The tdistribution table is a valuable tool in statistical analysis, particularly when dealing with small sample sizes and unknown population variances. Here’s an explanation of what it is and how to use it:
What is it?:
The tdistribution table summarizes the critical values of the tstatistic, a statistical test used for various purposes, including:
 Student’s ttest: Comparing the means of two independent groups.
 Paired ttest: Comparing the means of two related samples.
 Confidence intervals: Estimating the range within which the population mean is likely to lie.
Structure:
The table features two main sections:
 Onetailed: Used for onesided tests, where we are interested only in the probability of a value falling in one tail of the distribution (e.g., higher than a certain value).
 Twotailed: Used for twosided tests, where we consider both tails of the distribution (e.g., significantly different from a specific value).
Within each section, you’ll find:
 Degrees of freedom (df): Represents the number of independent pieces of information in your data, affecting the shape of the tdistribution.
 Significance level (α): Represents the probability of rejecting the null hypothesis (H0) when it’s actually true, typically 0.05 (5%) or 0.01 (1%).
 Critical values: These are specific thresholds for your calculated tstatistic based on df and α.
How to use it:

Calculate your tstatistic: This involves using your sample data and the appropriate formula for your chosen test (e.g., Student’s ttest, paired ttest).

Identify the appropriate section: Onetailed for onesided tests, twotailed for twosided tests.

Locate the row with your degrees of freedom (df).

Find the column with your chosen significance level (α).

Compare your calculated tstatistic to the critical value:
 Reject H0 if your tstatistic is more extreme (greater in absolute value) than the critical value. This indicates a statistically significant difference or effect.
 Fail to reject H0 if your tstatistic falls within the range defined by the critical values. This suggests insufficient evidence for a significant difference or effect.