Z-Test

What is a 'Z-Test'

A Z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large. The test statistic is assumed to have a normal distribution and nuisance parameters such as standard deviation should be known in order for an accurate z-test to be performed.

BREAKING DOWN 'Z-Test'

A one-sample location test, two-sample location test, paired difference test and maximum likelihood estimate are examples of tests that can be conducted as z-tests. Z-tests are closely related to t-tests, but t-tests are best performed when an experiment has a small sample size. Also, t-tests assume that the standard deviation is unknown, while z-tests assume that it is known. If the standard deviation of the population is unknown, the assumption that the sample variance equals the population variance is made.

RELATED TERMS
  1. T-Test

    A statistical examination of two population means. A two-sample ...
  2. Analysis Of Variance - ANOVA

    A statistical analysis tool that separates the total variability ...
  3. Standard Error

    The standard deviation of the sampling distribution of a statistic. ...
  4. Sample

    A subset containing the characteristics of a larger population. ...
  5. Sampling Distribution

    A probability distribution of a statistic obtained through a ...
  6. Variance

    The spread between numbers in a data set, measuring Variance ...
Related Articles
  1. Trading

    What's a T-Test?

    T-Test is a term from statistics that allows for the comparison of two data populations and their means. The test is used to see if the two sets of data are significantly different from one another. ...
  2. Investing

    Explaining Standard Error

    Standard error is a statistical term that measures the accuracy with which a sample represents a population.
  3. Markets

    Explaining Variance

    Variance is a measurement of the spread between numbers in a data set.
  4. Trading

    Trading With Gaussian Models Of Statistics

    The entire study of statistics originated from Gauss and allowed us to understand markets, prices and probabilities, among other applications.
  5. Markets

    What is a Representative Sample?

    In statistics, a representative sample accurately represents the make-up of various subgroups in an entire data pool.
  6. Markets

    Explaining the Empirical Rule

    The empirical rule provides a quick estimate of the spread of data in a normal statistical distribution.
  7. Trading

    Understanding Statistics

    Statistics provide the means to analyze data and then summarize it into a numerical form.
  8. Markets

    How to Use Stratified Random Sampling

    Stratified random sampling is a technique best used with a sample population easily broken into distinct subgroups. Samples are then taken from each subgroup based on the ratio of the subgroup’s ...
  9. Managing Wealth

    Calculating Portfolio Variance

    Portfolio variance is a measure of a portfolio’s volatility, and is a function of two variables.
  10. Investing

    A Simplified Approach To Calculating Volatility

    Volatility is sometimes greater than anticipated, but the way it’s measured can compound the problems that occur when it’s unexpected.
RELATED FAQS
  1. What assumptions are made when conducting a t-test?

    Learn what a t-test is, and discover the five standard assumptions that are made regarding the validity of sampling and data ... Read Answer >>
  2. What is the difference between variance and standard deviation?

    Explore the differences between standard deviation and variance. Learn more about how statisticians use these two concepts. Read Answer >>
  3. What is the difference between standard deviation and variance?

    Understand the difference between standard deviation and variance; learn how each is calculated and how these concepts are ... Read Answer >>
  4. How is standard deviation used to determine risk?

    Understand the basics of calculation and interpretation of standard deviation and how it is used to measure risk in the investment ... Read Answer >>
  5. What is the difference between standard deviation and average deviation?

    Understand the basics of standard deviation and average deviation, including how each is calculated and why standard deviation ... Read Answer >>
  6. Is variance good or bad for stock investors?

    Learn how high variance stocks are good for some investors and how diversified portfolios can reduce variance without compromising ... Read Answer >>
Hot Definitions
  1. Brazil, Russia, India And China - BRIC

    An acronym for the economies of Brazil, Russia, India and China combined. It has been speculated that by 2050 these four ...
  2. Brexit

    The Brexit, an abbreviation of "British exit" that mirrors the term Grexit, refers to the possibility of Britain's withdrawal ...
  3. Underweight

    1. A situation where a portfolio does not hold a sufficient amount of a particular security when compared to the security's ...
  4. Russell 3000 Index

    A market capitalization weighted equity index maintained by the Russell Investment Group that seeks to be a benchmark of ...
  5. Enterprise Value (EV)

    A measure of a company's value, often used as an alternative to straightforward market capitalization. Enterprise value is ...
  6. Security

    A financial instrument that represents an ownership position in a publicly-traded corporation (stock), a creditor relationship ...
Trading Center