📊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
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
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