# Tag Archives: statistics

## Type I & Type II Errors in Hypothesis Testing: Examples

This article describes Type I and Type II errors made during hypothesis testing, based on a couple of examples such as House on Fire, and Covid-19. You may want to note that it is key to understand type I and type II errors as these concepts will show up when we are evaluating a hypothesis such as those related to machine learning algorithms (linear regression, logistic regression, etc). For example, in the case of linear regression models, the significance value is compared with the p-value and, the null hypothesis that the parameter/coefficient is equal to zero is either rejected or failed to be rejected. You may want to check my …

## Data Science: P-Value Explained with Examples

Many describe p-value as the probability that the null hypothesis holds good. That is an incorrect definition. The concept of p-value is understood differently by different people and is considered as one of the most used & abused concepts in statistics. In this blog post, you will learn the P-VALUE concepts with multiple different examples. It is extremely important to get a good understanding of P-value if you are starting to learn data science/machine learning as the concepts of P-value are key to hypothesis testing. The following use cases and related hypotheses made about the population will either be accepted or rejected based on the P-VALUE: Whether a coin is fair …

## Binomial Distribution Explained with Examples

The binomial distribution is a probability distribution that applies to binomial experiments. It’s the number of successes in a specific number of tries. The binomial distribution may be imagined as the probability distribution of a number of heads that appear on a coin flip in a specific experiment comprising of a fixed number of coin flips. In this blog post, we will learn binomial distribution with the help of examples. If you are an aspiring data scientist looking forward to learning/understand the binomial distribution in a better manner, this post might be very helpful. What is a Binomial Distribution? The binomial distribution is a discrete probability distribution that represents the probabilities of binomial random …

## Poisson Distribution Explained with Python Examples

Poisson distribution is a probability distribution that can be used to model the number of events in a fixed interval. It is often referred to as “random poisson process” or “poisson process”. The poisson distribution describes how many occurrences of an event occur within a given time frame, for example, how many customers visit your store or restaurant every hour. In this post, you will learn about the concepts of Poisson probability distribution with Python examples. As a data scientist, you must get a good understanding of the concepts of probability distributions including normal, binomial, Poisson etc. What is Poisson distribution? Poisson distribution is the discrete probability distribution which represents the …

## Negative Binomial Distribution Python Examples

In this post, you will learn about the concepts of negative binomial distribution explained using real-world examples and Python code. We will go over some of the following topics to understand negative binomial distribution: What is negative binomial distribution? What is difference between binomial and negative binomial distribution? Negative binomial distribution real-world examples Negative binomial distribution Python example What is Negative Binomial Distribution? Negative binomial distribution is a discrete probability distribution representing the probability of random variable, X, which is number of Bernoulli trials required to have r number of successes. This random variable is called as negative binomial random variable. And, the experiment representing X number of Bernoulli trials required to product r successes is called …

## Geometric Distribution Explained with Python Examples

In this post, you will learn about the concepts of Geometric probability distribution with the help of real-world examples and Python code examples. It is of utmost importance for data scientists to understand and get an intuition of different kinds of probability distribution including geometric distribution. You may want to check out some of my following posts on other probability distribution. Normal distribution explained with Python examples Binomial distribution explained with 10+ examples Hypergeometric distribution explained with 10+ examples In this post, the following topics have been covered: Geometric probability distribution concepts Geometric distribution python examples Geometric distribution real-world examples Geometric Probability Distribution Concepts Geometric probability distribution is a discrete …

## Z-Score Explained with Ronaldo / Robert Example

In Champion’s league 2019-2020, here is the data related to their performance (ESPN.in). Player No. of Matches Played No. of Goals Scored Avg Goals / Matches Christiano Ronaldo 8 4 0.5 Robert Lewandowski 10 15 1.5 Table 1. Ronaldo / Robert performance in 2019-2020 Champion’s League . Well, the average goals / match indicates that Robert Lewandowski played much better than Christiano Ronaldo. However, can we conclude the same using statistical measures? How could we find out if they performed better than their own performance over last 7-8 years? This is where Z-Score comes into picture. In above evaluation, what is used to compare the performance is average goals / …

## Python – How to Add Trend Line to Line Chart / Graph

In this plot, you will learn about how to add trend line to the line chart / line graph using Python Matplotlib.As a data scientist, it proves to be helpful to learn the concepts and related Python code which can be used to draw or add the trend line to the line charts as it helps understand the trend and make decisions. In this post, we will consider an example of IPL average batting scores of Virat Kohli, Chris Gayle, MS Dhoni and Rohit Sharma of last 10 years, and, assess the trend related to their overall performance using trend lines. Let’s say that main reason why we want to …

## Beta Distribution Explained with Python Examples

In this post, you will learn about Beta probability distribution with the help of Python examples. As a data scientist, it is very important to understand beta distribution as it is used very commonly as prior in Bayesian modeling. In this post, the following topics get covered: Beta distribution intuition and examples Introduction to beta distribution Beta distribution python examples Beta Distribution Intuition & Examples Beta distribution is widely used to model the prior beliefs or probability distribution in real world applications. Here is a great article on understanding beta distribution with an example of baseball game. You may want to pay attention to the fact that even if the baseball …

## Bernoulli Distribution Explained with Python Examples

In this post, you will learn about the concepts of Bernoulli Distribution along with real-world examples and Python code samples. As a data scientist, it is very important to understand statistical concepts around various different probability distributions to understand the data distribution in a better manner. In this post, the following topics will get covered: Introduction to Bernoulli distribution Bernoulli distribution real-world examples Bernoulli distribution python code examples Introduction to Bernoulli Distribution Bernoulli distribution is a discrete probability distribution representing the discrete probabilities of a random variable which can take only one of the two possible values such as 1 or 0, yes or no, true or false etc. The probability of …

## Joint & Conditional Probability Explained with Examples

In this post, you will learn about joint and conditional probability differences and examples. When starting with Bayesian analytics, it is very important to have a good understanding around probability concepts. And, the probability concepts such as joint and conditional probability is fundamental to probability and key to Bayesian modeling in machine learning. As a data scientist, you must get a good understanding of probability related concepts. Joint & Conditional Probability Concepts In this section, you will learn about basic concepts in relation to Joint and conditional probability. Probability of an event can be quantified as a function of uncertainty of whether that event will occur or not. Let’s say an event A is …

## What, When & How of Scatterplot Matrix in Python

In this post, you will learn about some of the following in relation to scatterplot matrix. Note that scatter plot matrix can also be termed as pairplot. Later in this post, you would find Python code example in relation to using scatterplot matrix / pairplot (seaborn package). What is scatterplot matrix? When to use scatterplot matrix / pairplot? How to use scatterplot matrix in Python? What is Scatterplot Matrix? Scatter plot matrix is a matrix (or grid) of scatter plots where each scatter plot in the grid is created between different combinations of variables. In other words, scatter plot matrix represents bi-variate or pairwise relationship between different combinations of variables …

## Standard Deviation of Population & Sample – Python

In this post, you will learn about the statistics concepts of standard deviation with the help of Python code example. The following topics are covered in this post: What is Standard deviation? Different techniques for calculating standard deviation Standard deviation of population vs sample What is Standard Deviation? The Standard Deviation (SD) of a data set is a measure of how spread out the data is. Take a look at the following example using two different samples of 4 numbers whose mean are same but the standard deviation (data spread) are different. Here is the code for calculating the mean of the above sample. One can either write Python code …

## Difference between True Error & Sample Error

In this post, you will learn about some of the following in relation to evaluating a discrete-valued hypothesis when learning hypothesis (building models) using different machine learning algorithms. The discrete-valued hypothesis could also be understood as classification models built using machine learning algorithms and used to classify an instance drawn at random. What is a true error or true risk? What is a sample error or empirical risk? Difference between true error and sample error How to estimate the true error? In case you are a data scientist, you will want to understand the concept behind the true error and sample error. These concepts are key to understand for evaluating …

## Hypergeometric Distribution Explained with 10+ Examples

In this post, we will learn Hypergeometric distribution with 10+ examples. The following topics will be covered in this post: What is Hypergeometric Distribution? 10+ Examples of Hypergeometric Distribution If you are an aspiring data scientist looking forward to learning/understand the binomial distribution in a better manner, this post might be very helpful. The Binomial distribution can be considered as a very good approximation of the hypergeometric distribution as long as the sample consists of 5% or less of the population. One would need a good understanding of binomial distribution in order to understand the hypergeometric distribution in a great manner. I would recommend you take a look at some of my related posts on …

## Beta Distribution Example for Cricket Score Analysis

This post represents a real-world example of Binomial and Beta probability distribution from the sports field. In this post, you will learn about how the run scored by a Cricket player could be modeled using Binomial and Beta distribution. Ever wanted to predict the probability of Virat Kohli scoring a half-century in a particular match. This post will present a perspective on the same by using beta distribution to model the probability of runs that can be scored in a match. If you are a data scientist trying to understand beta and binomial distribution with a real-world example, this post will turn out to be helpful. First and foremost, let’s identify the random variable that we would like …