What is the degree of freedom?
The degree of freedom (DF) is the concept most used in statistics and physics. In both cases, it tends to define the limits of the system and position or size of what is analyzed, so it can be visually represented. The definition of DF in both fields is related, but not exactly the same.
in physics, the degree of freedom of objects or systems, and each stage refers to a position in time, space or other measurements. DF can be used synonymously with the term coordinates and usually means independent coordinates of the smallest number. The real degree of freedom is based on the fact that the system is described in the phase space or in all potential types of space that the system inhabits simultaneously. Each part of the phase space that occupies the system can be considered DF, helping to define the full reality of the system.
From a statistical point of view, the degree of freedom defines the distribution of populations or samples and is located when people do not study inference statistics: Hypotheses and intervation testingAly reliability. As with the scientific definition, the DF in statistics describes the shape or aspects of the sample or population depending on the data. Not all distributed representations have a certain degree of freedom to measure. Common normal distribution of normal standard is not defined by grades; Instead, it will be the same bell -shaped curve in all cases.
Similar distribution as standard normal is student-T. Student-T is partially defined by the degree of freedom in the formula N-1, where n is the size of the sample. This means that they were variables from distribution to be selected one by one, all except the last could be freely selected. There is no option to take the last and no freedom to choose another variable at this point. One variable is therefore not free; It's like having to choose the last SCRABBLE® tile, where there is no choice to choose the letter.
different distributions such as F and Chi-Square have different definitions of the degree of freedom and some even use more than one DF in the definition. The problem is confusing because the definition of DF is associated with the type of test and is not the same with different parametric (based on parameters) and non -parametric (not based on parameters). Basically, it won't always be N-1. The good testing of the pivot or emergency tables can use the chi-constructed distribution with different DFs than what evaluates scattering or standard deviations with individual variables.
What is important to remember is that every degree of freedom is used to define distribution, changes it. It can still have certain properties that do not change, but the size and appearance differ. When people draw distribution representations, especially two same distributions have a different DF, it is recommended that they look different to say that DF is not the same.