# Category Archives: statistics

## Neyman-Pearson Lemma: Hypothesis Test, Examples

Have you ever faced a crucial decision where you needed to rely on data to guide your choice? Whether it’s determining the effectiveness of a new medical treatment or assessing the quality of a manufacturing process, hypothesis testing becomes essential. That’s where the Neyman-Pearson Lemma steps in, offering a powerful framework for making informed decisions based on statistical evidence. The Neyman-Pearson Lemma holds immense importance when it comes to solving problems that demand decision making or conclusions to a higher accuracy. By understanding this concept, we learn to navigate the complexities of hypothesis testing, ensuring we make the best choices with greater confidence. In this blog post, we will explore …

## Pearson Correlation Coefficient: Formula, Examples

In the world of data science, understanding the relationship between variables is crucial for making informed decisions or building accurate machine learning models. Correlation is a fundamental statistical concept that measures the strength and direction of the relationship between two variables. However, without the right tools and knowledge, calculating correlation coefficients and p-values can be a daunting task for data scientists. This can lead to suboptimal decision-making, inaccurate predictions, and wasted time and resources. In this post, we will discuss what Pearson’s r represents, how it works mathematically (formula), its interpretation, statistical significance, and importance for making decisions in real-world applications such as business forecasting or medical diagnosis. We will …

## Logit vs Probit Models: Differences, Examples

Logit and Probit models are both types of regression models commonly used in statistical analysis, particularly in the field of binary classification. This means that the outcome of interest can only take on two possible values / classes. In most cases, these models are used to predict whether or not something will happen in form of binary outcome. For example, a bank might want to know if a particular borrower might default on loan or otherwise. In this blog post, we will explain what logit and probit models are, and we will provide examples of how they can be used. As data scientists, it is important to understand the concepts …

## Z-score or Z-statistics: Concepts, Formula & Examples

Z-score, also known as the standard score or Z-statistics, is a powerful statistical concept that plays a vital role in the world of data science. It provides a standardized method for comparing data points from different distributions, allowing data scientists to better understand and interpret the relative positioning of individual data points within a dataset. Z-scores represent a statistical technique of measuring the deviation of data from the mean. It is also used with Z-test which is a hypothesis testing statistical technique (one sample Z-test or two samples Z-test). As a data scientist, it is of utmost importance to be well-versed with the z-score formula and its various applications. Having …

## Histogram Plots using Matplotlib & Pandas: Python

Histograms are a graphical representation of the distribution of data. In Python, there are several ways to create histograms. One popular method is to use the Matplotlib library. In this tutorial, we will cover the basics of Histogram Plots and how to create different types of Histogram plots using the popular Python libraries, Matplotlib and Pandas. We will also explore some real-world examples to demonstrate the usefulness of Histogram Plots in various industries and applications. As data scientists, it is important to learn how to create visualizations to communicate our findings. Histograms are one way to do this effectively. What are Histogram plots? Histogram plots are a way of representing …

## Descriptive Statistics – Key Concepts & Examples

Descriptive statistics is a branch of statistics that deals with the analysis of data. It is concerned with summarizing and describing the characteristics of a dataset. It is one of the most fundamental tool for data scientists to understand the data as they get started working on the dataset. In this blog post, I will cover the key concepts of descriptive statistics, including measures of central tendency, measures of spread and statistical moments. What’s Descriptive Statistics & Why do we need it? Descriptive statistics is used to summarize and describe the characteristics of a dataset in terms of understanding its mean & related measures, spread or dispersion of the data …

## Quiz #85: MSE vs R-Squared?

Regression models are an essential tool for data scientists and statisticians to understand the relationship between variables and make predictions about future outcomes. However, evaluating the performance of these models is a crucial step in ensuring their accuracy and reliability. Two commonly used metrics for evaluating regression models are Mean Squared Error (MSE) and R-squared. Understanding when to use each metric and how they differ can greatly improve the quality of your analyses. Check out my related blog on this topic – Mean Squared Error vs R-Squared? Which one to use? To help you test your knowledge on MSE and R-squared (also known as coefficient of determination), we have created …

## Mastering f-statistics in Linear Regression: Formula, Examples

In this blog post, we will take a look at the concepts and formula of f-statistics in linear regression models and understand with the help of examples. F-test and F-statistics are very important concepts to understand if you want to be able to properly interpret the summary results of training linear regression machine learning models. We will start by discussing the importance of f-statistics in building linear regression models and understand how they are calculated based on the formula of f-statistics. We will, then, understand the concept with some real-world examples. As data scientists, it is very important to understand both the f-statistics and t-statistics and how they help in …

## Degree of Freedom in Statistics: Meaning & Examples

The degree of freedom (DOF) is a term that statisticians use to describe the degree of independence in statistical data. A degree of freedom can be thought of as the number of variables that are free to vary, given one or more constraints. When you have one degree, there is one variable that can be freely changed without affecting the value for any other variable. As a data scientist, it is important to understand the concept of degree of freedom, as it can help you do accurate statistical analysis and validate the results. In this blog, we will explore the meaning of degree of freedom in statistics, its importance in …

## Fixed vs Random vs Mixed Effects Models – Examples

Have you ever wondered what fixed effect, random effect and mixed effects models are? Or, more importantly, how they differ from one another? In this post, you will learn about the concepts of fixed and random effects models along with when to use fixed effects models and when to go for fixed + random effects (mixed) models. The concepts will be explained with examples. As data scientists, you must get a good understanding of these concepts as it would help you build better linear models such as general linear mixed models or generalized linear mixed models (GLMM). What are fixed, random & mixed effects models? First, we will take a real-world example and try and understand …

## Positively Skewed Probability Distributions: Examples

Probability distributions are an essential concept in statistics and data analysis. They describe the likelihood of different outcomes or events occurring and provide valuable insights into the characteristics of a given data set. Skewness is an important aspect of probability distributions that can have a significant impact on data analysis and decision-making. In this blog, we will focus on positively skewed probability distributions and explore some real-life examples where these distributions occur. We will discuss what a positively skewed distribution is, what are its different types with formula and definitions. By the end of this blog, you will have a better understanding of positively skewed distributions and be able to …

## Statistics Terminologies Cheat Sheet & Examples

Have you ever felt overwhelmed by all the statistics terminology out there? From sampling distribution to central limit theorem to null hypothesis to p-values to standard deviation, it can be hard to keep up with all the statistical concepts and how they fit into your research. That’s why we created a Statistics Terminologies Cheat Sheet & Examples – a comprehensive guide to help you better understand the essential terms and their use in data analysis. Our cheat sheet covers topics like descriptive statistics, probability, hypothesis testing, and more. And each definition is accompanied by an example to help illuminate the concept even further. Understanding statistics terminology is critical for data …

## Difference between Probability & Statistics

Are you confused about the difference between probability and statistics? You are not alone! Many struggle to determine the key distinctions between these two closely related topics. In this blog, we will discuss the major differences between probability and statistics with the help of examples, as well as how they are used in the field of data science. By understanding the nuances between probability and statistics, you will be able to use these concepts appropriate when solving data science related problems. So here we go! Probability & Statistics Difference – By Example Take a bag of marbles. You got your hand in the bag blindly and grabbed a handful of …

## Geometric Distribution Concepts, Formula, Examples

Geometric Distribution, a widely used concept in probability theory, is used to represent the probability of achieving success or failure in a series of independent trials, where the probability of success remains constant. It is one of the essential tools used in a wide range of fields, including economics, engineering, physics, and statistics. As data scientists / statisticians, it is of utmost important to understand its concepts and applications in a clear manner. In this blog, we will introduce you to the basics of Geometric distribution, starting with its definition and properties. We will also explore the geometric distribution formula and how it is used to calculate the probability of …

## Two-way ANOVA Test: Concepts, Formula & Examples

The two-way analysis of variance (ANOVA) test is a powerful tool for analyzing data and uncovering relationships between a dependent variable and two different independent variables. It’s used in fields like psychology, medicine, engineering, business, and other areas that require a deep understanding of how two separate variables interact and impact dependent variable. With the right knowledge, you can use this test to gain valuable insights into your data. Through a two-way ANOVA, data scientists are able to assess complex relationships between multiple variables and draw meaningful conclusions from the data. This helps them make informed decisions and identify patterns in the data that may have gone unnoticed otherwise. Let’s …

## Population & Samples in Statistics: Examples

In statistics, population and sample are two fundamental concepts that help us to better understand data. A population is a complete set of objects from which we can obtain data. A population can include all people, animals, plants, or things in a given area. On the other hand, a sample is a subset of the population that is used for observation and analysis. In this blog, we will further explore the concepts of population and samples and provide examples to illustrate the differences between them in statistics. What is a population in statistics? In statistics, population refers to the entire set of objects or individuals about which we want to …

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