The Chisquare Distribution Table, also known as the Chisquare table, is a vital tool in statistical analysis for testing hypotheses about categorical data. Here’s an explanation of its purpose and usage:
What it shows:
 The Chisquare distribution table lists critical values for the Chisquare statistic (χ²), a statistical measure used to assess the discrepancy between observed and expected frequencies in categorical data.
 It features two main sections:
 Onetailed: Used for onesided tests, where we are interested 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 an expected value).
 Within each section, you’ll find:
 Degrees of freedom (df): Represents the number of independent categories in your data, affecting the shape of the Chisquare distribution.
 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 Chisquare statistic based on df and α.
How to use it:

Calculate your Chisquare statistic (χ²): This involves comparing observed and expected frequencies in your categorical data using a specific formula based on your chosen test (e.g., Chisquare test of independence, goodnessoffit test).

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 Chisquare statistic to the critical value:
 Reject H0 if your Chisquare statistic is greater than or equal to the critical value. This indicates a statistically significant difference or association between the variables or a deviation from the expected distribution.
 Fail to reject H0 if your Chisquare statistic falls below the critical value. This suggests insufficient evidence for a significant difference or association.