- Thread starter joeb33050
- Start date

As far as a threshold I think computers make the question irrelevant since the software will pretty much make this decision for you. If you was workin off tables then I guess youd just pull from z-table at some point. The table in the back of my linear models book only goes to df=120 and has a gap from 60 to 120.

When you don't know the standard deviation you should use the t-test which uses the sample standard deviation.

The t distribution has heavier tails to compensate for the inaccurate sample standard deviation.

A long time ago when people didn't have computers we used tables instead of a computer.

The normal distribution has the advantage of a more detailed table as you don't need to have table for every DF like in the t distribution.

With DF tend to infinity the t-distribution tent to the normal distribution

With DF=30 the t-distribution is not too far from the z distribution. (but still not so accurate)

Maybe the more detailed z table of the compensate for the not accurate values.

But today you should use the t distribution.

The average of a sample size of 30 tends to distribute normally per CLT, but this is a different story ...

Even if R put the line on df=1000, you may decide to put the line on 5000.

It is probably related to the precision level and performance, If I remember correctly R distributions give the precision of 7 digits.

So if df=121 will give a precision level of 7 digits, and the calculation is faster than the T distribution calculation, it is more efficient to use the normal distribution.

As a user, if you use the sample standard deviation you should just use the T distribution.