Degrees Of Freedom

AAA

DEFINITION of 'Degrees Of Freedom'

In statistics, the number of values in a study that are free to vary. For example, if you have to take ten different courses to graduate, and only ten different courses are offered, then you have nine degrees of freedom. Nine semesters you will be able to choose which class to take; the tenth semester, there will only be one class left to take - there is no choice, if you want to graduate.


Degrees of freedom are commonly discussed in relation to chi-square and other forms of hypothesis testing statistics. It is important to calculate the degree(s) of freedom when determining the significance of a chi square statistic and the validity of the null hypothesis.

INVESTOPEDIA EXPLAINS 'Degrees Of Freedom'

There are two types of chi square tests: the goodness-of-fit test (does a coin tossed 100 times turn up heads 50 times and tails 50 times?) and the test of independence (is there a relationship between gender and a perfect SAT score?).


Degrees of freedom are used to then determine whether a particular null hypothesis can be rejected based on the number of variables and samples of in the experiment. For example, while a sample size of 50 students might not be large enough to obtain significant information, obtaining the same results from a study of 500 samples can be judged as being valid.




RELATED TERMS
  1. Goodness-Of-Fit

    Used in statistics and statistical modelling to compare an anticipated ...
  2. Nonparametric Statistics

    A statistical method wherein the data is not required to fit ...
  3. Sampling Error

    A statistical error to which an analyst exposes a model simply ...
  4. Statistics

    A type of mathematical analysis involving the use of quantified ...
  5. Null Hypothesis

    A type of hypothesis used in statistics that proposes that no ...
  6. Descriptive Statistics

    A set of brief descriptive coefficients that summarizes a given ...
Related Articles
  1. Investing Basics

    What Are The Odds Of Scoring A Winning Trade?

    Just because you're on a winning streak doesn't mean you're a skilled trader. Find out why.
  2. Investing Basics

    Regression Basics For Business Analysis

    This tool is easy to use and can provide valuable information on financial analysis and forecasting. Find out how.
  3. Active Trading

    The Linear Regression Of Time and Price

    This investment strategy can help investors be successful by identifying price trends while eliminating human bias.
  4. Economics

    What's the relationship between r squared and beta?

    Learn about the relationship between R-squared and Beta. Explore how the concepts are related and often used in conjunction with portfolio Alpha.
  5. Economics

    What are some limitations of the consumer price index (CPI)?

    Explore some of the basic limitations of the widely used economic indicator, the consumer price index, or CPI, and examine the criticism of its accuracy.
  6. Economics

    Is the consumer price index (CPI) a cost of living index?

    Explore the consumer price index (CPI) and understand why it is not an actual cost of living index although it is often identified as one.
  7. Economics

    Where do funds report their r-squared?

    Learn where to find R-squared calculations for mutual funds. Explore R-squared, Alpha and Beta and how these calculations measure securities' performance.
  8. Fundamental Analysis

    How do you calculate r-squared in Excel?

    Calculate R-squared in Microsoft Excel by creating two data ranges to correlate. Use the Correlate formula to correlate both sets of data, or x and y.
  9. Fundamental Analysis

    What are the most common issues with Serial Correlation in stocks?

    Read about the concept of serial correlation in stock returns, and learn why market analysts are divided about the efficacy of trading based on stock patterns.
  10. Trading Strategies

    How far back in a stock's history should you go when gauging its volatility?

    Discover why it can be difficult for investors to figure out how far back to go into a stock's history when gauging its volatility.

You May Also Like

Hot Definitions
  1. Command Economy

    A system where the government, rather than the free market, determines what goods should be produced, how much should be ...
  2. Prospectus

    A formal legal document, which is required by and filed with the Securities and Exchange Commission, that provides details ...
  3. Treasury Bond - T-Bond

    A marketable, fixed-interest U.S. government debt security with a maturity of more than 10 years. Treasury bonds make interest ...
  4. Weight Of Ice, Snow Or Sleet Insurance

    Financial protection against damage caused to property by winter weather specifically, damage caused if a roof caves in because ...
  5. Weather Insurance

    A type of protection against a financial loss that may be incurred because of rain, snow, storms, wind, fog, undesirable ...
  6. Portfolio Turnover

    A measure of how frequently assets within a fund are bought and sold by the managers. Portfolio turnover is calculated by ...
Trading Center