Degrees Of Freedom

What are '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.

BREAKING DOWN '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. Null Hypothesis

    A type of hypothesis used in statistics that proposes that no ...
  2. Alpha Risk

    The risk in a statistical test that a null hypothesis will be ...
  3. Hypothesis Testing

    A process by which an analyst tests a statistical hypothesis. ...
  4. Chi Square Statistic

    A measurement of how expectations compare to results. The data ...
  5. Type II Error

    A statistical term used within the context of hypothesis testing ...
  6. Goodness-Of-Fit

    Used in statistics and statistical modelling to compare an anticipated ...
Related Articles
  1. Active Trading Fundamentals

    Hypothesis Testing in Finance: Concept & Examples

    When you're indecisive about an investment, the best way to keep a cool head might be test various hypotheses using the most relevant statistics.
  2. Fundamental Analysis

    What is a Null Hypothesis?

    In statistics, a null hypothesis is assumed true until proven otherwise.
  3. Professionals

    A Double Undergrad Can Cost You Your MBA

    At college, many students prefer to do a double undergrad to broaden their education, but this can hinder you - financially and professionally - in the long run.
  4. Professionals

    3 MBA Double Majors That Boost Your Value

    Find out how to fast track with a double major, and give you career the edge it needs.
  5. Term

    How Statistical Significance is Determined

    If something is statistically significant, it’s unlikely that it happened by chance.
  6. Personal Finance

    When Is Grad School Worth It?

    How to figure whether the payback you get from going to grad school – earnings, lifestyle, career opportunities – is worth the cost.
  7. Professionals

    Online MBA Programs: Study From Home And Succeed!

    The freedoms available with online MBA programs can outweigh the hardships. Find out if an online program is right for you.
  8. Personal Finance

    Master's Degrees: The US vs. The UK

    When deciding whether to pursue a master's degree in the US or UK, consider degree structure, cost, and quality of education.
  9. Personal Finance

    When Is College The Wrong Investment?

    Attending a very expensive college with the wrong degree could turn into a bad investment due to low salaries and high debt.
  10. Credit & Loans

    Student Borrowing: University Payment Plans Vs. Federal Student Loans

    University payment plans are a great option for reducing student loan borrowing, but only if you know the details.
RELATED FAQS
  1. What does a strong null hypothesis mean?

    Find out what null hypothesis is and why it is important to the scientific method. See how statisticians and economists use ... Read Answer >>
  2. What is the relationship between confidence inferrals and a null hypothesis?

    Learn about the relationship between confidence intervals and the null hypothesis in scientific research and empirical experimentation. Read Answer >>
  3. What's the difference between a representative sample and a convenience sample?

    Learn the difference between convenience sampling and representative sampling and the advantages and disadvantages of each ... Read Answer >>
  4. I did not receive my Bachelor's degree in the United States. How can I determine ...

    CFA institute indicates that a Bachelor's degree is a level of study that would qualify an individual for a graduate program ... Read Answer >>
  5. What percentage of the population do you need in a representative sample?

    Learn about representative samples and how they are used in conjunction with other strategies to create useful data with ... Read Answer >>
  6. How can a representative sample lead to sampling bias?

    Learn how using representative samples alone is not enough to make sampling bias negligible and why elements such as randomization ... Read Answer >>
Hot Definitions
  1. Physical Capital

    Physical capital is one of the three main factors of production in economic theory. It consists of manmade goods that assist ...
  2. Reverse Mortgage

    A type of mortgage in which a homeowner can borrow money against the value of his or her home. No repayment of the mortgage ...
  3. Labor Market

    The labor market refers to the supply and demand for labor, in which employees provide the supply and employers the demand. ...
  4. Demand Curve

    The demand curve is a graphical representation of the relationship between the price of a good or service and the quantity ...
  5. Goldilocks Economy

    An economy that is not so hot that it causes inflation, and not so cold that it causes a recession. This term is used to ...
  6. White Squire

    Very similar to a "white knight", but instead of purchasing a majority interest, the squire purchases a lesser interest in ...
Trading Center