What is the degree of freedom for the two-sample t-test comparing the means of two independent samples with sizes 12 and 14?

• The degree of freedom (df) for a two-sample t-test is calculated as:
df = n1 + n2 – 2

• where:
● n1 is the size of the first sample (12 in this case)
● n2 is the size of the second sample (14 in this case)

• Therefore, the degrees of freedom for this test are:
df = 12 + 14 – 2 = 24
However, this calculation assumes equal variances between the two populations. If the variances are unequal, a different formula is used for the t-test (Welch's t-test), which incorporates an estimate of the pooled variance. The degrees of freedom for Welch's t-test are calculated differently and depend on the specific method used to estimate the pooled variance.

• Important Note:
It is important to consider the assumption of equal variances before performing a two-sample t-test. If the variances are unequal, using the degrees of freedom calculated above (24) could lead to inaccurate results. In such cases, it is recommended to use Welch's t-test with appropriate degrees of freedom based on the chosen method for estimating the pooled variance.