統計を英語で勉強する　その３

Here are further technical terms with their detailed descriptions, continuing from the previously outlined statistical concepts:

21. Regression Analysis

• Definition: A statistical method used to examine the relationship between one or more independent variables and a dependent variable.

• Application: Commonly used for prediction and forecasting, where it can help indicate the strength and character of the relationship between variables.

22. Correlation Coefficient

• Definition: A numerical measure of some type of correlation, meaning a statistical relationship between two variables. Values range from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

• Application: Used to assess the strength and direction of the linear relationship between two quantitative variables.

23. T-test

• Definition: A type of inferential statistic used to determine if there is a significant difference between the means of two variables, which may be related in certain features.

• Types: Includes one-sample, two-sample, and paired t-tests, each designed for specific situations in comparing means.

24. ANOVA (Analysis of Variance)

• Definition: A statistical method used to compare the means of three or more samples (using the F distribution). It tests the hypothesis that the means of several groups are equal.

• Usage: Widely used in situations where T-tests could be applied, but for more than two groups.

25. Chi-Square Test

• Definition: A statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance. It's especially used in the analysis of contingency tables.

• Application: Useful for testing relationships between categorical variables.

26. Non-Parametric Tests

• Definition: Statistical tests that do not assume a specific distribution form for the data. They are used when the data doesn't meet the assumptions necessary for parametric testing, such as normality.

• Examples: Includes the Mann-Whitney U test, Kruskal-Wallis test, and Spearman's rank correlation.

27. Likelihood Ratio Test

• Definition: A statistical test used to compare the fit of two models, one of which (the null model) is a special case of the other (the alternative model). It evaluates whether the addition of parameters in the alternative model significantly improves the model's fit.

• Application: Often used in nested model comparisons.

28. Bayesian Statistics

• Definition: A statistical method that applies probability to statistical problems, involving prior knowledge as well as current evidence. Bayesian statistics provide a mathematical procedure to update beliefs based on new evidence.

• Characteristic: Distinctive for its use of probability distributions to express uncertainty about parameters.

29. Random Variable

• Definition: A variable whose possible values are numerical outcomes of a random phenomenon. There are two types of random variables, discrete and continuous.

• Application: Fundamental in probability theory and statistics for modeling random processes.

30. Expectation Value (Expected Value)

• Definition: The weighted average of all possible values that a random variable can take on, with the weights being the probabilities of each outcome. It represents the mean of a random variable over the long term.

• Formula: For a discrete random variable, (E[X] = \sum x_i p_i); for a continuous one, (E[X] = \int x f(x) dx), where (f(x)) is the PDF.

These terms delve deeper into statistical testing, model comparison, and the probabilistic foundation of statistics, highlighting the breadth of concepts and methods used in the field.