Complete Guide to Statistical Analysis Methods 2025

Q: What is the difference between parametric and non-parametric tests?

Parametric tests assume data follows a specific distribution (usually normal) and work with interval/ratio data. Non-parametric tests make no distribution assumptions and work with ordinal or non-normal data. Parametric tests are more powerful when assumptions are met.

Q: When should I use a t-test vs ANOVA?

Use a t-test when comparing means between two groups only. Use ANOVA when comparing means across three or more groups. ANOVA prevents inflated Type I error that occurs with multiple t-tests.

Q: What p-value indicates statistical significance?

Traditionally, p < 0.05 indicates statistical significance. However, consider your field's standards, effect sizes, and practical significance. Some fields use p < 0.01 or p < 0.001 for stronger evidence.

What is Statistical Analysis?

Statistical analysis is the science of collecting, exploring, organizing, and interpreting data to uncover patterns, test hypotheses, and make data-driven decisions. In 2025, with AI-powered tools like DataStatPro, statistical analysis has become more accessible and accurate than ever.

                🎯 Key Benefits of Statistical Analysis
                Make evidence-based decisions with confidence
Identify significant patterns and relationships in data
Validate research hypotheses scientifically
Predict future trends and outcomes
Communicate findings with statistical rigor

            

Find Your Perfect Statistical Test

Answer a few questions to get a personalized recommendation

What type of data do you have?

Comprehensive Guide to Statistical Tests

📊 T-Tests: Comparing Means

When to use: Comparing means between groups or against a known value with continuous data

Types of T-Tests:

One-sample t-test: Compare sample mean to a known population mean
Example: Is average student height different from national average?
Independent samples t-test: Compare means of two independent groups
Example: Do males and females differ in test scores?
Paired samples t-test: Compare means of same subjects at different times
Example: Is there improvement after training intervention?

⚠️ Assumptions to Check:

Data should be approximately normally distributed
Observations must be independent
For independent t-test: equal variances (use Levene's test)
No significant outliers

📈 ANOVA: Analysis of Variance

When to use: Comparing means across three or more groups

Types of ANOVA:

One-way ANOVA: One independent variable with 3+ levels
Example: Compare effectiveness of 3 teaching methods
Two-way ANOVA: Two independent variables
Example: Effect of gender AND age group on salary
Repeated measures ANOVA: Same subjects measured multiple times
Example: Patient recovery at 1, 3, and 6 months
MANOVA: Multiple dependent variables
Example: Effect on both satisfaction AND performance

Post-hoc tests: Tukey HSD, Bonferroni, Scheffé (when ANOVA is significant)

📉 Regression Analysis: Predicting Outcomes

When to use: Predicting outcomes and understanding relationships between variables

Types of Regression:

Simple Linear Regression: One predictor, continuous outcome
Example: Predict sales from advertising spend
Multiple Linear Regression: Multiple predictors, continuous outcome
Example: Predict house price from size, location, age
Logistic Regression: Binary outcome (yes/no)
Example: Predict customer churn (stay/leave)
Polynomial Regression: Non-linear relationships
Example: U-shaped relationship between stress and performance

                    💡 Key Metrics to Report:
                    R² (coefficient of determination): Model fit
β coefficients: Effect size and direction
p-values: Statistical significance
Confidence intervals: Precision of estimates

                

🔲 Chi-Square Tests: Categorical Data Analysis

When to use: Analyzing relationships between categorical variables

Types of Chi-Square Tests:

Chi-square test of independence: Are two variables related?
Example: Is gender associated with product preference?
Chi-square goodness of fit: Does data match expected distribution?
Example: Are birth days equally distributed across the week?
McNemar's test: Paired categorical data
Example: Change in voting preference before/after debate

Effect size: Cramér's V (small: 0.1, medium: 0.3, large: 0.5)

🔗 Correlation Analysis: Measuring Relationships

When to use: Measuring strength and direction of relationships between variables

Types of Correlation:

Pearson correlation: Linear relationship between continuous variables
Range: -1 to +1 (perfect negative to perfect positive)
Spearman correlation: Monotonic relationship, ordinal data
Use when: Data is ranked or non-normal
Kendall's tau: Alternative to Spearman, better for small samples
More robust but less powerful than Spearman
Point-biserial: One continuous, one binary variable
Example: Correlation between pass/fail and study hours

⚠️ Remember: Correlation ≠ Causation

A strong correlation doesn't imply one variable causes the other. Consider confounding variables and use experimental design for causal inference.

🎯 Non-parametric Tests: Distribution-Free Methods

When to use: When parametric assumptions are violated or with ordinal/ranked data

Common Non-parametric Tests:

Mann-Whitney U test: Alternative to independent t-test
Compare medians of two independent groups
Wilcoxon signed-rank test: Alternative to paired t-test
Compare paired observations
Kruskal-Wallis test: Alternative to one-way ANOVA
Compare 3+ independent groups
Friedman test: Alternative to repeated measures ANOVA
Compare 3+ related groups

Advantages: No distribution assumptions, robust to outliers, work with ordinal data

Disadvantages: Less statistical power when parametric assumptions are met

Quick Reference: Choosing the Right Test

Research Question	Data Type	Number of Groups	Recommended Test
Compare 2 group means	Continuous	2	Independent t-test
Compare 3+ group means	Continuous	3+	One-way ANOVA
Predict continuous outcome	Continuous	N/A	Linear regression
Predict binary outcome	Binary	N/A	Logistic regression
Test association	Categorical	2+	Chi-square test
Measure relationship	Continuous	N/A	Pearson correlation
Compare paired observations	Continuous	2	Paired t-test
Non-normal data comparison	Any	2+	Non-parametric tests

Understanding P-Values and Statistical Significance

What is a P-Value?

The p-value is the probability of obtaining results as extreme as observed, assuming the null hypothesis is true. It's NOT the probability that your hypothesis is correct!

Common Significance Levels:

p < 0.001: Very strong evidence against null hypothesis (***)
p < 0.01: Strong evidence against null hypothesis (**)
p < 0.05: Moderate evidence against null hypothesis (*)
p ≥ 0.05: Insufficient evidence to reject null hypothesis (ns)

                    🎯 Best Practices for Reporting P-Values:
                    Report exact p-values (e.g., p = 0.023) not just "p < 0.05"
Always include effect sizes alongside p-values
                        
Consider practical significance, not just statistical significance
Use confidence intervals for better interpretation
Adjust for multiple comparisons when appropriate (Bonferroni, FDR)

                

⚠️ Common P-Value Misconceptions:

P-value is NOT the probability the null hypothesis is true
P-value is NOT the probability your results occurred by chance
Statistical significance ≠ practical importance
Non-significant results don't prove the null hypothesis

Effect Sizes: Beyond Statistical Significance

Why Effect Sizes Matter

While p-values tell you whether an effect exists, effect sizes tell you how large and meaningful that effect is. Always report both!

Common Effect Size Measures:

Cohen's d (t-tests): Small = 0.2, Medium = 0.5, Large = 0.8
Eta squared (ANOVA): Small = 0.01, Medium = 0.06, Large = 0.14
R² (Regression): Small = 0.02, Medium = 0.13, Large = 0.26
Odds Ratio (Logistic): Small = 1.5, Medium = 2.5, Large = 4.0
Correlation r: Small = 0.1, Medium = 0.3, Large = 0.5

💡 Interpreting Effect Sizes:

Effect size interpretation depends on context. A "small" effect in medicine might be clinically important, while a "large" effect in social sciences might be typical.

Statistical Power and Sample Size

Planning Your Study: Power Analysis

Statistical power is the probability of detecting an effect if it truly exists. Aim for at least 80% power.

Factors Affecting Power:

Sample size: Larger samples = more power
Effect size: Larger effects = easier to detect
Alpha level: Higher α (e.g., 0.05 vs 0.01) = more power
One vs two-tailed: One-tailed tests have more power

                    🎯 Sample Size Guidelines:
                    T-test: ~30 per group for medium effect
ANOVA: ~20 per group for medium effect
Correlation: ~85 for medium effect (r = 0.3)
Chi-square: ~100-200 total for medium effect
Regression: 10-15 cases per predictor minimum

                

Avoid These Common Statistical Mistakes

🚫 Top 10 Statistical Errors to Avoid:

P-hacking: Running multiple tests until finding significance
Ignoring assumptions: Using parametric tests on non-normal data
Confusing correlation with causation: Inferring cause from association
Neglecting effect sizes: Focusing only on p-values
Inadequate sample size: Underpowered studies miss real effects
Multiple comparisons: Not adjusting for family-wise error
Cherry-picking results: Reporting only favorable outcomes
Misinterpreting non-significance: "No evidence" ≠ "evidence of no effect"
Ignoring outliers: Not checking for influential data points
Wrong test selection: Using ANOVA for categorical outcomes

Frequently Asked Questions

What's the difference between parametric and non-parametric tests?

Parametric tests assume your data follows a specific distribution (usually normal) and work with interval/ratio data. They include t-tests, ANOVA, and Pearson correlation. Non-parametric tests make no distribution assumptions and work with ordinal or non-normal data. They include Mann-Whitney U, Wilcoxon, and Spearman correlation. Use parametric tests when assumptions are met for more statistical power.

When should I use a t-test vs ANOVA?

Use a t-test when comparing means between exactly two groups (e.g., treatment vs control). Use ANOVA when comparing means across three or more groups (e.g., low dose vs medium dose vs high dose vs placebo). Running multiple t-tests instead of ANOVA inflates Type I error rate.

What p-value indicates statistical significance?

The traditional threshold is p < 0.05, meaning less than 5% chance of observing results this extreme if the null hypothesis were true. However, consider your field's standards and the context. Some fields use p < 0.01 or p < 0.001 for stronger evidence. Always report exact p-values and effect sizes.

How do I know if my data is normally distributed?

Check normality using: 1) Visual inspection (histogram, Q-Q plot), 2) Statistical tests (Shapiro-Wilk for n < 50, Kolmogorov-Smirnov for n > 50), 3) Skewness and kurtosis (should be between -2 and +2). For large samples (n > 30), slight deviations from normality are often acceptable due to the Central Limit Theorem.

What's the difference between Type I and Type II errors?

Type I error (false positive) occurs when you reject a true null hypothesis - finding an effect that doesn't exist. The probability is your alpha level (usually 0.05). Type II error (false negative) occurs when you fail to reject a false null hypothesis - missing a real effect. The probability is beta, and power = 1 - beta.

Should I use one-tailed or two-tailed tests?

Use two-tailed tests unless you have a strong theoretical reason to expect effects in only one direction AND you would not be interested in effects in the opposite direction. Two-tailed tests are more conservative and generally preferred in research. One-tailed tests have more power but require strong justification.

Ready to Master Statistical Analysis?

Join thousands of researchers using DataStatPro's AI-powered statistical analysis platform

Start Free Analysis → Watch Demo ▶

Complete Guide to Statistical Analysis Methods