Statistics Calculator Comprehensive statistical analysis including descriptive statistics, probability distributions, hyp...
Statistics Calculator
Comprehensive statistical analysis including descriptive statistics, probability distributions, hypothesis testing, and regression analysis.
Descriptive Statistics summarize and describe the main features of a dataset.
Probability Distributions describe how probabilities are distributed over the values of a random variable.
Hypothesis Testing is a method of statistical inference used to test hypotheses about population parameters.
Regression Analysis examines the relationship between dependent and independent variables.
✅ When to Use What**:
- Descriptive**: Initial data exploration and summary
- Probability**: Understanding likelihood of events
- Hypothesis Testing**: Making decisions about populations
- Regression**: Predicting outcomes and relationships
⚠️ Avoid these critical errors:
- Confusing correlation with causation**: Correlation doesn't imply causation
- p-hacking**: Manipulating data to achieve statistical significance
- Small sample sizes**: Results may not be representative
- Ignoring assumptions**: Each test has specific assumptions that must be met
- Multiple comparisons**: Increases chance of false positives
✅ Best Practices**:
- Always visualize your data before analysis
- Check assumptions for each statistical test
- Report effect sizes along with p-values
- Use appropriate corrections for multiple comparisons
- Consider confidence intervals for more robust inference
Statistical analysis is essential in:
- Business**: Market research, quality control, forecasting
- Healthcare**: Clinical trials, epidemiology, diagnostic testing
- Science**: Experimental design, data analysis, hypothesis testing
- Finance**: Risk assessment, portfolio optimization, econometrics
- Government**: Census analysis, policy evaluation, economic indicators
📊 Example Use Cases**:
- A/B Testing**: Determine if new website design increases conversion
- Quality Control**: Monitor manufacturing process for defects
- Clinical Research**: Test effectiveness of new medication
- Economic Forecasting**: Predict GDP growth and unemployment rates
➡️ Descriptive Statistics
"Analyze test scores [85, 92, 78, 96, 88]" → Mean=87.8, Std Dev=7.1
➡️ Probability Distributions
"Normal distribution, x=1.5, df=10" → P(X≤1.5)=0.919
➡️ Hypothesis Testing
"Sample mean=85.5, n=25, α=0.05" → Reject null hypothesis
➡️ Regression Analysis
"X=[1,2,3,4,5], Y=[2,4,5,4,5]" → y = 2.2 + 0.6x, R²=0.64
Note: The calculator handles data cleaning, validation, and provides comprehensive statistical analysis with visualizations.