Student’s t Table
Student's t Table
The Student’s t Table is a valuable tool for statisticians, researchers, and anyone involved in statistical analysis. It provides a convenient way to determine critical values and probabilities associated with the Student’s t-distribution.
Using the table is straightforward. The table consists of rows and columns representing degrees of freedom (df) and confidence levels, respectively. Degrees of freedom are typically associated with the size of the sample used in statistical analysis.
To use the table, locate the row corresponding to the degrees of freedom for your data. Then, find the column closest to the specified value you are interested in. The entry at the intersection of the row and column will give you the upper tail area, which represents the probability of P(t > specified value) for that specific degrees of freedom.
For example, with 10 degrees of freedom, if you want to find the probability of P(t > 1.81246), locate the row with 10 degrees of freedom and find the column closest to the value 1.81246. The entry at the intersection will give you the upper tail area, which in this case is 0.05.
The formula for calculating the t statistic is:
In this formula:
t represents the t-statistic.
x is the sample mean.
μ is the hypothesized population mean.
s is the sample standard deviation.
n is the sample size.
Student’s t Distribution PDF Formula
The probability density function (PDF) for a Student’s t distribution is given by:
Where:
is the probability density function
is the random variable
is the degrees of freedom
is the gamma function
Student’s t Distribution CDF Formula
The cumulative density function (PDF) for a Student’s t distribution is given by:
Where:
is the cumulative distribution function
is the beta function