Statistical Analysis Methods Flashcards: Definitions and Key Characteristics
Correlation Analysis
Definition:
Correlation analysis measures the degree and direction of association between two variables. It tells us if the variables move together (positive correlation), move in opposite directions (negative correlation), or have no relationship (zero correlation).
Key Characteristics:
It provides a numerical value called the correlation coefficient, ranging from -1 to +1. A correlation coefficient close to -1 or +1 indicates a strong relationship, while a value close to 0 suggests a weak or no relationship.
Simple Linear Regression
Definition:
Simple linear regression predicts the value of one variable based on the value of another variable. It assumes a linear relationship between the two variables, meaning that a change in one variable is associated with a proportional change in the other.
Key Characteristics:
The regression equation takes the form of Y = a + bX, where Y is the dependent variable, X is the independent variable, ‘a’ is the intercept, and ‘b’ is the slope of the line. The regression line minimizes the squared differences between observed and predicted values.
Multiple Linear Regression
Definition:
Multiple linear regression extends simple linear regression to predict the value of a dependent variable based on two or more independent variables. It allows for the simultaneous consideration of multiple predictors in the prediction model.
Key Characteristics:
The regression equation becomes more complex, incorporating multiple independent variables. It estimates the contribution of each predictor while controlling for the effects of other variables in the model.
Chi-square Test of Independence
Definition:
The chi-square test of independence assesses whether there is a significant association between two categorical variables. It compares observed frequencies with expected frequencies to determine if the variables are independent of each other.
Key Characteristics:
It produces a chi-square statistic and a p-value. A significant p-value indicates that there is a relationship between the variables, while a non-significant p-value suggests independence.
Logistic Regression:
Definition:
Logistic regression predicts the probability of a binary outcome (e.g., yes/no, success/failure) based on one or more independent variables. It models the relationship between the predictors and the probability of belonging to a particular category.
Key Characteristics:
The logistic function transforms the linear regression equation to constrain predicted probabilities between 0 and 1. It provides odds ratios, indicating the change in odds of the outcome for a one-unit change in the predictor.
Spearman’s Rank-Order Correlation:
Definition:
Spearman’s rank-order correlation assesses the strength and direction of the monotonic relationship between two variables. It does not assume linearity and is suitable for ordinal or interval variables.
Key Characteristics:
It uses rank-order data instead of actual values, making it robust to outliers and non-normal distributions. The correlation coefficient ranges from -1 to +1, with higher absolute values indicating stronger associations.
Partial Correlation
Definition:
Partial correlation measures the relationship between two variables while controlling for the influence of one or more additional variables. It helps isolate the unique association between the variables of interest.
Key Characteristics:
By removing the shared variance with other variables, partial correlation reveals the direct relationship between the variables under investigation. It is often used to assess the specific effect of an independent variable on the dependent variable after accounting for confounding variables.
