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Statistical Techniques Using R - Coggle Diagram
Statistical Techniques Using R
Types Of Distributions
Normal Distribution
Symmetric, bell-shaped Curve
Mean = Median = Mode
Parameters: Mean (μ), Standard deviation (σ)
Binomial Distribution
For binary outcomes (success / failure)
Parameters: n (numbers of trials), p (probability of success)
Poisson Distribution
For counting events in a fixed interval
Parameters: λ (rate of occurrence)
Exponential Distribution
Time between events in a Poisson process
Parameters: λ (rate parameter)
Probability Distributions
Discrete Probability Distribution
Ex.
Binomial
Poisson
Geometric
Takes countable values
Continuous Probability Distribution
Ex.
Normal
Exponential
Uniform
Takes a infinite number of values within a range
Parametric Tests
T - Test
Test if means of two groups are equal
Z - Test
For large samples (n > 30))
ANOVA (Analysis Of Variance)
Compares means of multiple groups
Probability Concepts
Probability Density Function (PDF)
For continuous random variables
Area under the curve = 1
Probability Mass Function (PMF)
For discrete random variables
Cumulative Distribution Function (CDF)
Gives the probability that a random variable is less than or equal to a certain value
Non - Parametric Test
Chi - Square Test
Test association between categorical variables
Mann - Whitney U test
Non-parametric alternative to T-test
Wilcoxon Signed - Rank Test
For paired samples
Kruskal - Wallis Test
Non-parametric alternative to ANOVA
Hypothesis Testing
Null Hypothesis [H0]
No effect or difference
Alternative Hypothesis [H1]
There is an effect or difference
P - Value
Probability of obtaining extreme results under [H0]
Confidence Intervals
Range of values likely to contain the population parameter
Steps in Hypothesis Testing
Formulate Hypothesis (H) and H1)
Choose Significance level (α)
Choose Test (T-test, Z-test, etc.)
Compute Test Statistics
Decision (Reject / Fail to Reject [H0])
