PsychStatsWiki

独立样本t检验的统计前提（The statistical assumptions of independent samples t-test）

• 使用独立样本t检验有三个前提条件（There are three assumptions for conducting an independent samples t-test）：1.观察间彼此独立（Observations are independent of each other）；2.两个总体均为正态分布（Both populations are normally distributed.）；3.两个总体具有相等的方差（方差同质性）（Both populations have equal variances (homogeneity of variance)）。

• 一般情况下，独立样本t检验对于违反前提条件的情况有一定的耐受性。当使用双尾检验或当样本量不是很小时，t检验都是很稳健（robust）的。如果因为某些原因我们觉得总体可能不是正态分布，那么应该尽量选用相对较大的样本。
• In general, independent samples t-test exhibits a certain degree of tolerance towards violations of its assumptions. It remains robust when employing two-tailed tests or when sample sizes are not very large. If there are concerns about the populations not being normally distributed for some reasons, it's advisable to opt for relatively larger sample sizes.

• 方差同质性（homogeneity of variance），也称方差齐性，即要比较两个总体是否具有相同的方差。t统计量公式中的联合方差是对两个样本方差进行平均以后得到的，而这样的操作只有当这两个值用来估计同一总体的方差时才有意义。
• Homogeneity of variance, also known as homoscedasticity, refers to comparing whether two populations have equal variances. The pooled variance in the formula of the t-statistic averages the variances of the two samples, which is meaningful only when these variances are estimates of the variance of the same population.

• Hartley最大F值检验（Hartley's Fmax test）,检验方差是否同质的方法。Fmax为两方差的比值，把较大的样本方差置于分子，较小的置于分母，这样Fmax的值总是大于1的。
• Hartley's Fmax test is a method for testing homogeneity of variance. Fmax is the ratio of the two variances, with the larger sample variance in the numerator and the smaller one in the denominator, ensuring that the value of Fmax is always greater than 1.

• 拇指原则：对于小样本(n＜10) ，如果一个方差是另一个的四倍以上，则不满足方差齐性；对于大样本，标准为2倍。
• The “rule of thumb”: For small samples (n < 10), if one variance is more than four times the other, homogeneity of variance is not met; for large samples, the standard is two times.