Calculate the p-value from a chi-square score with given degrees of freedom. Choose your significance level to check if your p-value meets the threshold.
P-Value:
Understanding the Chi-Square Test
The Chi-Square Test assesses whether observed data aligns with expected values or if two categorical variables are independent. The test results in a chi-square score, which, combined with degrees of freedom, is used to calculate a p-value. A lower p-value indicates stronger evidence against the null hypothesis, suggesting that the observed pattern is unlikely to occur by chance.
How the P-Value is Calculated
The p-value represents the probability of obtaining a chi-square score as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true. Chi-square tests are always right-tailed, focusing on the area in the upper tail of the distribution. Here’s how it’s calculated:
- Calculate degrees of freedom: For contingency tables, degrees of freedom are calculated as \( (r - 1)(c - 1) \), where \( r \) is the number of rows and \( c \) is the number of columns.
- Find the right-tail probability: Using the chi-square distribution with the calculated degrees of freedom, find the probability of observing a test statistic equal to or greater than the observed value. This probability corresponds to the area under the chi-square distribution curve to the right of the observed chi-square score.
- Compare to significance level: If the p-value is less than or equal to the chosen significance level (α, often 0.05), the null hypothesis is rejected, indicating a statistically significant result.
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Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.