# Statistics

## 1. Descriptive Statistics

Descriptive statistics summarize and organize characteristics of a dataset.

* **Mean**: Average of the data
* **Median**: Middle value when sorted
* **Mode**: Most frequent value
* **Standard Deviation (SD)**: Spread of data around the mean
* **Variance**: Squared standard deviation
* **Range**: Difference between max and min
* **Interquartile Range (IQR)**: Range of the middle 50% of the data

## 2. Inferential Statistics

Inferential statistics make predictions or inferences about a population based on a sample.

* **Hypothesis Testing**: T-tests, ANOVA
* **Confidence Intervals**: Estimate of population parameters
* **P-value**: Probability of obtaining observed results if the null hypothesis is true
* **Effect Size**: Quantifies the magnitude of a difference (e.g., Cohen's d)

## 3. Probability Distributions

* **Normal Distribution**: Symmetrical, bell-shaped
* **Binomial Distribution**: Discrete distribution for binary outcomes
* **Poisson Distribution**: Counts of events in a fixed interval
* **Exponential Distribution**: Time between events in a Poisson process

## 4. Correlation and Regression

* **Correlation**: Measures linear relationship between variables (e.g., Pearson's r)
* **Simple Linear Regression**: One independent variable predicting one dependent variable
* **Multiple Linear Regression**: Multiple predictors

## 5. Categorical Data Analysis

* **Chi-square Test**: Tests association between categorical variables
* **Contingency Table**: Frequency distribution for categorical variables
* **Odds Ratio / Relative Risk**: Measures of association

## 6. Statistical Assumptions

* **Normality**: Data should be normally distributed for parametric tests
* **Homoscedasticity**: Equal variances across groups
* **Independence**: Observations should be independent

## 7. Sampling Methods

* **Random Sampling**: Every member has an equal chance
* **Stratified Sampling**: Dividing population into subgroups
* **Cluster Sampling**: Randomly selecting entire groups

## 8. Common Statistical Tests

| Test            | Use Case                                  |
| --------------- | ----------------------------------------- |
| T-test          | Comparing two group means                 |
| ANOVA           | Comparing multiple group means            |
| Chi-square test | Association between categorical variables |
| Mann-Whitney U  | Non-parametric test for two groups        |
| Kruskal-Wallis  | Non-parametric ANOVA                      |
