# Category Archives: statistics

## Spearman Correlation Coefficient: Formula, Examples

Have you ever wondered how you might determine the relationship between two sets of data that aren’t necessarily linear, or perhaps don’t adhere to the assumptions of other correlation measures? Enter the Spearman Rank Correlation Coefficient, a non-parametric statistic that offers robust insights into the monotonic relationship between two variables – perfect for dealing with ranked variables or exploring potential relationships in a new, exploratory dataset. In this blog post, we will learn the concepts of Spearman correlation coefficient with the help of Python code examples. Understanding the concept can prove to be very helpful for data scientists. Whether you’re exploring associations in marketing data, results from a customer satisfaction …

## Binomial Distribution Explained with Examples

Have you ever wondered how to predict the number of successes in a series of independent trials? Or perhaps you’ve been curious about the probability of achieving a specific outcome in a sequence of yes-or-no questions. If so, we are essentially talking about the binomial distribution. It’s important for data scientists to understand this concept as binomials are used often in business applications. The binomial distribution is a discrete probability distribution that applies to binomial experiments (experiments with binary outcomes). It’s the number of successes in a specific number of trials. Sighting a simple yet real-life example, the binomial distribution may be imagined as the probability distribution of a number …

## How to Choose Right Statistical Tests: Examples

Whether you are a researcher, data analyst, or data scientist, selecting the appropriate statistical test is crucial for accurate and reliable data analysis. With numerous tests available, it can be overwhelming to determine the right one for your research question and data type. In this blog, the aim is to simplify the process, providing you with a systematic approach to choosing the right statistical test. This blog will be particularly helpful for those who are new to statistical analysis and are unsure which test to use for their specific needs. You will learn a clear and structured method for selecting the appropriate statistical test. By considering factors such as data …

## One-way ANOVA test: Concepts, Formula & Examples

The one-way analysis of variance (ANOVA) test is a statistical procedure commonly used to compare the means values on a specific variable between three or more groups. The significance of the difference between the means of two samples can be judged through either t-test or z-test depending upon different criteria, but it becomes tricky when there is a need to simultaneously evaluate the significance of the difference amongst three or more sample means. This is where one-way ANOVA test comes to rescue. The ANOVA technique enables us to perform this simultaneous test and as such is considered to be an important tool of analysis. As data scientists, it is of …

## 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 …

## 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 …

## 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 …

## 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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