are rarely used, and sampling surveys are usually used. The purpose of univariate inference statistics is to infer the overall situation through the data obtained in the sample survey. It can be carried out from two aspects: interval estimation and hypothesis testing.
(1) Perform interval estimation
Interval estimation refers to establishing a confidence interval within a certain standard deviation range, and then linking the credibility of this interval to infer the sample statistical value into the overall parameter value. Its essence is to use a certain range of sample statistical values to "frame" the overall parameter value under a certain degree of confidence, that is, to estimate the parameter value by the distance between two values.
(2) Perform hypothesis testing
Hypothesis testing is to first make a hypothesis on a certain parameter of the population, and then use the statistics of the sample to verify it to determine whether the hypothesis is acceptable to the population.