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. Cash and Carry Transaction

    A type of transaction in the futures market in which the cash or spot price of a commodity is below the futures contract price. Cash and carry transactions are considered arbitrage transactions.
  2. Amplitude

    The difference in price from the midpoint of a trough to the midpoint of a peak of a security. Amplitude is positive when calculating a bullish retracement (when calculating from trough to peak) and negative when calculating a bearish retracement (when calculating from peak to trough).
  3. Ascending Triangle

    A bullish chart pattern used in technical analysis that is easily recognizable by the distinct shape created by two trendlines. In an ascending triangle, one trendline is drawn horizontally at a level that has historically prevented the price from heading higher, while the second trendline connects a series of increasing troughs.
  4. National Best Bid and Offer - NBBO

    A term applying to the SEC requirement that brokers must guarantee customers the best available ask price when they buy securities and the best available bid price when they sell securities.
  5. Maintenance Margin

    The minimum amount of equity that must be maintained in a margin account. In the context of the NYSE and FINRA, after an investor has bought securities on margin, the minimum required level of margin is 25% of the total market value of the securities in the margin account.
  6. Leased Bank Guarantee

    A bank guarantee that is leased to a third party for a specific fee. The issuing bank will conduct due diligence on the creditworthiness of the customer looking to secure a bank guarantee, then lease a guarantee to that customer for a set amount of money and over a set period of time, typically less than two years.
Trading Center