Statistical Tests Explained

• Statistical tests are tools used to analyze data and draw conclusions.

Descriptive Statistics

• Used to summarize dataset features
• Provides measures of central tendency and variability
• Example: Calculating average age and standard deviation of students in a class

Z-Test

• Used with large samples and known population variance
• Compares a sample mean to a known population mean
• Example: Testing if average customer spending differs from the known population average

T-Test (Student's)

• Used with smaller samples and unknown population variance
• Compares means from two groups
• Example: Comparing girls' heights with boys' heights

Paired T-Test

• Used when comparing two related samples
• Assesses the difference in means between paired observations
• Example: Comparing the weight of infants before and after a feed

Welch's T-Test

• Used when there are unequal variances and/or sample sizes
• T-test adaptation for unequal variances
• Example: Comparing test scores between two classes with different sizes

Chi-Squared Test

• Used for categorical data analysis
• Tests the association between categorical variables
• Example: Assessing whether acceptance into medical school is related to an applicant's country of birth

Fisher's Exact Test

• Used with small samples and 2x2 contingency tables
• Tests the association between classifications
• Example: Analyzing if a new drug is effective in a small clinical trial

Mann-Whitney U Test

• A non-parametric test for two groups
• Compares two independent groups
• Example: Comparing customer satisfaction scores between two product lines

ANOVA

• Used when comparing means of 3+ groups
• Analyzes variance between multiple groups
• Example: Determining if plasma glucose level differs at one, two, or three hours after a meal

Kruskal-Wallis Test

• A non-parametric alternative to ANOVA
• Compares 3+ independent samples
• Example: Comparing satisfaction levels across different departments in a company

Pearson's Correlation

• Used for measuring the association between variables
• Assesses linear relationship strength
• Example: Assessing whether plasma HbA1 concentration is related to plasma triglyceride concentration in diabetic patients

Spearman's Rank Correlation

• A non-parametric correlation method
• Measures monotonic relationship strength
• Example: Analyzing the relationship between education level and income

Simple Linear Regression

• Used to find the relationship between two variables
• Models linear relationship between variables
• Example: Seeing how peak expiratory flow rate varies with height

Multiple Regression

• Used with one dependent and multiple independent variables
• Predicts dependent variable from multiple predictors
• Example: Determining how age, body fat, and sodium intake influence blood pressure

Logistic Regression

• Used with a binary dependent variable
• Predicts the probability of a binary outcome
• Example: Predicting the likelihood of heart disease based on various health factors

Factor Analysis

• Used for identifying underlying factors
• Reduces variables to a smaller set of factors
• Example: Identifying underlying personality traits from a set of survey questions