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 chisquare 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 goodnessoffit 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.

GoodnessOfFit
Used in statistics and statistical modelling to compare an anticipated ... 
Nonparametric Statistics
A statistical method wherein the data is not required to fit ... 
Sampling Error
A statistical error to which an analyst exposes a model simply ... 
Statistics
A type of mathematical analysis involving the use of quantified ... 
Null Hypothesis
A type of hypothesis used in statistics that proposes that no ... 
Descriptive Statistics
A set of brief descriptive coefficients that summarizes a given ...

What assumptions are made when conducting a ttest?
The common assumptions made when doing a ttest include those regarding the scale of measurement, random sampling, normality ... Read Full Answer >> 
What are some of the more common types of regressions investors can use?
The most common types of regression an investor can use are linear regressions and multiple linear regressions. Regressions ... Read Full Answer >> 
What types of assets produce negative portfolio variance?
Assets that have a negative correlation with each other produce negative portfolio variance. Variance is one measure of the ... Read Full Answer >> 
When is it better to use systematic over simple random sampling?
Under simple random sampling, a sample of items is chosen randomly from a population, and each item has an equal probability ... Read Full Answer >> 
What are some common financial sampling methods?
There are two areas in finance where sampling is very important: hypothesis testing and auditing. The type of sampling methods ... Read Full Answer >> 
How can I measure portfolio variance?
Portfolio variance measures the dispersion of returns of a portfolio. It is calculated using the standard deviation of each ... Read Full Answer >>

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. 
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. 
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. 
Economics
Explaining the Liquidity Coverage Ratio
The liquidity coverage ratio requires banks and other financial institutions to hold enough cash and liquid assets on hand to weather market stress. 
Fundamental Analysis
Calculating Valuation
Valuation is the process of determining what an asset is worth. 
Economics
Will the Selloff in China Hurt the Global Economy?
Though China is the world’s second largest economy, its volatility in the stock market is unlikely to have an impact on the global or Chinese economy. 
Fundamental Analysis
Understanding Qualitative Analysis
Qualitative analysis is a general term describing the nonmathematical scrutiny used by investors and managers to make investment and business decisions. 
Economics
Signs The U.S. Recovery Is Solid
Many market observers lately have been making some pretty pessimistic evaluations of the U.S. economy, declaring that it’s stagnating and soft. 
Fundamental Analysis
Explaining the Monte Carlo Simulation
Monte Carlo simulation is an analysis done by running a number of different variables through a model in order to determine the different outcomes. 
Fundamental Analysis
Explaining the Empirical Rule
The empirical rule provides a quick estimate of the spread of data in a normal statistical distribution.