How do you calculate the degrees of freedom for unequal sample sizes and unequal variance (independent t test)
Degrees of freedom for unequal sample sizes and unequal variances =
(s1^2/n1 + s2^2/n2)^2
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(s1^2/n1)^2/(n1-1) + (s2^2/n2)^2/(n2-1)
Note: ^2 means squared.
To calculate the degrees of freedom for an independent t-test with unequal sample sizes and unequal variances, you can use the Welch-Satterthwaite equation. This equation is given as:
df = (s1^2 / n1 + s2^2 / n2)^2 / ((s1^2 / n1)^2 / (n1 - 1) + (s2^2 / n2)^2 / (n2 - 1))
In this equation, s1^2 and s2^2 refer to the variances of the two samples, n1 and n2 refer to the sizes of the two samples.
Here are the step-by-step instructions to calculate the degrees of freedom:
Step 1: Calculate the variances of both samples (s1^2 and s2^2).
Step 2: Determine the sizes of both samples (n1 and n2).
Step 3: Substitute the values of s1^2, s2^2, n1, and n2 into the Welch-Satterthwaite equation:
df = (s1^2 / n1 + s2^2 / n2)^2 / ((s1^2 / n1)^2 / (n1 - 1) + (s2^2 / n2)^2 / (n2 - 1))
Step 4: Simplify the equation.
Step 5: Calculate the final value of df.
Note: You can use statistical software or online calculators to simplify and calculate the final value of df more easily.
To calculate the degrees of freedom for an independent t test with unequal sample sizes and unequal variances, you can follow these steps:
Step 1: Determine the sample sizes of both groups.
Let's say you have Group A with a sample size of n1 and Group B with a sample size of n2.
Step 2: Calculate the variances of both groups.
Compute the variance (s1^2) of Group A and the variance (s2^2) of Group B.
Step 3: Calculate the degrees of freedom.
The degrees of freedom in this case can be estimated using Welch's approximation formula, which takes into account the unequal sample sizes and unequal variances. The degrees of freedom can be calculated using the following formula:
df = ((s1^2 / n1 + s2^2 / n2)^2) / (((s1^2 / n1)^2) / (n1 - 1) + ((s2^2 / n2)^2) / (n2 - 1))
In the formula, df represents the degrees of freedom.
By plugging in the sample sizes (n1 and n2) and the variances (s1^2 and s2^2) into the equation, you can calculate the degrees of freedom for your independent t test with unequal sample sizes and unequal variances.