Basic Examples (3) 

Calculate the Student’s t-value for two degrees of freedom:

In[1]:=

Out[1]=

Scale the error of an around by the Student’s t-value:

In[2]:=

Out[2]=

Calculate the value of a measurement with a Student’s t-value scaled error:

In[3]:=

Out[3]=

Scope (3) 

The function can return an exact value in the single argument form. Use N to get a numerical value:

In[4]:=

Out[4]=

In[5]:=

Out[5]=

The function can handle a list of Around values:

In[6]:=

Out[6]=

StudentTValue can handle asymmetric Around:

In[7]:=

Out[7]=

Options (1) 

StudentTValue will calculate the Student’s t-value according to the specified ConfidenceLevel (which is per default at 0.683…=1σ):

In[8]:=

Out[8]=

Applications (1) 

Calculate the statistical uncertainty for measurements with only a few data points:

In[9]:=

Out[10]=

Properties and Relations (2) 

The Student’s t-value for a List is equal to the Student’s t-value of the resulting MeanAround of the data with the degrees of freedom equal to the number of data points minus one:

In[11]:=

Out[11]=

For many measurements, StudentTValue will tend towards one (if the ConfidenceLevel option is set to Automatic as default):

In[12]:=

Out[12]=

Possible Issues (2) 

The function only accepts integers as the degree of freedom parameter ν:

In[13]:=

Out[13]=

The function returns an infinitely-big error interval for just one value:

In[14]:=

Out[14]=

Neat Examples (1) 

The error interval from StudentTValue always encloses the one from MeanAround but converges for a high enough number of measurements:

In[15]:=

Out[16]=