Making statistics intuitive
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 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 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
The difference between a standard deviation and a standard error can seem murky. Let’s clear that up in this post!
Standard deviation (SD) and standard error (SE) both measure variability. High values of either statistic indicate more dispersion. However, that’s where the similarities end. The standard deviation is not the same as the standard error. [Read more…] about Difference Between Standard Deviation and Standard Error
The beta distribution is a continuous probability distribution that models random variables with values falling inside a finite interval. Use it to model subject areas with both an upper and lower bound for possible values. Analysts commonly use it to model the time to complete a task, the distribution of order statistics, and the prior distribution for binomial proportions in Bayesian analysis. [Read more…] about Beta Distribution: Uses, Parameters & Examples
The geometric distribution is a discrete probability distribution that calculates the probability of the first success occurring during a specific trial. In other words, during a series of attempts, what is the probability of success first occurring during each attempt? Use this distribution when you need to understand how many attempts are necessary to produce the first successful outcome. [Read more…] about Geometric Distribution: Uses, Calculator & Formula
A conditional distribution is a distribution of values for one variable that exists when you specify the values of other variables. This type of distribution allows you to assess the dispersal of your variable of interest under specific conditions, hence the name. [Read more…] about Conditional Distribution: Definition & Finding
A marginal distribution is a distribution of values for one variable that ignores a more extensive set of related variables in a dataset.
That definition sounds a bit convoluted, but the concept is simple. The idea is that when you have a larger set of related variables that you collected for a study, you might want to focus on one of them to answer a specific question. [Read more…] about Marginal Distribution: Definition & Finding
A contingency table displays frequencies for combinations of two categorical variables. Analysts also refer to contingency tables as crosstabulation and two-way tables. [Read more…] about Contingency Table: Definition, Examples & Interpreting
Cumulative frequency is the running total of frequencies in a table. Use cumulative frequencies to answer questions about how often a characteristic occurs above or below a particular value. It is also known as a cumulative frequency distribution.
For example, how many students are in the 4th grade or lower at a school? [Read more…] about Cumulative Frequency: Finding & Interpreting
The chi-square goodness of fit test evaluates whether proportions of categorical or discrete outcomes in a sample follow a population distribution with hypothesized proportions. In other words, when you draw a random sample, do the observed proportions follow the values that theory suggests. [Read more…] about Chi-Square Goodness of Fit Test: Uses & Examples
A bimodal distribution has two peaks. In the context of a continuous probability distribution, modes are peaks in the distribution. The graph below shows a bimodal distribution. [Read more…] about Bimodal Distribution: Definition, Examples & Analysis
Quartiles are three values that split your dataset into quarters. [Read more…] about Quartile: Definition, Finding, and Using
Kurtosis is a statistic that measures the extent to which a distribution contains outliers. It assesses the propensity of a distribution to have extreme values within its tails. There are three kinds of kurtosis: leptokurtic, platykurtic, and mesokurtic. Statisticians define these types relative to the normal distribution. Higher kurtosis values indicate that the distribution has more outliers falling relatively far from the mean. Distributions with smaller values have a lower tendency for producing extreme values. When you’re assessing a sample, outliers have the greatest impact on this statistic. [Read more…] about Kurtosis: Definition, Leptokurtic & Platykurtic
The binomial distribution is a discrete probability distribution that calculates the likelihood an event will occur a specific number of times in a set number of opportunities. Use this distribution when you have a binomial random variable. These variables count how often an event occurs within a fixed number of trials. They have only two possible outcomes that are mutually exclusive. [Read more…] about Binomial Distribution: Uses, Calculator & Formula
These F-tables provide the critical values for right-tail F-tests. Your F-test results are statistically significant when its test statistic is greater than this value. [Read more…] about F-table
A sampling distribution of a statistic is a type of probability distribution created by drawing many random samples of a given size from the same population. These distributions help you understand how a sample statistic varies from sample to sample. [Read more…] about Sampling Distribution: Definition, Formula & Examples