Question

What to do if a problem has non-tabled degrees of freedom? For example, often when working with t-students or other similar tables such as ${{\chi }^{2}}$, you only see common degrees of freedom like 1 to 40, 45, 50. But what if the problem has 49 degrees of freedom? Do I use the 50 or 45? So, we can’t do it because it doesn’t have the amount? What if the amount of degrees of freedom is something like 222?

Answer 1

In this problem, we can see what happens if the degree of freedom changes. We should know that if a degree of freedom is very high, then the value of inverse function changes at a very slow rate. This is in case for a student's t-distribution where we use the normal table to look up a value which corresponds to some cumulative probability being met. We can now see it briefly.

Complete step by step solution:
Here we are asked so many questions such as What to do if a problem has non-tabled degrees of freedom? What if the problem has 49 degrees of freedom? Do I use the 50 or 45? What if the amount of degrees of freedom is something like 222?
Where we should know that as the degree of freedom gets very large the change becomes insignificant. So, most tables jump from a high number like 30 to infinity.
So, the rule of thumb is to choose the table row closest to the degree of freedom that we have.
The error in doing so will be small, but we can interpolate between values.
If the degree of freedom is larger than the largest integer, then use the value for infinity.
Therefore, we can choose the closest value in the table.

Note: We should always remember that if a degree of freedom is very high, then the value of inverse function changes at a very slow rate. This is in case for a student's t-distribution where we use the normal table to look up a value which corresponds to some cumulative probability being met.