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Introduction to the basics of medical statistics
This is a mind map about the basic introduction to medical statistics. It applies mathematical principles and methods to research the collection, organization and analysis of data, and makes scientific inferences on uncertain data.
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Introduction to the basics of medical statistics
- bacteria
This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
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Introduction to the basics of medical statistics
1.1 Medical Statistics
Statistics: A discipline that applies mathematical principles and methods to research the collection, organization and analysis of data, and makes scientific inferences about uncertain data.
statistical tasks
Descriptive statistics: Summarizing, describing, and exploring data. The branch of statistics dedicated to these applications is called descriptive statistics.
Inferential statistics: Use sample data information to infer the characteristics of the population distribution. The branch of statistics for this purpose is called inferential statistics.
1.2 Several basic concepts in statistics
population and sample
Population: the entire population of research objects determined according to the purpose of the research
Individual: Each basic unit (one or some indicators) that constitutes the population
finite population
infinite population
Sample: a portion of individuals drawn from the population
Sample size: the number of individuals included in the sample
Sampling: The process of obtaining samples from a population. The process of sample extraction should follow the principle of randomization
Random sample: In the random sampling process, each individual in the population has a non-zero probability of being selected.
Simple random sample: During the random sampling process, each individual in the population has the same probability of being selected.
The relationship between the population and the sample
The sample comes from the population and is a part of the population. The characteristics of the sample can reflect the characteristics of the population to some extent.
Obtaining representative samples is the basis for reasonable inferences about the population
The sample satisfies the principle of independent identical distribution (i.i.d.) - the sample is independent of the population, each observation is independent of each other, and the distribution of the sample is the same as the distribution of the population.
homogeneity and variation
Homogeneity: Individuals in a population have something in common. The nature, influencing conditions or background of individuals in the same population are the same or very similar, which is the basis of the research question
Variation: Individual differences existing in a homogeneous population are the premise of research problems
Relationship: describe the homogeneity of the same population in the context of variation and reveal the heterogeneity of different populations
Parameters and Statistics
Parameter: A summary numerical measure used to describe an overall characteristic
Statistics: a statistical indicator calculated from sample observations
Relationship: Parameters are usually unknown and fixed constants. Statistics are calculated from sample data and will change as the sample changes.
type of data
Variable: An indicator obtained by observing and measuring a certain variation characteristic
Measurement data: Data obtained by measuring the size of an indicator for each observation unit. ① Observed values have units of measurement; ② There are quantitative differences between each observed value
Categorical data: qualitative data
Unordered categorical data: Data obtained by grouping observations according to certain attributes or categories (two categories and multiple categories), and then counting and summarizing the frequencies of each group. The variables corresponding to unordered categorical data are called nominal variables.
Ordered categorical data: Data obtained by grouping observation units according to different degrees of certain attributes, and then counting and summarizing the frequencies of each group. Semi-quantitative data
error
Error: The difference between the actual observed value and the overall true value (parameter). The accuracy and reliability of the data obtained need to be considered
random error
Non-constant and randomly changing errors are affected by a variety of uncertain factors. The size and direction of change of the error are uncertain
objective existence and unavoidable
Sampling error: It is a kind of random error. The possible difference between sample statistics and population parameters caused by sampling is the main content of statistical inference research. Under a large number of repetitions, the sampling error changes randomly. Sex will show certain regularity
Systematic error: An error caused by the influence of certain certain factors during the actual observation process. It has a fixed size and a directional systematic deviation from the true value. It cannot be completely eliminated, but it can be reduced to a minimum through strict experimental design and technical measures.
Non-systematic errors - gross errors: errors caused by accidental errors by researchers in experiments, which can be eliminated through inspection
1.3 Basic steps of statistics in medical research
The process of statistical analysis is induction (building a model based on data) and deduction (using models to make inferences). Its essence is a scientific process of answering real-life questions by finding distribution patterns in random phenomena.
Statistical design: important foundation
Data collection: Collecting representative data is a prerequisite for drawing correct conclusions.
Statistical analysis: Statistical description and statistical modeling, fully exploring the unknown information hidden in the data, and displaying it with appropriate statistical charts
statistical inference