Bartlett χ² aprox

The Bartlett χ² approximation calculator tests the homogeneity of variances across groups, a key assumption for analyses like ANOVA. It compares the pooled variance of the sample (s²_p) with individual group variances (s²_i) using the formula: (N−k)·ln(s²_p) − Σ(n_i−1)·ln(s²_i), where N is the total sample size, k the number of groups, and n_i the size of each group. The result follows an approximate chi-square distribution to assess statistical significance of variance differences.

This test is applied in studies requiring group comparisons under normal distribution. For instance, in scientific experiments to determine if factors like temperature or dosage affect result variability. The formula calculates the discrepancy between expected and observed group variances. High values suggest heterogeneity, while low values indicate homogeneity.

A critical caution is ensuring data approximates normality. If not, the test may misestimate differences. Alternatives like Levene’s or Fligner-Killeen tests are recommended for non-normal data. The calculator is suitable for preliminary analysis but does not replace full statistical validation.