Chi-Square Test
Definition
A goodness-of-fit test comparing the observed digit frequencies in a dataset to the expected Benford frequencies, producing a test statistic that is compared against a critical value at a chosen significance level.
- Compares
- Observed vs expected digit frequencies
- Applied to
- Benford's Law digit analysis
- Output
- Test statistic vs critical value
- Decision basis
- Chosen significance level
Common questions
What does a significant chi-square result mean in a Benford's Law analysis?+
It means the dataset's digit distribution deviates from what Benford's Law predicts by more than chance would explain, which raises suspicion of manipulation, but it does not by itself prove fraud, since many legitimate datasets do not follow Benford's Law at all.
Why choose the chi-square test over other Benford conformity tests?+
It is simple to compute and widely understood, but it is sensitive to sample size and can flag statistically significant but practically trivial deviations in large datasets, so examiners often pair it with effect-size measures like the mean absolute deviation.
Related terms
- Benford's Law
- An empirical regularity in naturally occurring numerical datasets: the leading digit follows a logarithmic distribution, with 1 appearing about 30% of the...
- Mean Absolute Deviation (MAD)
- A practical Benford conformity measure that averages the absolute differences between observed and expected proportions across all leading digits, with Nigrini benchmarks...
- Second-Digit Test
- Analysis of the second significant digit in isolation, where 0 is expected to appear about 11.97% of the time. A spike in...
- Two-Digit Test
- An extension of Benford's Law to the first two significant digits, producing 90 possible combinations each with a predicted frequency, which is...
- Z-Statistic
- A per-digit test that calculates whether the deviation between an observed frequency and the Benford expected frequency for that single digit is...