Degrees Of Freedom

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.


Filed Under:

comments powered by Disqus
Hot Definitions
  1. Benchmark Bond

    A bond that provides a standard against which the performance of other bonds can be measured. Government bonds are almost always used as benchmark bonds. Also referred to as "benchmark issue" or "bellwether issue".
  2. Market Capitalization

    The total dollar market value of all of a company's outstanding shares. Market capitalization is calculated by multiplying a company's shares outstanding by the current market price of one share. The investment community uses this figure to determine a company's size, as opposed to sales or total asset figures.
  3. Oil Reserves

    An estimate of the amount of crude oil located in a particular economic region. Oil reserves must have the potential of being extracted under current technological constraints. For example, if oil pools are located at unattainable depths, they would not be considered part of the nation's reserves.
  4. Joint Venture - JV

    A business arrangement in which two or more parties agree to pool their resources for the purpose of accomplishing a specific task. This task can be a new project or any other business activity. In a joint venture (JV), each of the participants is responsible for profits, losses and costs associated with it.
  5. Aggregate Risk

    The exposure of a bank, financial institution, or any type of major investor to foreign exchange contracts - both spot and forward - from a single counterparty or client. Aggregate risk in forex may also be defined as the total exposure of an entity to changes or fluctuations in currency rates.
  6. Organic Growth

    The growth rate that a company can achieve by increasing output and enhancing sales. This excludes any profits or growth acquired from takeovers, acquisitions or mergers. Takeovers, acquisitions and mergers do not bring about profits generated within the company, and are therefore not considered organic.
Trading Center