Chi-square Distribution Table

The Chi-square Distribution Table, also known as the Chi-square 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 Chi-square distribution table lists critical values for the Chi-square statistic (χ²), a statistical measure used to assess the discrepancy between observed and expected frequencies in categorical data.
  • It features two main sections:
    • One-tailed: Used for one-sided 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).
    • Two-tailed: Used for two-sided 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 Chi-square 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 Chi-square statistic based on df and α.

How to use it:

  1. Calculate your Chi-square statistic (χ²): This involves comparing observed and expected frequencies in your categorical data using a specific formula based on your chosen test (e.g., Chi-square test of independence, goodness-of-fit test).

  2. Identify the appropriate section: One-tailed for one-sided tests, two-tailed for two-sided tests.

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

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

  5. Compare your calculated Chi-square statistic to the critical value:

    • Reject H0 if your Chi-square 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 Chi-square statistic falls below the critical value. This suggests insufficient evidence for a significant difference or association.