Degree of freedom
A degree of freedom is an independent quantity that can vary in a system or statistical calculation after constraints are accounted for.
Effective Data Analysis
Degrees of freedom are the number of independent values available to estimate a statistical quantity or determine a test distribution.
- How it is used
- Uses degrees of freedom with an alpha level to select a critical t-value and assess a t-test result.
- How deep it goes
- Gives sample-size calculations and table lookup, but does not derive the formulas.
- Examples
- Uses 200 observations, two groups of 31 observations, and a t-distribution table of critical values.
- What you can do after
- Evaluate/understand it by calculating degrees of freedom for the illustrated t-tests and locating a critical t-value at a chosen alpha level.
Read how Effective Data Analysis explains degree of freedom →
Grokking Statistics
Degrees of freedom are the number of independent values available to estimate a quantity after accounting for constraints.
- How it is used
- Uses degrees of freedom to select and parameterize t-distributions for small-sample confidence intervals and hypothesis tests.
- How deep it goes
- Defines degrees of freedom as n − 1 and applies them in interval and test calculations, without deriving the general theory.
- Examples
- Uses candle burn times with 10 observations and exam scores with 21 observations to demonstrate confidence intervals and directional tests.
- What you can do after
- Apply degrees of freedom in Python with SciPy to calculate t-based confidence intervals and hypothesis-test p-values.
Statistics Every Programmer Needs
Degrees of freedom are the number of independently varying values contributing to a statistical calculation after constraints are accounted for.
- How it is used
- Supports interpreting chi-square tests by determining the p-value and statistical significance.
- How deep it goes
- Defines degrees of freedom, gives a row-and-category calculation, and connects the result to p-values without deriving the underlying distribution.
- Examples
- Uses leading-digit counts from world population data, a chi-square statistic of 7.1925, and 8 degrees of freedom.
- What you can do after
- Evaluate chi-square significance by deriving degrees of freedom and interpreting an exact or table-based p-value.
Read how Statistics Every Programmer Needs explains degree of freedom →
Related concepts
- student's t-distributionpart of · Student’s t-distribution is a family of continuous probability distributions with heavier tails than the normal distribution, used in inference when variability is estimated from data.
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