Here’s a quick overview of some of the concepts in statistics:
Data: Statistics involves collecting, organizing, and analyzing data. Data can be collected in many different forms, such as measurements, counts, or categorical variables.
Descriptive statistics: These are techniques used to summarize and describe the characteristics of a dataset. Examples include measures of central tendency (e.g. mean, median, mode) and measures of spread (e.g. range, standard deviation).
Inferential statistics: These are techniques used to draw conclusions about a population based on a sample of data. Inferential statistics allows us to make predictions and test hypotheses about the population.
Probability: Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
Normal distribution: The normal distribution is a common probability distribution that is bell-shaped and symmetrical. Many real-world phenomena follow a normal distribution, such as heights, test scores, and measurement errors.
Confidence intervals: A confidence interval is a range of values that is likely to contain the true value of a population parameter. For example, if you survey a sample of people and estimate the mean income of the population based on the sample, you can use a confidence interval to give a range of values that is likely to include the true mean income of the population.
T-tests: A t-test is a statistical test used to compare the means of two groups. There are several different types of t-tests, including the one-sample t-test, the independent samples t-test, and the paired samples t-test. T-tests are used to determine whether the difference between the means of two groups is statistically significant.
ANOVA: ANOVA, or analysis of variance, is a statistical test used to compare the means of three or more groups. It is used to determine whether there are significant differences between the means of the different groups.
Regression: Regression is a statistical method used to predict a continuous outcome variable (the dependent variable) based on one or more predictor variables (the independent variables). Regression can be used to understand the relationship between the predictor variables and the outcome variable and to make predictions about the outcome variable based on the predictor variables.
Chi-square test: The chi-square test is a statistical test used to determine whether there is a significant difference between the observed frequencies in a categorical data set and the expected frequencies under a null hypothesis. It is used to test hypotheses about the relationships between categorical variables.
Correlation: Correlation is a statistical measure that describes the strength and direction of the relationship between two variables. A positive correlation indicates that as one variable increases, the other variable also increases. A negative correlation indicates that as one variable increases, the other variable decreases. The strength of the correlation is measured by the correlation coefficient, which ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation).
Nonparametric tests: Nonparametric tests are statistical tests that do not assume that the data follow a particular distribution. They can be used when the data are not normally distributed or when the sample size is small. Examples of nonparametric tests include the Mann-Whitney U test and the Wilcoxon signed-rank test.
Multivariate analysis: Multivariate analysis is a statistical method used to analyze data with more than one dependent variable. It allows researchers to understand the relationships between multiple variables and how they jointly affect the dependent variables. Examples of multivariate analysis techniques include multiple regression, factor analysis, and principal component analysis.
Sampling: Sampling is the process of selecting a subset of a population to study. The goal of sampling is to choose a representative sample that accurately reflects the characteristics of the entire population. There are several different types of sampling methods, including random sampling, stratified sampling, and cluster sampling.
Power analysis: Power analysis is a statistical method used to determine the sample size needed for a study to have a high probability of detecting a true effect, if one exists. It is used to ensure that a study has sufficient statistical power to detect a meaningful difference between groups or to reject the null hypothesis.
Multivariate regression: Multivariate regression is a type of regression analysis that involves more than one independent variable. It allows researchers to understand how multiple variables jointly predict a dependent variable. For example, a researcher might use multivariate regression to understand how income, education level, and age jointly predict life expectancy.
Logistic regression: Logistic regression is a type of regression analysis used when the dependent variable is binary (e.g. 0 or 1, yes or no). It is used to predict the probability of a particular outcome occurring based on one or more predictor variables.
Discriminant analysis: Discriminant analysis is a statistical method used to predict which of several groups an individual belongs to based on one or more predictor variables. It is used to classify individuals into different categories based on their characteristics.
Factor analysis: Factor analysis is a statistical method used to identify underlying patterns in a set of variables. It is used to identify a smaller number of “factors” that are related to a larger number of observed variables. Factor analysis is often used in psychological and sociological research to understand the underlying structure of complex sets of data.
Principal component analysis (PCA): Principal component analysis (PCA) is a statistical method used to reduce the dimensionality of a dataset by identifying a smaller number of “principal components” that capture the majority of the variance in the data. It is often used in data visualization and machine learning applications to reduce the complexity of the data and make it easier to analyze.
Cluster analysis: Cluster analysis, also known as clustering, is a statistical method used to group data into clusters based on the similarity of their characteristics. It is often used in data mining and machine learning applications to discover patterns and relationships in data.
Principal component regression (PCR): Principal component regression (PCR) is a statistical method that combines principal component analysis (PCA) with linear regression. It is used to reduce the dimensionality of a dataset while still allowing the prediction of a continuous outcome variable.
Partial least squares regression (PLS): Partial least squares regression (PLS) is a statistical method that combines principal component analysis (PCA) with multiple linear regression. It is used to predict a continuous outcome variable based on multiple predictor variables, and it is particularly useful in situations where there are a large number of predictor variables and the relationships between the variables are complex.
Structural equation modeling (SEM): Structural equation modeling (SEM) is a statistical method used to test and estimate the relationships between multiple variables. It allows researchers to test hypotheses about the relationships between variables and to estimate the strength and direction of these relationships. SEM is often used in social and behavioral research to understand the underlying structure of complex datasets.
Survival analysis: Survival analysis is a statistical method used to analyze data on the time it takes for an event of interest to occur. It is often used in medical research to study the time to disease onset, time to death, or time to recovery.
Longitudinal data analysis: Longitudinal data analysis is a statistical method used to analyze data collected over time from the same individuals. It allows researchers to understand how variables change over time and how they are related to one another.
Mixed effects modeling: Mixed effects modeling is a statistical method used to analyze data with both fixed and random effects. It is often used in research to understand the relationships between variables while taking into account the inherent structure of the data, such as repeated measures or clustering.
Generalized linear models (GLMs): Generalized linear models (GLMs) are a class of statistical models that extend the linear regression model to allow for response variables that are not normally distributed. They are used to analyze data with a wide variety of response distributions, including binary, count, and categorical data.
Hierarchical linear modeling (HLM): Hierarchical linear modeling (HLM) is a statistical method used to analyze data with a nested structure, such as data collected from individuals within groups or data collected from repeated measures. It allows researchers to understand how variables at different levels of the hierarchy (e.g. individual and group level) are related to one another.
Mediation analysis: Mediation analysis is a statistical method used to understand how one variable (the mediator) affects the relationship between two other variables (the predictor and the outcome). It is used to understand the mechanisms through which an intervention or treatment affects an outcome and to identify potential targets for intervention.
Moderation analysis: Moderation analysis is a statistical method used to understand how the relationship between two variables (the predictor and the outcome) varies as a function of a third variable (the moderator). It is used to understand how the strength and direction of the relationship between the predictor and the outcome depends on the level of the moderator.
Structural time series modeling: Structural time series modeling is a statistical method used to analyze time series data that are influenced by both regular patterns (e.g. seasonal patterns) and irregular events (e.g. shocks or interventions). It allows researchers to identify and forecast the underlying trends in the data, as well as to understand the impact of irregular events on the data.
Multilevel modeling: Multilevel modeling is a statistical method used to analyze data with a hierarchical structure, such as data collected from individuals nested within groups or data collected from repeated measures. It allows researchers to understand how variables at different levels of the hierarchy (e.g. individual and group level) are related to one another and to account for the inherent structure of the data in the analysis.
Mixture modeling: Mixture modeling is a statistical method used to identify subgroups or “mixtures” within a population based on the characteristics of the individuals. It allows researchers to identify patterns and relationships within the data that may not be apparent when analyzing the data as a whole.
Bayesian statistics: Bayesian statistics is a statistical approach that involves using prior knowledge and data to update beliefs about an unknown quantity. It involves constructing a probability distribution over possible values of the unknown quantity, called the posterior distribution, based on both the prior distribution (reflecting prior knowledge) and the data.
Machine learning: Machine learning is a subfield of artificial intelligence that involves the use of algorithms to learn from data and make predictions or decisions. It involves training a model on a dataset and using the model to make predictions or decisions about new data.
Decision trees: Decision trees are a type of machine learning algorithm that involves building a tree-like model of decisions and their possible consequences. Each internal node of the tree represents a “test” on an attribute, and each leaf node represents a class label. Decision trees are used for classification and regression tasks.
Random forests: Random forests are a type of machine learning algorithm that involves building a large number of decision trees and aggregating their predictions. The trees in a random forest are trained on different samples of the data and use different subsets of the features, which helps to reduce overfitting and improve the accuracy of the model.
Support vector machines (SVMs): Support vector machines (SVMs) are a type of machine learning algorithm that involves finding the hyperplane in a high-dimensional space that maximally separates the different classes. They are used for classification tasks and are particularly effective in cases where the number of dimensions is greater than the number of samples.
Neural networks: Neural networks are a type of machine learning algorithm inspired by the structure and function of the brain. They are composed of layers of interconnected “neurons” that process and transmit information. Neural networks are used for a wide variety of tasks, including classification, regression, and prediction.
Deep learning: Deep learning is a subfield of machine learning that involves the use of neural networks with many layers (also known as “deep” neural networks). Deep learning algorithms are able to learn and represent very complex patterns in data, and they have been successful in a wide range of applications, including image and speech recognition, natural language processing, and machine translation.
Reinforcement learning: Reinforcement learning is a type of machine learning algorithm in which an agent learns by interacting with its environment and receiving rewards or punishments for its actions. The goal of the agent is to maximize the cumulative reward over time by learning which actions are most likely to lead to positive outcomes. Reinforcement learning has been applied to a wide range of tasks, including robot control, game playing, and natural language processing.
Unsupervised learning: Unsupervised learning is a type of machine learning in which the algorithm is not given any labeled training data. Instead, it must discover patterns and relationships in the data on its own. Examples of unsupervised learning tasks include clustering and dimensionality reduction.
Semi-supervised learning: Semi-supervised learning is a type of machine learning that involves using both labeled and unlabeled data to learn a model. It can be useful in situations where it is costly or time-consuming to label large amounts of data, but some labeled data is still available.
Transfer learning: Transfer learning is a machine learning technique in which a model trained on one task is used to improve the performance of a model on a different task. It can be useful in situations where there is a limited amount of data available for a particular task, but a large amount of data is available for a related task.
Ensemble learning: Ensemble learning is a machine learning technique in which multiple models are trained and their predictions are combined to make a final prediction. Ensemble methods can improve the performance of a model by reducing overfitting, improving generalization, and increasing the stability of the model. Examples of ensemble methods include boosting, bagging, and stacking.
Hyperparameter optimization: Hyperparameter optimization is the process of choosing the best values for the hyperparameters of a machine learning model. Hyperparameters are values that are set prior to training the model and control the overall behavior of the model. Optimizing hyperparameters can improve the performance of a model by finding the values that lead to the best fit to the data.
Cross-validation: Cross-validation is a statistical method used to evaluate the performance of a machine learning model. It involves dividing the data into a number of “folds,” training the model on some of the folds, and evaluating the model on the remaining folds. Cross-validation is used to estimate the generalization error of a model and to tune the hyperparameters of the model.
Overfitting: Overfitting is a problem that can occur in machine learning when a model is too complex and is able to fit the training data too well, but does not generalize well to new data. Overfitting can lead to poor performance on unseen data and is usually caused by having too many parameters relative to the amount of data available.
Underfitting: Underfitting is a problem that can occur in machine learning when a model is too simple and is not able to capture the underlying patterns in the data. Underfitting can lead to poor performance on both the training data and new data and is usually caused by having too few parameters relative to the amount of data available.
Bias-variance tradeoff: The bias-variance tradeoff is a fundamental concept in machine learning that refers to the tradeoff between the model’s ability to fit the data well (low bias) and the model’s ability to generalize well to new data (low variance). In general, models with low bias tend to have high variance and vice versa. Finding the right balance between bias and variance is an important part of building a successful machine learning model.
Regularization: Regularization is a technique used in machine learning to prevent overfitting by adding a penalty term to the objective function that the model is trying to optimize. The penalty term serves to constrain the model and prevent it from becoming too complex. Common types of regularization include L1 (Lasso) and L2 (Ridge) regularization.
Confusion matrix: A confusion matrix is a table used to evaluate the performance of a classification model. It displays the number of true positive, true negative, false positive, and false negative predictions made by the model. The confusion matrix can be used to calculate a variety of evaluation metrics, including accuracy, precision, recall, and F1 score.
ROC curve: A receiver operating characteristic (ROC) curve is a plot used to evaluate the performance of a binary classification model. It displays the true positive rate on the y-axis and the false positive rate on the x-axis. The ROC curve is a useful tool for comparing the performance of different models and for selecting the optimal probability threshold for a given application.
Precision-recall curve: A precision-recall curve is a plot used to evaluate the performance of a binary classification model. It displays the precision (the proportion of true positive predictions among all positive predictions) on the y-axis and the recall (the proportion of true positive predictions among all actual positive cases) on the x-axis. The precision-recall curve is a useful tool for comparing the performance of different models and for selecting the optimal probability threshold for a given application.
Lift curve: A lift curve is a plot used to evaluate the performance of a binary classification model in a marketing context. It displays the percentage of positive cases in the population on the x-axis and the percentage of positive predictions made by the model on the y-axis. The lift curve is a useful tool for understanding the relative effectiveness of a model compared to a random selection process.
Gain curve: A gain curve is a plot used to evaluate the performance of a binary classification model in a marketing context. It displays the percentage of the population on the x-axis and the percentage of positive cases predicted by the model on the y-axis. The gain curve is a useful tool for understanding the effectiveness of a model at different levels of the population.
Information value (IV): Information value (IV) is a measure of the predictive power of a variable in a binary classification model. It is calculated as the difference between the distribution of the variable in the positive and negative cases. Higher values of IV indicate that the variable is a better predictor of the outcome.
AUC-ROC: The area under the receiver operating characteristic (ROC) curve (AUC-ROC) is a measure of the overall performance of a binary classification model. It is calculated as the area under the ROC curve and ranges from 0 to 1, with higher values indicating better performance.
AUC-PR: The area under the precision-recall curve (AUC-PR) is a measure of the overall performance of a binary classification model. It is calculated as the area under the precision-recall curve and ranges from 0 to 1, with higher values indicating better performance.
False positive rate: The false positive rate is a measure of the performance of a binary classification model. It is defined as the proportion of negative cases that are incorrectly classified as positive. A low false positive rate is desirable, as it indicates that the model is not making many incorrect positive predictions.
True positive rate: The true positive rate, also known as sensitivity or recall, is a measure of the performance of a binary classification model. It is defined as the proportion of positive cases that are correctly classified as positive. A high true positive rate is desirable, as it indicates that the model is making many correct positive predictions.
False negative rate: The false negative rate is a measure of the performance of a binary classification model. It is defined as the proportion of positive cases that are incorrectly classified as negative. A low false negative rate is desirable, as it indicates that the model is not making many incorrect negative predictions.
Precision: Precision is a measure of the performance of a binary classification model. It is defined as the proportion of positive predictions that are correct. A high precision is desirable, as it indicates that the model is making many correct positive predictions and not many incorrect positive predictions.
F1 score: The F1 score is a measure of the performance of a binary classification model that combines precision and recall. It is defined as the harmonic mean of precision and recall and ranges from 0 to 1, with higher values indicating better performance. The F1 score is a useful metric when there is a need to balance precision and recall, such as in cases where false positives and false negatives have different costs.
Accuracy: Accuracy is a measure of the overall performance of a classification model. It is defined as the proportion of correct predictions made by the model. Accuracy is a useful metric when the classes are balanced and there is no need to differentiate between false positive and false negative errors.
Type I error: A type I error, also known as a false positive, is a statistical error that occurs when a hypothesis test incorrectly rejects the null hypothesis. The probability of a type I error is equal to the significance level of the test.
Type II error: A type II error, also known as a false negative, is a statistical error that occurs when a hypothesis test fails to reject the null hypothesis when it is actually false. The probability of a type II error is equal to beta.
Power: The power of a hypothesis test is the probability of correctly rejecting the null hypothesis when it is false. It is equal to 1 minus the probability of a type II error and is an important consideration in the design of hypothesis tests.
P-value: The p-value is a measure of the strength of the evidence against the null hypothesis in a hypothesis test. It is the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. A small p-value indicates that the observed data are unlikely to have occurred by chance and provides strong evidence against the null hypothesis.
One-tailed test: A one-tailed test is a hypothesis test in which the alternative hypothesis specifies the direction of the effect. For example, a one-tailed test might test the hypothesis that the mean of a population is greater than a certain value. One-tailed tests are used when the direction of the effect is known or expected based on previous research or theory.
Two-tailed test: A two-tailed test is a hypothesis test in which the alternative hypothesis does not specify the direction of the effect. For example, a two-tailed test might test the hypothesis that the mean of a population is different from a certain value. Two-tailed tests are used when the direction of the effect is not known or expected.