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

Continuous Probability Distribution

Ex.

Normal

Exponential

Uniform

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

Takes countable values

Takes a infinite number of values within a range

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])