Question about Degrees of Freedom

In summary, degrees of freedom refer to the number of independent values that can vary in a statistical procedure. Having more choices for degrees of freedom does not necessarily make a statistical procedure easier or more reliable, as different degrees of freedom can lead to different probability distributions. When designing an experiment, it may be simpler to have problems with small degrees of freedom.
  • #1
musicgold
304
19
Hi,

I generally know the concept of degrees of freedom based on the commonly used explanation about how using the average of a sample reduces the the avaialble choices by 1. For example, I generally understand what is explained here.


What is not clear to me is how having more choices for a value or freedom helps in a statistical procedure, say, the hypothesis testing or the regression.

Thanks.
 
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  • #2
musicgold said:
What is not clear to me is how having more choices for a value or freedom helps in a statistical procedure, say, the hypothesis testing or the regression.

More degrees of freedom doesn't necessarily help - in the sense of making a statistical procedure easier to compute or more reliable. Statistical methods rely on probability distributions. Random variables with different degrees of freedom with respect to sample values usually have different probability distributions. The important thing in a given problem is to use the probability distribution that has the correct degrees of freedom.

If you don't have "a given problem" and are instead designing an experiment and thus inventing the statistical problems to be solved then its an interesting question whether you should create problems with large degrees of freedom or small degrees of freedom. It seems to me that, in general, it's simpler to have problems with small degrees of freedom.
 

1. What is "degrees of freedom" in statistics?

"Degrees of freedom" is a term used in statistics to describe the number of independent variables or quantities that can vary in a given statistical analysis. It is also used to describe the number of values that are free to vary in a mathematical equation or model.

2. Why is degrees of freedom important in statistical analysis?

Degrees of freedom are important because they determine the number of values that can vary in a statistical analysis. This affects the accuracy and reliability of the results, as having too few degrees of freedom can lead to biased or inaccurate conclusions.

3. How is degrees of freedom calculated?

The formula for calculating degrees of freedom varies depending on the specific statistical test or analysis being performed. In general, it is calculated by subtracting the number of fixed constraints or parameters in a model from the total number of observations or data points.

4. What is the relationship between sample size and degrees of freedom?

The relationship between sample size and degrees of freedom is inverse. As the sample size increases, the degrees of freedom decrease. This is because as more data points are added, there are fewer remaining degrees of freedom to estimate the variability in the data.

5. Can degrees of freedom be negative?

No, degrees of freedom cannot be negative. It is a concept that represents the number of independent pieces of information available in a dataset, so it cannot have a negative value.

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