Kernel density plots with ggplot2 in R

Kernel density function is a nonparametric method to find the drawing density curve of random samples, and it is often used to draw a smoothed curve in data visualization. In R programming with ggplot2 package, a chaining of functions ggplot() and geom_density() is often used to draw different smoothed curves showing the distribution of continuous variables.

Using a function with a while loop in Python

A function in Python is a group of code statements wrapped together to perform specific tasks. After a function is defined, then it can be called by passing real values to its arguments and get the returning results. A while loop in Python is a group of conditional statements bundled in a statement beginning with keyword ‘while’, and the codes will run forever until the condition returns false. By including a user-defined function inside a while loop in Python, many iterative tasks can be fulfilled.

Calculating Type I Error and Type II Error in Hypothesis Testing using Python

In hypothesis testing, the possibility of the other side than the conclusion usually exists, and the analysis commits so-called Type I and Type II errors, with respect to the truth and the decision made upon the random sample and hypotheses. In particular, a Type I error measures the probability that a true Null hypothesis (H0) is incorrectly rejected, and a Type II error says the probability that a false H0 not being rejected, respectively.

Calculating The Power of a Test in Hypothesis Testing with R

In hypothesis testing, the analyst has chance to commit both Type I and Type II errors. The Type I error (α) refers to the probability of wrongly rejecting a true Null hypothesis – H0, while the Type II error (ß) represents the probability that failing to reject a false H0. The value of 1- ß is called the Power of Test in hypothesis testing. Its value says the ability of correctly rejecting a false H0, under the specified Null hypothesis – H0 and Alternative hypothesis – H1.