STATISTICS: Bivariate Analysis

Parametric test of means

Statistical tests used to compare means assuming a specific distribution of the data.

Non-parametric test of medians

Statistical tests used to compare medians without assuming a specific distribution of the data.

Pearson Correlation Coefficient

Measures the statistical relationship between two continuous variables.

Linear Regression

Predictive analysis to determine the relationship between predictor variables and an outcome variable.

Spearman Correlation Coefficient (rho)

Nonparametric measure of association between two variables on an ordinal scale.

Kendall Correlation Coefficient (tau)

Nonparametric measure of association between two variables on an ordinal scale.

Mann-Whitney U test

Compares differences between two independent groups with ordinal or continuous data.

Wilcoxon matched-pairs signed-ranks test

Nonparametric test to compare two sets of scores from the same participants.

Kruskal-Wallis test

Nonparametric test to compare more than two independent groups on a continuous or ordinal dependent variable.

McNemar chi-square test

Determines differences on a dichotomous dependent variable between two related groups.

T-test

Compares means of two groups; can be one-sample, two-sample, or paired.

ANOVA (F-test)

Compares statistical models fitted to data to identify the best fit for the population.

Chi-square test

Used for testing relationships between categorical variables.

Simple Linear Regression

Which variables are significant predictors of the outcome variable, and in what way do they indicated by the magnitude and sign of the beta estimates-impact the outcome variable?

Multiple Linear Regression

1 dependent variable (interval or ratio), 2+ independent variables (interval or ratio or dichotomous)

Logistic Regression

1 dependent variable (dichotomous), 2+ independent variable(s) (interval or ratio or dichotomous)

Ordinal Regression

1 dependent variable (ordinal), 1+ independent variable(s) (nominal or dichotomous)

Multinomial Regression

1 dependent variable (nominal), 1+ independent variable(s) (interval or ratio or dichotomous)

Discriminant Analysis

1 dependent variable (nominal), 1+ independent variable(s) (interval or ratio)

Mann-Whitney U test

Appropriate test if the first variable is ordinal and the second variable is dichotomous.

Bivariate Analysis

It is used to find patterns, relationships, and associations between two variables. This can aid in making predictions and inferences.

Correlation Coefficient

Measures the strength and direction of the relationship between two continuous variables

Scatter Plots

Visual representation showing the relationship between two continuous variables.

Simple Linear Regression

Models the linear relationship between two continuous variables.

Steps in Bivariate Analysis

Define the variable, select the appropriate technique, visualize data, compute statistical measure, and interpret the results.

Correlation

Indicates the degree to which two variables move in relation to each other.

Regression Analysis

A statistical method to model and analyze the relationships between variables.

Linearity

Assumption that the relationship between variables is linear, which can be assessed using scatter plots or correlation coefficients.

Homoscedasticity

The variance of residuals should be constant across all levels of the independent variable.

Independence

This is crucial for valid inferential statistics.

Confidence intervals

Provide a range within which the true value of the parameter lies with a certain level of confidence.

p-Value

Indicates the probability that the observed relationship is due to chance.

Applications of Bivariate Analysis

Business and Economics, Healthcare, and Social Sciences.

Outliers

It can significantly affect the results of bivariate analysis.

Challenges and consideration in using Bivariate Analysis

Outliers, Non-linearity, and confounding variables

Ethical Considerations in using Bivariate Analysis

Transparency, Bias and Fairness

Cross tabulation (Contingency tables)

Displays the frequency distribution of variables.

Normality

Assumption that the data is normally distributed.

Healthcare

Studying the relationship between patient age and recovery time, or smoking and lung cancer incidence.

Social Sciences

Investigating the relationship between education level and income, or social media use and mental health.