The following are collectively known as statistical methods or statistical techniques. They are used in various fields of research and industry to analyze and make inferences from data. They can also be grouped based on the specific field of study, for example, in econometrics, the methods are known as econometric techniques.
In statistics, these methods are usually studied under the following categories:

• Descriptive Statistics: Summarizing large sets of data in a way that is easy to understand. For example, calculating the mean, median, and standard deviation of a set of exam scores to understand how well a class performed on a test.

• Exploratory Data Analysis (EDA): Understanding the basic characteristics of a dataset, such as its distribution, outliers, and relationships between variables. For example, creating a scatter plot to investigate the relationship between age and income.

• Inferential Statistics: Making inferences about a population based on a sample of data. For example, using a t-test to determine if the average weight of a group of apples from one orchard is different from the average weight of a group of apples from another orchard.

• Predictive Modeling: Building models to make predictions about future outcomes based on historical data. For example, using linear regression to predict the price of a house based on its size, location, and other factors.

• Multivariate Statistics: Analyzing data that has more than one variable. For example, using multiple regression to predict the price of a house based on its size, location, and other factors.

• Time Series Analysis: Analyzing data that is collected over time. For example, using a moving average to forecast the next month’s sales based on past sales.

• Survival Analysis: Analyzing time-to-event data, such as time to failure or time to death. For example, using a Cox proportional hazards model to determine the factors that influence survival time after a heart attack.

• Bayesian Statistics: Incorporating prior knowledge into the analysis of data. For example, using a Bayesian hierarchical model to estimate the average height of adult men in a population, while taking into account prior information about the distribution of heights in similar populations.

• Statistical Learning: Building models to make predictions about future outcomes based on historical data. For example, using a decision tree to predict whether a customer will churn or not.

• Machine Learning: A field of study that gives computers the ability to learn without being explicitly programmed. For example, using a neural network to classify images.

These categories are not mutually exclusive and some methods may fall under multiple categories.

Sure, here is a more extensive list of statistical tools that are commonly used in various fields of research and industry:

Bootstrapping: a method that uses resampling with replacement to estimate the distribution of a statistic.

Ridge Regression: a method that is used to estimate the parameters of a linear model when the data may have multicollinearity.

Lasso Regression: a method that is used to estimate the parameters of a linear model while also performing feature selection.

Elastic Net Regression: a method that is a combination of Ridge and Lasso Regression.

Support Vector Machines (SVMs): a method that is used for classification and regression tasks using a boundary that maximizes the margin between different classes.

Decision Trees: a method that is used for both classification and regression tasks using a tree-like model of decisions.

Random Forest: a method that is an ensemble of Decision Trees.

Gradient Boosting: a method that is an ensemble of decision trees where the next tree is built to correct the errors made by the previous tree.

Neural Networks: a method that is used for tasks such as classification, regression, and prediction using a layered architecture of interconnected nodes.

K-Means Clustering: a method that is used to group similar observations together into clusters.

Hierarchical Clustering: a method that groups similar observations together into clusters and create a hierarchy of clusters.

Principal Component Analysis (PCA): a method that is used to decompose a multivariate dataset into a set of linearly uncorrelated variables called principal components.

Factor Analysis: a method that is used to identify the underlying structure in a dataset by identifying the underlying factors that explain the observed variables.

Cluster Analysis: a method that is used to group similar observations together into clusters.

Multidimensional Scaling: a method that is used to visualize the similarity or dissimilarity between a set of observations in a lower-dimensional space.

Time Series Analysis: a method that is used to analyze, model, and forecast time-dependent data.

Survival Analysis: a method that is used to analyze time to event data, such as time to failure or time to death.

Structural Equation Modeling (SEM): a method that is used to estimate the relationships between a set of observed and latent variables.

Item Response Theory (IRT): a method that is used to model the relationships between items and individuals on a test or survey.

Where would you use each of these tools:

Here are some examples of when certain statistical methods might be a good fit to use:

• Bootstrapping: Estimating the uncertainty of a statistic, such as the mean or standard deviation, when the underlying distribution is unknown or the sample size is small. For example, using bootstrapping to estimate the standard error of the mean of a new medical treatment’s effectiveness.

• Ridge Regression: Handling multicollinearity in linear regression models, which can cause unstable estimates of the regression coefficients. For example, using Ridge Regression to predict the price of a house based on its size, location, and other factors when the variables are highly correlated.

• Lasso Regression: Performing feature selection in linear regression models by shrinking the less important variables’ coefficients to zero. For example, using Lasso Regression to predict which genes are related to a certain disease by reducing the number of predictor variables.

• Elastic Net Regression: A combination of Ridge and Lasso Regression, it can perform both regularization and feature selection. For example, using Elastic Net Regression to predict the stock prices based on a set of economic indicators and financial ratios.

• Support Vector Machines (SVMs): Classification problems with complex boundaries. For example, using SVM to classify images of handwritten digits.

• Decision Trees: Explaining how a specific prediction is made. For example, using a Decision Tree to understand how a credit card company decides to approve or reject a loan application.

• Random Forest: Handling large number of input variables and reducing overfitting in decision trees. For example, using Random Forest to predict the likelihood of a customer defaulting on a loan.

• Gradient Boosting: Improving the performance of weak models by combining them. For example, using Gradient Boosting to improve the accuracy of a model that predicts customer churn.

• Neural Networks: Handling problems with large number of input variables and non-linear relationships. For example, using a Neural Network to classify images of animals.

• K-Means Clustering: Grouping similar observations together based on their characteristics. For example, using K-Means Clustering to segment customers into different groups based on their purchasing behavior.

• Hierarchical Clustering: Creating a hierarchy of clusters. For example, using Hierarchical Clustering to understand the relationships between different species of animals based on their genetic makeup.

• Principal Component Analysis (PCA): Reducing the dimensionality of a dataset and visualizing the relationships between variables. For example, using PCA to reduce the number of variables in a dataset of gene expression levels and visualizing the relationships between different types of cancer.

• Factor Analysis: Identifying the underlying structure in a dataset. For example, using Factor Analysis to identify the factors that influence job satisfaction among employees.

• Cluster Analysis: Grouping similar observations together based on their characteristics. For example, using Cluster Analysis to segment customers into different groups based on their demographics and purchasing behavior.

• Multidimensional Scaling: Visualizing the similarity or dissimilarity between a set of observations in a lower-dimensional space. For example, using Multidimensional Scaling to visualize the relationships between different brands of cars based on their features and prices.

• Time Series Analysis: Analyzing and forecasting time-dependent data. For example, using Time Series Analysis to forecast the demand for a product based on past sales data.

• Survival Analysis: Analyzing time-to-event data, such as time to failure or time to death. For example, using Survival Analysis to estimate the probability of survival of patients with a certain disease and identify the factors that influence survival time.

• Structural Equation Modeling (SEM): Estimating the relationships between a set of observed and latent variables. For example, using SEM to understand the relationships between different aspects of customer satisfaction, such as product quality and customer service.

• Item Response Theory (IRT): Modeling the relationships between items and individuals on a test or survey. For example, using IRT to determine which questions on a job satisfaction survey are most effective at measuring job satisfaction and which questions are most likely to be affected by response bias.