Bartlett’s Test is a statistical test used to determine if k samples have equal variances. It’s particularly useful in the context of 分散分析（ANOVA） (分析 of Variance), where the assumption of equal variances is critical to the validity of the results. The test was developed by Maurice Stevenson Bartlett in 1937.
その 帰無仮説 (H0) of Bartlett’s Test states that all groups have the same variance, while the alternative hypothesis (H1) posits that at least one group has a different variance. This test calculates a test statistic based on the ratio of the variances of the samples and their respective sizes. This statistic follows a chi-squared distribution under the null hypothesis.
To conduct Bartlett’s Test, one must first gather data from the k different groups. The steps typically include:
- 各グループの標本分散を計算します。
- コンピューティング the 全体の分散 と検定統計量。
- Comparing the test statistic against a critical value from the chi-squared distribution with k – 1 degrees of freedom.
If the test statistic exceeds the critical value, the null hypothesis is rejected, indicating that there is significant evidence to suggest that at least one group variance is different. It’s important to note that Bartlett’s Test is sensitive to departures from normality; thus, if the data are not normally distributed, alternative tests such as Levene’s Test may be more appropriate.