Making statistics intuitive
Marginal probability is the chance that an event will happen without considering other variables. Statisticians write this as p(A), denoting the probability of event A. You can think of it as an unconditional probability. It tells you how likely something will happen on its own, independently of other variables. [Read more…] about Marginal Probability: Definition, Formula & Examples
The conjunction fallacy is a cognitive bias that occurs when someone mistakenly believes that two events occurring together are more likely than either of the two events alone. In other words, it’s the mistaken belief that a precisely detailed, multifaced outcome is more likely to occur than a more generalized version of that outcome. [Read more…] about Conjunction Fallacy: Definition & Example
Base rate fallacy is a cognitive bias that occurs when a person misjudges an outcome by giving too much weight to case-specific details and overlooks crucial probability information that applies to all cases in a population. That vital probability is the outcome’s base rate of occurrence in the population. [Read more…] about Base Rate Fallacy Overview & Examples
What’s the risk? People discuss risk frequently, but it’s not always clearly understood. It is your exposure to danger or adverse outcomes. Statistically, we define risk as the probability of a negative outcome occurring, and there are several ways to calculate it. [Read more…] about Risk Calculations: Relative vs Absolute & Risk Reduction
Use the binomial distribution formula to calculate the likelihood an event will occur a specific number of times in a set number of opportunities. I’ll show you the binomial distribution formula to calculate these probabilities manually.
In this post, I’ll walk you through the formulas for how to find the probability, mean, and standard deviation of the binomial distribution and provide worked examples. [Read more…] about Binomial Distribution Formula: Probability, Standard Deviation & Mean
The expected value in statistics is the long-run average outcome of a random variable based on its possible outcomes and their respective probabilities. Essentially, if an experiment (like a game of chance) were repeated, the expected value tells us the average result we’d see in the long run. Statisticians denote it as E(X), where E is “expected value,” and X is the random variable. [Read more…] about Expected Value: Definition, Formula & Finding
The Bernoulli distribution is a discrete probability distribution that models a binary outcome for one trial. Use it for a random variable that can take one of two outcomes: success (k = 1) or failure (k = 0), much like a coin toss. Statisticians refer to these trials as Bernoulli trials. [Read more…] about Bernoulli Distribution: Uses, Formula & Example
Joint probability is the likelihood that two or more events will coincide. Knowing how to calculate them allows you to solve problems such as the following. What is the probability of:
[Read more…] about Joint Probability: Definition, Formula & Examples
Independent events in statistics are those in which one event does not affect the next event. More specifically, the occurrence of one event does not affect the probability of the following event happening. [Read more…] about Independent Events: Definition & Probability
A random variable is a variable where chance determines its value. They can take on either discrete or continuous values, and understanding the properties of each type is essential in many statistical applications. Random variables are a key concept in statistics and probability theory. [Read more…] about Random Variable: Discrete & Continuous
A probability mass function (PMF) is a mathematical function that calculates the probability a discrete random variable will be a specific value. PMFs also describe the probability distribution for the full range of values for a discrete variable. A discrete random variable can take on a finite or countably infinite number of possible values, such as the number of heads in a series of coin flips or the number of customers who visit a store on a given day. [Read more…] about Probability Mass Function: Definition, Uses & Example
A cumulative distribution function (CDF) describes the probabilities of a random variable having values less than or equal to x. It is a cumulative function because it sums the total likelihood up to that point. Its output always ranges between 0 and 1. [Read more…] about Cumulative Distribution Function (CDF): Uses, Graphs & vs PDF
Monte Carlo simulation uses random sampling to produce simulated outcomes of a process or system. This method uses random sampling to generate simulated input data and enters them into a mathematical model that describes the system. The simulation produces a distribution of outcomes that analysts can use to derive probabilities. [Read more…] about Monte Carlo Simulation: Make Better Decisions
The hypergeometric distribution is a discrete probability distribution that calculates the likelihood an event happens k times in n trials when you are sampling from a small population without replacement. [Read more…] about Hypergeometric Distribution: Uses, Calculator & Formula
The negative binomial distribution describes the number of trials required to generate an event a particular number of times. When you provide an event probability and the number of successes (r), this distribution calculates the likelihood of observing the Rth success on the Nth attempt. Statisticians also refer to this discrete probability distribution as the Pascal distribution. [Read more…] about Negative Binomial Distribution: Uses, Calculator & Formula
Benford’s law describes the relative frequency distribution for leading digits of numbers in datasets. Leading digits with smaller values occur more frequently than larger values. This law states that approximately 30% of numbers start with a 1 while less than 5% start with a 9. According to this law, leading 1s appear 6.5 times as often as leading 9s! Benford’s law is also known as the First Digit Law. [Read more…] about Benford’s Law Explained with Examples
A hazard ratio (HR) is the probability of an event in a treatment group relative to the control group probability over a unit of time. This ratio is an effect size measure for time-to-event data. Use hazard ratios to estimate the treatment effect in clinical trials when you want to assess time-to-event.
For example, HRs can determine whether a medical treatment reduces the duration of symptoms or prolongs survival in cancer patients. [Read more…] about Hazard Ratio: Interpretation & Definition
Relative risk is the ratio of the probability of an adverse outcome in an exposure group divided by its likelihood in an unexposed group. This statistic indicates whether exposure corresponds to increases, decreases, or no change in the probability of the adverse outcome. Use relative risk to measure the strength of the association between exposure and the outcome. Analysts also refer to this statistic as the risk ratio. [Read more…] about Relative Risk: Definition, Formula & Interpretation
A probability density function describes a probability distribution for a random, continuous variable. Use a probability density function to find the chances that the value of a random variable will occur within a range of values that you specify. More specifically, a PDF is a function where its integral for an interval provides the probability of a value occurring in that interval. For example, what are the chances that the next IQ score you measure will fall between 120 and 140? In statistics, PDF stands for probability density function. [Read more…] about Probability Density Function: Definition & Uses
The t distribution is a continuous probability distribution that is symmetric and bell-shaped like the normal distribution but with a shorter peak and thicker tails. It was designed to factor in the greater uncertainty associated with small sample sizes.
The t distribution describes the variability of the distances between sample means and the population mean when the population standard deviation is unknown and the data approximately follow the normal distribution. This distribution has only one parameter, the degrees of freedom, based on (but not equal to) the sample size. [Read more…] about T Distribution: Definition & Uses