Statistics is a broad field that can be categorized into two main branches: descriptive statistics and inferential statistics. These branches are further divided into various subfields.
The branches of statistics are disciplines on which statistics relies to analyze data from different perspectives.
Let us remember that statistics is a branch of mathematics, which is responsible for the collection, analysis, interpretation, presentation and organization of data (set of qualitative variable values or quantitative).
This discipline seeks to explain the relationships and dependencies of a phenomenon (physical or natural).
Statistics is a transversal science, that is, applicable to a variety of disciplines, ranging from physics to social sciences, health sciences or quality control.
In addition, it has great value in business or government activities, where the study of the data obtained makes it possible to facilitate decision making or make generalizations.,
Main branches of statistics
Statistics is divided into two large areas: descriptive statistics and inferential statistics, which comprise applied statistics.
In addition to these two areas, there is mathematical statistics, which includes the theoretical bases of statistics.
1. Descriptive Statistics:
- Measures of Central Tendency
- Measures of Dispersion or Variability
- Measures of Shape
- Frequency Distributions
- Graphical Representation
2. Inferential Statistics
- Probability Theory
- Hypothesis Testing
- Regression Analysis
- Analysis of Variance (ANOVA)
- Non-parametric Statistics
3. Applied Statistics
- Social Statistics
- Business Statistics
4. Mathematical Statistics
- Probability Distributions
- Statistical Inference
1. Descriptive statistics
descriptive statistics is the branch of statistics that describes or summarizes in a quantitative (measurable) way characteristics of a collection of information.
That is, descriptive statistics is responsible for summarizing a statistical sample (set of data obtained from a population) instead of learning about the population that the sample represents.
Some of the measures commonly used in descriptive statistics to describe a set of data are measures of central tendency and measures of variability or dispersion.
Regarding measures of central tendency, measures such as the mean, median and mode are used. While in variability measures, variance, kurtosis, etc. are used.
An example of descriptive statistics might be considering a number to summarize how well a baseball batter is performing.
Thus, the number is obtained by the number of hits a batter has given, divided by the number of times he has been at bat. However, this study will not provide more specific information, such as which of those hits were home runs.
Other examples of descriptive statistics studies can be: the average age of citizens living in a certain geographic area, the average length of all books referring to a specific topic, the variation with respect to the time that visitors spend browsing a Internet page.
2. Inferential statistics
inferential statistics differs from descriptive statistics mainly by the use of inference and induction.
That is, this branch of statistics seeks to deduce properties of a studied population, that is, it not only collects and summarizes the data, but also seeks to explain certain properties or characteristics from the data obtained.
In this sense, inferential statistics involves obtaining the correct conclusions from a statistical analysis carried out using descriptive statistics.
For this reason, many of the experiments in social sciences involve a small population group, and through inferences and generalizations it is possible to determine how the general population behaves.
The conclusions obtained through inferential statistics are subject to randomness (absence of patterns or regularities) but by applying the appropriate methods it is possible to obtain relevant results.
Thus, both descriptive statistics and inferential statistics they go hand in hand.
Inferential statistics is divided into:
It includes statistical procedures based on the distribution of real data, which are determined by a finite number of parameters (a number that summarizes the amount of data derived from a statistical variable).
To apply parametric procedures, for the most part, it is required to previously know the shape of distribution for the resulting shapes of the studied population.
Therefore, if the distribution of the data obtained is completely unknown, a non-parametric procedure must be used.
This branch of inferential statistics includes the procedures applied in statistical tests and models, in which their distribution does not conform to the so-called parametric criteria. Since the data studied are those that define its distribution, it cannot be previously defined.
Non-parametric statistics is the procedure that should be chosen when it is unknown whether the data fit a known distribution, so that it can be a prior step to the parametric procedure.
Likewise, in a non-parametric test, the chances of error are decreased by using adequate sample sizes.
3. Mathematical statistics
The existence of mathematical statistics as a discipline of statistics has also been mentioned.
This consists of a previous scale in the study of statistics, in which they use probability theory (branch of mathematics that studies random phenomena) and other branches of mathematics.
Mathematical statistics consists of obtaining information from data and uses mathematical techniques such as mathematical analysis, linear algebra, stochastic analysis, differential equations, etc.
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