The t-Distribution

The T-DISTRIBUTION is a probability distribution that has a mean of 0 and is symmetrical and bell-shaped, similar to the normal distribution, but with heavier tails.  The t-distribution provides a more accurate and conservative estimates of population parameters when dealing with small samples (n<30) or when population standard deviations are unknown (which is usually the case in social science research).

The shape of the t-distribution — how tall/short the center of the distribution is and how thin/thick the tails of the distribution are (i.e., the dispersion of the distribution) — is determined by the DEGREES OF FREEDOM (df).  The degrees of freedom for a single sample is equal to the sample size, minus one; as a formula: df=n-1.  As degrees of freedom increase, the t-distribution approaches the normal distribution.

To interpret a t-distribution, you will need to reference a T-DISTRIBUTION TABLE (i.e., a T-TABLE).  Using a t-table is similar to using a z-table:

• Rows correspond to different degrees of freedom 
• Columns correspond to different confidence levels (90%, 95%, 99%) or SIGNIFICANCE LEVELS (α), which are equal to 1 minus the confidence level (α = 0.10, 0.05, 0.01)
• Table cells report the CRITICAL VALUES of the t-distribution, given the degrees of freedom and the confidence level/significance level; critical values are helpful in hypothesis testing and determining confidence intervals