What are 'Degrees Of Freedom'

Degrees of freedom are the number of values in a study that have the freedom to vary. They are commonly discussed in relationship to various forms of hypothesis testing in statistics, such as a chi-square. It is essential to calculate degrees of freedom when trying to understand the importance of a chi square statistic and the validity of the null hypothesis.

BREAKING DOWN 'Degrees Of Freedom'

For example, consider a student needs to take nine courses to graduate, and there are only nine courses offered the student can take. In this example, there are eight degrees of freedom; the student is able to choose eight of the classes that are available, but the ninth class is the only class left, and the student has to enroll in it to graduate.

Chi Square Tests

There are two different kinds of chi square tests: the test of independence, which asks a question of relationship, such as, "Is there a relationship between gender and SAT scores?"; and the goodness-of-fit test, which asks something like "If a coin is tossed 100 times, will it come up heads 50 times and tails 50 times?" For these tests, degrees of freedom are utilized to determine if a certain null hypothesis can be rejected based on the total number of variables and samples within the experiment. For example, when considering students and course choice, a sample size of 30 or 40 students is likely not large enough to generate significant data. Getting the same or similar results from a study using a sample size of 400 or 500 students is more valid.

History of Degrees of Freedom

The earliest and most basic concept of degrees of freedom was noted in the early 1800s, intertwined in the works of mathematician and astronomer Carl Friedrich Gauss. The modern usage and understanding of the term was expounded upon first by William Sealy Gosset, an English statistician, in his article "The Probable Error of a Mean," published in Biometrika in 1908 under a pen name to preserve his anonymity. In his writings, Gosset did not specifically use the term "degrees of freedom." He did, however, give an explanation for the concept throughout the course of developing what would eventually be known as Student’s t-distribution. The actual term was not made popular until 1922. English biologist and statistician Ronald Fisher began using the term "degrees of freedom" when he started publishing reports and data on his work developing chi squares.

RELATED TERMS
  1. Chi Square Statistic

    A measurement of how expectations compare to results. The data ...
  2. T Distribution

    A type of probability distribution that is theoretical and resembles ...
  3. Tax Freedom Day

    The day that the average American has earned enough money (in ...
  4. Student Debt

    Money owed on a loan taken out to pay for educational expenses. ...
  5. Freedom Shares

    Original issue discount bonds issued by the U.S. Treasury from ...
  6. Alpha Risk

    The risk in a statistical test that a null hypothesis will be ...
Related Articles
  1. Personal Finance

    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.
  2. Personal Finance

    Does It Make Sense to Go to College in Europe?

    If you're deciding whether to get a degree abroad, first do your research and talk to alumni who have completed the same program.
  3. Personal Finance

    3 Alternative Ways To Save for College

    The cost of college is skyrocketing at a time of record student loan debt. But there are ways to earn a college degree without traditional borrowing.
  4. Personal Finance

    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.
  5. Personal Finance

    10 Ways Student Debt Can Destroy Your Life

    If you're getting a student loan, think critically about how you will manage your loan. Student debt could have a profound negative impact on your life.
  6. Personal Finance

    Looking for a Tuition-Free College? Move Abroad

    College tuition abroad is free in some cases, allowing students to get a debt-free jump on life. But you might need to brush up on your German.
  7. 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.
  8. Personal Finance

    The Benefits Of An Accelerated Bachelor's/Master's Degree

    Accelerating your post-secondary education can save you major time and money.
  9. Personal Finance

    5 Worst Money Mistakes You Can Make In College

    Watch out for these costly mistakes while in school.
  10. Personal Finance

    All About Student Loans

    Student loans bridge the gap between college savings, scholarships and earnings from part-time work.
RELATED FAQS
  1. Is it legal to invest my student loan money?

    Take a risk investing student loans and encounter a legal and moral gray area as well as possible financial challenges along ... Read Answer >>
  2. Can student loans be used to pay rent?

    In most cases, loans can be used for housing costs, but students should still plan to have some cash on hand. Read Answer >>
  3. Why are private student loans generally more expensive than federal loans?

    Make the right decision between a federal student loan and a private student loan when looking for financial aid for your ... Read Answer >>
  4. 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 >>
  5. What is the difference between certified and non-certified private student loans?

    Learn the main differences between certified and non-certified private student loans, and see why non-certified student loans ... Read Answer >>
Hot Definitions
  1. Graduate Management Admission Test - GMAT

    A standardized test intended to measure a test taker's aptitude in mathematics and the English language. The GMAT is most ...
  2. Magna Cum Laude

    An academic level of distinction used by educational institutions to signify an academic degree which was received "with ...
  3. Cover Letter

    A written document submitted with a job application explaining the applicant's credentials and interest in the open position. ...
  4. 403(b) Plan

    A retirement plan for certain employees of public schools, tax-exempt organizations and certain ministers. Generally, retirement ...
  5. Master Of Business Administration - MBA

    A graduate degree achieved at a university or college that provides theoretical and practical training to help graduates ...
  6. Liquidity Event

    An event that allows initial investors in a company to cash out some or all of their ownership shares and is considered an ...
Trading Center