Population: The totality of a certain variable value of research objects with the same or similar properties determined according to the purpose of the research.

Sample: A set of variable values ​​of some individuals randomly selected from the population.

Overall parameters: indicators that describe overall characteristics, referred to as parameters. It is a fixed constant and generally unknown.

Statistics: An indicator that describes the characteristics of a sample. It is calculated from the sample observation values ​​and does not contain any unknown parameters.

Sampling error: The difference between a sample statistic and the corresponding population parameter caused by random sampling.

Frequency: If event A occurs m times in n independent repeated trials, m is called frequency. Call m/n the frequency or relative frequency of event A in n trials.

Probability: The constant stabilized by frequency is called probability.

Statistical description: Use appropriate statistical indicators (sample statistics), statistical charts, and statistical tables to characterize and describe the quantitative characteristics and distribution patterns of the data.

Statistical inference: including parameter estimation and hypothesis testing. Using sample statistical indicators (statistics) to infer the overall corresponding indicators (parameters) is called parameter estimation. Using sample differences or differences between samples and the population to infer whether there may be differences between populations is called hypothesis testing.

(1) Quantitative data: measurement data

(2) Classification information:

Paired design

group design

central tendency

Dispersion trend

Frequency distribution characteristics

Mean & standard deviation ======== Normal or approximately normal distribution

Median & Interquartile Range === Skewed Distribution

Geometric mean & logarithmic standard deviation === Lognormal distribution

Rate: Describes the frequency or intensity of a phenomenon. (Case fatality rate is not equal to death rate)

Component ratio: describes the proportion or distribution of the internal components of a phenomenon, often expressed as a percentage.

Relative ratio: Also known as ratio, it is the ratio of two related indicators A and B, indicating how many times or percentages A is B. Two indicators can be of the same nature or different.

Compare the prevalence, incidence, mortality and other data of two different groups to eliminate the impact of their internal composition (age, gender, length of service, length of disease, severity of illness) on the rate

Only function: comparison (cannot be used to reflect actual levels)

1. The denominator for calculating relative numbers should not be too small;

2. The composition ratio cannot be used instead of rate when analyzing;

3. For several rates with different numbers of observation units, the average rate cannot be calculated directly by adding them together;

4. When comparing relative numbers, attention should be paid to their comparability;

5. The comparison of sample rates (or composition ratios) should follow random sampling and perform hypothesis testing.

Structure: It consists of titles, headings, lines and numbers.

Requirements for preparing statistical tables:

Histogram: represents the frequency distribution of continuous data; the area of ​​the straight rectangle represents the frequency of each group

Line graph: used for continuous data, used to illustrate the development and changes of things over time, or the change of one phenomenon with another phenomenon;

boxplot

Error bar chart: data used for [mutual comparison];

②Circle chart and percentage bar chart: suitable for [percent composition ratio data], indicating the [proportion or composition] of each component of a thing;

⑤Scatter plot: suitable for linear correlation analysis to illustrate the quantitative relationship and changing trend between two variables.

standard error

central limit theorem

t distribution

Confidence interval (credible interval) - find the population mean μ

Interval estimation of [population mean] (interval estimation of a single normal population mean μ)

Interval estimation of [difference between two population means]

Interval estimation of [difference in probability between two populations]

(1) Basic idea

(2) Basic steps

two types of errors

Type 1 error is rejecting the correct null hypothesis. The significance level a is the highest level that can be tolerated for rejecting the null hypothesis, and it is also the maximum tolerable probability of a Type I error. p is the minimum requirement to reject the null hypothesis. If p>a, that is, the maximum significance set by the measurement test result must be less than the minimum level required to reject the null hypothesis. In other words, the minimum I require is greater than the maximum set, therefore, the null hypothesis cannot be rejected.