Articles

Probability Tree

October 13, 2026
Statistics Notes
EN

Probability trees are a visual representation of all possible outcomes of a probabilistic experiment and the paths leading to these outcomes. They are especially helpful in understanding sequences of events, particularly when these events are conditional on previous outcomes...

Descriptive Statistics

October 13, 2026
Statistics Notes
EN

Descriptive statistics summarize the main characteristics of a dataset or sample. They help us understand data by describing its frequency, center, spread, and overall distribution...

Introduction to Statistics

October 13, 2026
Statistics Notes
EN

Statistics is the science of learning from data. It provides methods for collecting, summarizing, analyzing, and interpreting observations so that we can describe patterns, quantify uncertainty, and make informed decisions...

F Distribution

October 13, 2026
Statistics Notes
EN

The F-distribution, also known as the Fisher-Snedecor distribution, is a continuous probability distribution of the ratio $F=(U/d_1)/(V/d_2)$ of two independent chi-square variables $U\sim\chi^2(d_1)$ and $V\sim\chi^2(d_2)$, each divided by its degrees of freedom. It arises in hypothesis testing whe...

Student T Distribution

October 13, 2026
Statistics Notes
EN

Student's t-distribution is a continuous probability distribution that arises when a normally distributed quantity is standardized using an estimated standard deviation rather than a known population standard deviation. Formally, if $Z\sim N(0,1)$ and $V\sim\chi^2(\nu)$ are independent, then $T=Z/\s...

Chi Square Distribution

October 13, 2026
Statistics Notes
EN

A chi-square distribution is a continuous probability distribution of the sum of the squares of k independent standard normal random variables. The chi-square distribution is denoted as $X \sim \chi^2(k)$, where k is the number of degrees of freedom...

Central Limit Theorem

October 13, 2026
Statistics Notes
EN

The Central Limit Theorem (CLT) is a fundamental result in statistics. It explains why the distribution of sample means often approaches a normal distribution as the sample size increases, even when the population itself is not normally distributed...

Standard Error and Lln

October 13, 2026
Statistics Notes
EN

Expected Value (E), also known as the mean, is the long-run average of a random variable, representing the value we anticipate on average from repeated random draws from a population...

Bayesian vs Frequentist

October 13, 2026
Statistics Notes
EN

Bayesian and frequentist statistics are two major approaches to statistical inference. Both use sample data to learn about an underlying population or data-generating process, but they differ in how they interpret probability, represent uncertainty, and draw conclusions about unknown parameters...

Multiple Regression

October 13, 2026
Statistics Notes
EN

Multiple linear regression is a statistical technique used to model the relationship between a single dependent variable and two or more independent variables. It extends the concept of simple linear regression by incorporating multiple predictors to explain the variability in the dependent variable...

Logistic Regression

October 13, 2026
Statistics Notes
EN

Logistic regression is a statistical method used for modeling the probability of a binary outcome based on one or more predictor variables. It is widely used in various fields such as medicine, social sciences, and machine learning for classification problems where the dependent variable is dichotom...

Simple Linear Regression

October 13, 2026
Statistics Notes
EN

Simple linear regression is a statistical method used to model the relationship between a single dependent variable and one independent variable. It aims to find the best-fitting straight line through the data points, which can be used to predict the dependent variable based on the independent varia...

Analysis of Variance

October 13, 2026
Statistics Notes
EN

Does peer assessment enhance student learning...

Statistical Moments

October 13, 2026
Statistics Notes
EN

In both statistics and mechanics the word moment measures how much "leverage" the values of a quantity exert about a chosen reference point. In statistics the leverage is exerted by probability mass, in mechanics by physical mass, but the mathematics is identical: take a distance from the reference ...

Normal Curve and z Score

October 13, 2026
Statistics Notes
EN

A normal distribution (often referred to as the normal curve or Gaussian distribution) is a continuous probability distribution that is symmetric about the mean, where most of the observations cluster around the central peak and taper off symmetrically towards both ends. Many real-world datasets suc...

Introduction to Distributions

October 13, 2026
Statistics Notes
EN

A distribution is a function that describes the probability of a random variable. It helps to understand the underlying patterns and characteristics of a dataset. Distributions are widely used in statistics, data analysis, and machine learning for tasks such as hypothesis testing, confidence interva...

Validation and Model Selection

October 13, 2026
Statistics Notes
EN

A fitted model is optimized using observed data. Model assessment asks a different question: how well will the modeling procedure perform on new data generated under comparable conditions...

Metrics

October 13, 2026
Statistics Notes
EN

Evaluation metrics are essential tools for assessing the performance of statistical and machine learning models. They provide quantitative measures that help us understand how well a model is performing and where improvements can be made. In both classification and regression tasks, selecting approp...

Resampling

October 13, 2026
Statistics Notes
EN

Statistical inference often involves estimating population parameters and constructing confidence intervals based on sample data. Traditional methods rely on assumptions about the sampling distribution of estimators, such as normality and known standard errors. However, these assumptions may not hol...

Geostatistics

October 13, 2026
Statistics Notes
EN

Geostatistics is used when observations are tied to locations and nearby values may be more similar than distant values...

Spatial Weights

October 13, 2026
Statistics Notes
EN

A spatial weights matrix turns a qualitative statement such as...

Point Processes

October 13, 2026
Statistics Notes
EN

A spatial point process is used when the observed data are the event locations themselves...

Spatial Autocorrelation

October 13, 2026
Statistics Notes
EN

Spatial autocorrelation asks whether values attached to locations show a systematic spatial pattern...

Kriging

October 13, 2026
Statistics Notes
EN

Kriging is a method for predicting a spatial variable at unsampled locations using a model of spatial dependence...

Spatial Data and Distance

October 13, 2026
Statistics Notes
EN

Spatial analysis begins before any spatial statistic is calculated...

Spatial Regression

October 13, 2026
Statistics Notes
EN

Regression models the mean relationship between an outcome and its predictors...

Spatial Validation

October 13, 2026
Statistics Notes
EN

Spatial model performance depends not only on which observations are held out, but also on where those observations are located relative to the training data...

Covariance

October 13, 2026
Statistics Notes
EN

Covariance is a fundamental statistical measure that quantifies the degree to which two random variables change together. It indicates the direction of the linear relationship between variables...

Correlation

October 13, 2026
Statistics Notes
EN

Correlation is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It is a fundamental concept in statistics, enabling researchers and analysts to understand how one variable may predict or relate to another. The most commonly used corre...

Negative Binomial Distribution

October 13, 2026
Statistics Notes
EN

A discrete random variable X follows a negative binomial distribution if it represents the number of trials required to achieve a specified number of successes in a sequence of independent Bernoulli trials. The negative binomial distribution is often denoted as $X \sim \text{NegBinomial}(r, p)$, whe...

Binomial Distribution

October 13, 2026
Statistics Notes
EN

A discrete random variable $X$ follows a binomial distribution if it represents the number of successes in a fixed number of Bernoulli trials with the same probability of success. The binomial distribution is denoted as $X \sim \text{Binomial}(n, p)$, where $n$ is the number of trials and $p$ is the...

Geometric Distribution

October 13, 2026
Statistics Notes
EN

A discrete random variable X follows a geometric distribution if it represents the number of trials needed to get the first success in a sequence of Bernoulli trials. The geometric distribution is denoted as $X \sim \text{Geometric}(p)$, where $p$ is the probability of success on each trial. The sup...

Poisson Distribution

October 13, 2026
Statistics Notes
EN

A discrete random variable X follows a Poisson distribution if the events occur independently and at a constant average rate. The Poisson distribution is denoted as $X \sim \text{Poisson}(\lambda)$, where $\lambda$ is the average rate (or mean) of events occurring in a given interval...

Log Normal Distribution

October 13, 2026
Statistics Notes
EN

A continuous random variable X follows a log-normal distribution if its natural logarithm is normally distributed. The log-normal distribution is useful in modeling continuous random variables that are constrained to be positive. It is denoted as $X \sim \text{LogNormal}(\mu, \sigma^2)$, where $\mu...

Beta Distribution

October 13, 2026
Statistics Notes
EN

A continuous random variable $X$ follows a beta distribution when its support is the interval $[0,1]$ and its shape is governed by two positive parameters. The beta distribution is denoted as $X \sim \text{Beta}(\alpha, \beta)$, where $\alpha$ and $\beta$ are shape parameters. A shifted and scaled b...