R + Stats

The Following course material is very useful for R + Stats Combinations. It's a great material for R learning. Captured below are notes from 5,6,7,8 chapters

What is a central limit theorem?

The central limit theorem states that the sampling distribution of the mean of any independent, random variable will be normal or nearly normal. In practice, some statisticians say that a sample size of 30 is large enough when the population distribution is roughly bell-shaped

Binomial Probability - Only two mutually exclusive events often referred as success, failure. Also called bernouli trial (Link )

R commands - The dbinom and pbinom functions

Discrete Probability Distributions

R command - pnorm

Command Syntax - pnorm(x, mean = , sd = , lower.tail= )

Two-Tailed Tests - Testing for the possibility of the relationship in both directions. This means that .025 is in each tail of the distribution

One-Tailed Tests - one-tailed test allots all of your alpha to testing the statistical significance in the one direction of interest. This means that .05 is in one tail of the distribution of your test statistic.

Alternative hypothesis has the > operator, right-tailed test 

Right-Tailed Tests: P-value = pnorm(zx¯, lower.tail=FALSE)

Alternative hypothesis has the < operator, left-tailed test 

Left-Tailed Tests: P-value = pnorm(zx¯, lower.tail=TRUE)

Alternative hypothesis has the ≠ operator, two-tailed (left and right) test

Two-Tailed Tests: P-value = 2 * pnorm( abs(zx¯), lower.tail=FALSE)

pnorm(x, µ, σ), 

• x is an observation from a normal distribution 
• mean µ 
• standard deviation σ

Computing P value from t value 

pt(abs(t-value), df=degree of freedom)

Reference

Link1

Link2

Happy Learning!!!