ELI5- In statistics, what do you mean by degree of freedom? And why do you lose a degree when moving from population to a sample?
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Think of degrees of freedom as a giant swath. Having more people in our swath means we have more room to be wrong, as one person in our swath has probably had a similar response. In a Population, we know what EVERY persons response is. In a sample, we don’t. Losing a degree of freedom accounts for that unknown.
Think about heights for a minute. What’s the average height of everyone in the world? Assuming we had a population, we know what every single individuals height is. However, we can’t know what every single persons height is, so we use samples. What if your sample has a lot of tall people? Short people? It skews your data. Losing a degree of freedom let’s us account for the unknown other heights
DoF is the number of elements that are free to take independent or unknown values (free to change).
Let’s say you know you have 10 people and you know the total height of these people. How many individuals can have unknown heights? Only 9. Once you know the height of 9 people, the height is of the 10th is known with certainty. It is the total height minus the heights of the other 9. It doesn’t have the freedom to change so that degree (element) of freedom (uncertainty) is lost.
The sum total of probabilities is always 1. So once every element but the last is determined, the last element is known so a degree (element) of freedom (uncertainty) is lost.
>Why do you lose a degree when moving from population to a sample?
Because when you take sample, the statistic of the values you obtained are slightly more representative of the sample you took than representative of the population. When you try to guess the population via the sample, the result you get is influenced by the sample you used.
The degree of freedom, is n – 1, because that’s number of values that describe the population without being influenced by the sample.
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