Statistical Tests for Data Analysis

Statistical tests are essential tools in data analysis, helping to determine relationships and differences within data. Understanding these tests enhances collaborative data science efforts, allowing teams to make informed decisions based on solid statistical evidence.

1. T-test

   • Compares the means of two groups to determine if they are statistically different from each other.
   • Types include independent, paired, and one-sample t-tests, each serving different scenarios.
   • Assumes normal distribution of data and equal variances for independent samples.
   • Commonly used in experiments to assess the effect of treatments or interventions.

2. ANOVA (Analysis of Variance)

   • Tests for differences in means among three or more groups.
   • Helps identify if at least one group mean is significantly different from the others.
   • Variants include one-way ANOVA (one independent variable) and two-way ANOVA (two independent variables).
   • Assumes normality and homogeneity of variances across groups.

3. Chi-square test

   • Assesses the association between categorical variables.
   • Compares observed frequencies in each category to expected frequencies under the null hypothesis.
   • Useful for contingency tables and goodness-of-fit tests.
   • Requires a minimum sample size and expected frequency in each category.

4. Correlation analysis

   • Measures the strength and direction of the relationship between two continuous variables.
   • The correlation coefficient (e.g., Pearson's r) ranges from -1 to 1, indicating negative, no, or positive correlation.
   • Does not imply causation; correlation does not equal causation.
   • Useful for exploratory data analysis to identify potential relationships.

5. Linear regression

   • Models the relationship between a dependent variable and one independent variable using a linear equation.
   • Estimates the slope and intercept to predict outcomes based on input values.
   • Assumes linearity, independence, homoscedasticity, and normality of residuals.
   • Widely used for forecasting and trend analysis.

6. Multiple regression

   • Extends linear regression to include multiple independent variables.
   • Assesses the impact of several predictors on a single outcome variable.
   • Helps control for confounding variables and understand complex relationships.
   • Assumes similar conditions as linear regression, with added complexity in interpretation.

7. Logistic regression

   • Used for binary outcome variables to model the probability of an event occurring.
   • Estimates the relationship between one or more independent variables and a binary dependent variable.
   • Outputs odds ratios, which indicate the change in odds for a one-unit change in the predictor.
   • Assumes independence of observations and a linear relationship between the logit of the outcome and predictors.

8. Mann-Whitney U test

   • A non-parametric test that compares differences between two independent groups.
   • Used when data does not meet the assumptions of the t-test, particularly for ordinal data or non-normal distributions.
   • Ranks all data points and assesses whether one group tends to have higher or lower values than the other.
   • Useful in small sample sizes or when data is skewed.

9. Kruskal-Wallis test

   • A non-parametric alternative to one-way ANOVA for comparing three or more independent groups.
   • Tests whether samples originate from the same distribution without assuming normality.
   • Ranks data and evaluates differences in medians across groups.
   • Ideal for ordinal data or when assumptions of ANOVA are violated.

10. F-test

    • Compares variances between two or more groups to assess if they are significantly different.
    • Commonly used in ANOVA to determine if group means are equal based on variance.
    • Assumes normal distribution and homogeneity of variances.
    • Helps in model selection and validation in regression analysis.