# Statistics Help

## Cox Regression

Cox Regression Cox regression, also known as the Cox proportional hazards model, is a statistical technique used to explore the relationship between the survival time of subjects and one or more predictor variables. It is used in medical research, particularly for time-to-event data, where the goal is to investigate how certain factors influence the time […]

## Exploratory Factor Analysis

Exploratory Factor Analysis Exploratory Factor Analysis (EFA) is a statistical technique to identify underlying relationships between measured variables. It aims to uncover the latent structure (factors) within a set of observed variables without imposing any preconceived structure on the outcome. EFA is often employed in the early stages of research to explore a dataset’s dimensionality […]

## Confirmatory Factor Analysis

Confirmatory Factor Analysis Confirmatory Factor Analysis (CFA) is a statistical technique used to test the hypothesis that a relationship exists between observed variables and their underlying latent constructs. Unlike Exploratory Factor Analysis (EFA), which explores the data to identify potential underlying structures without preconceived notions, CFA confirms whether the data fit a hypothesized measurement model. […]

## Hierarchical Linear Modeling

Hierarchical Linear Modeling Hierarchical Linear Modeling (HLM), also known as multilevel modeling or mixed-effects modeling, is a statistical technique used to analyze nested data. This approach is particularly useful when dealing with data where observations are grouped at multiple levels, such as students within classrooms, employees within companies, or patients within hospitals. HLM accounts for […]

## Time Series Analysis

Time series analysis is a statistical technique used to analyze data points collected or recorded at specific intervals. Unlike other data types, time series data are chronological, meaning each data point depends on the preceding values. This characteristic makes time series analysis particularly useful for identifying trends, cycles, and seasonal patterns and forecasting future values […]

## Moderation Analysis

Moderation analysis is a statistical technique used to examine whether the strength or direction of the relationship between an independent variable (X) and a dependent variable (Y) changes across levels of a third variable, known as the moderator (M). It explores the conditions under which specific effects occur, offering insights into the variability of the […]

## Mediation Analysis

Mediation Analysis Mediation analysis is a statistical method used to understand the mechanism through which an independent variable (X) influences a dependent variable (Y) via a third variable, known as the mediator (M). It helps researchers determine whether the presence of M can wholly or partially explain the relationship between X and Y. The classic […]

## Structural Equation Modeling

Structural Equation Modeling Structural Equation Modeling (SEM) is a statistical technique that allows researchers to examine complex relationships among observed and latent variables. It is a comprehensive method that combines factor analysis and multiple regression analysis, enabling the analysis of both measurement and structural models simultaneously. In simpler terms, SEM allows us to understand the […]

## One-Way ANOVA

One-Way ANOVA If you aim to investigate whether there are any statistically significant distinctions in the means of two or more distinct groups, you can employ a one-way analysis of variance (ANOVA). For instance, consider a situation where you wish to determine if there are variations in the performance of athletes in a track event […]

## Binomial Logistic Regression

Binomial Logistic Regression Binomial logistic regression is a statistical test for predicting the likelihood of an observation belonging to one of two possible categories of a binary dependent variable. This prediction is based on one or more independent variables, which can be continuous or categorical. This form of regression shares similarities with linear regression, except […]

## Two-Way ANCOVA

Two-Way ANCOVA The two-way ANCOVA is a statistical test to assess whether there is an interaction effect between two distinct, independent variables on a continuous dependent variable. In simpler terms, it helps us understand if these two variables have a combined influence on the outcome. This analysis considers one or more continuous covariates and additional […]

## One-Way MANCOVA

One-Way MANCOVA The one-way multivariate analysis of covariance (one-way MANCOVA) extends the capabilities of the one-way MANOVA and one-way ANCOVA by incorporating either a continuous covariate or multiple dependent variables. This addition enhances the sensitivity of the analysis to detect differences among groups of a categorical independent variable. The one-way MANCOVA is employed to determine […]

## HMR

Hierarchical Multiple Regression Like standard multiple regression, hierarchical multiple regression (also known as sequential multiple regression) allows you to predict a dependent variable based on multiple independent variables. However, the procedure that it uses to do this in SPSS Statistics, and the goals of hierarchical multiple regression, are different from standard multiple regression. In standard multiple regression, […]

## PCA

Principal Components Analysis Principal components analysis (i.e., PCA) is a variable-reduction technique that shares many similarities to exploratory factor analysis. Its aim is to reduce a larger set of variables into a smaller set of ‘artificial’ variables (called principal components) that account for most of the variance in the original variables. Although principal components analysis […]

## Two-Way MANOVA

Two-Way MANOVA The two-way multivariate analysis of variance (MANOVA) is an analytical technique that extends the principles of the two-way ANOVA to scenarios with multiple dependent variables. It is particularly useful in determining how two independent variables interact in their combined influence on several dependent variables. For example, consider a study to evaluate the impact […]

## One-Way RM ANOVA

One-Way Repeated Measures ANOVA The one-way repeated measures analysis of variance (ANOVA) is a statistical technique that extends the concept of the paired-samples t-test. It is utilized to identify if there are any significant differences between the means of three or more levels of a within-subjects factor, where the same cases (such as participants) are […]

## Two-Way ANOVA

Two-Way ANOVA The two-way ANOVA is an extension of the one-way ANOVA that assesses the interaction effect between two independent variables on a continuous dependent variable. It is also called a “factorial ANOVA” or, more specifically, a “two-way between-subjects ANOVA.” In the context of an experiment, the two-way ANOVA can be extremely useful in understanding […]

## One-Way MANOVA

One-Way MANOVA The one-way multivariate analysis of variance (MANOVA) is a statistical method that extends the one-way ANOVA by accommodating two or more dependent variables instead of one. The one-way MANOVA assesses the differences in a combined set of dependent variables, known as a ‘linear composite’ or vector, across groups defined by an independent variable. […]

## One-Way ANCOVA

One-Way ANCOVA ANCOVA is a statistical method that extends the one-way ANOVA to include a covariate variable. This covariate is linearly related to the dependent variable, and its inclusion into the analysis can increase the accuracy of detecting differences between groups of an independent variable. ANCOVA can be used in various scenarios. For instance, suppose […]

## Two-Way RM ANOVA

Two-Way Repeated Measures ANOVA  The two-way repeated measures ANOVA is a statistical test used to identify whether there is a significant interaction effect between two within-subjects factors on a continuous dependent variable. This type of ANOVA extends the one-way repeated measures ANOVA, which considers only one within-subjects factor. In this guide, we will refer to […]

## Three-Way RM ANOVA

Three-Way Repeated Measures ANOVA The three-way repeated measures ANOVA is a robust statistical test used in experimental psychology and other scientific fields. The three-way repeated measures ANOVA enables researchers to explore complex interactions among three within-subject factors on a continuous outcome, thus extending the capabilities of the two-way repeated measures ANOVA by incorporating an additional […]

## Independent-Samples T-Test

Independent-Samples T-Test The independent-samples t-test is used to determine if a difference exists between the means of two independent groups on a continuous dependent variable. More specifically, it will let you determine whether the difference between these two groups is statistically significant. This test is also known by a number of different names, including the […]

## Multiple Regression Analysis

Multiple Regression A multiple regression is used to predict a continuous dependent variable based on multiple independent variables. As such, it extends simple linear regression, which is used when you have only one continuous independent variable. Multiple regression also allows you to determine the overall fit (variance explained) of the model and the relative contribution of […]

## Regression Analysis

Regression Analysis A simple linear regression analysis is a statistical method that helps to predict the value of a dependent variable based on the value of an independent variable. It assesses the linear relationship between two continuous variables and provides insights into the relationship’s direction, magnitude, and statistical significance. For instance, you can use simple […]

## Correlation Analysis

Correlation Analysis The correlation analysis is used to determine the strength and direction of a linear relationship between two continuous variables. More specifically, the test generates a coefficient called the Pearson correlation coefficient, denoted as r (i.e., the italic lowercase letter r), and it is this coefficient that measures the strength and direction of a linear […]

## Paired-Samples T-Test

Paired-Samples T-Test The paired-samples t-test serves the purpose of assessing whether the mean discrepancy between interconnected observations is statistically significant. These observations may involve the same individuals evaluated at two distinct time points or be subjected to two conditions concerning the same dependent variable. Alternatively, you might have two sets of participants matched based on […]

## Chi-Square Test

Chi-Square Test The chi-square test can be used to test a variety of sizes of contingency tables, as well as more than one type of null and alternative hypotheses. This guide focuses on contingency tables that are greater than 2 x 2, which are often referred to as r x c contingency tables, and tests whether […]

## Kaplan-Meier Analysis

Kaplan-Meier Analysis The Kaplan-Meier analysis (Kaplan & Meier, 1958) (also known as the “product-limit method”) is a nonparametric method used to estimate the probability of survival past given time points (i.e., it calculates a survival distribution). Furthermore, the survival distributions of two or more groups of a between-subjects factor can be compared for equality. For […]

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