How to find the standard deviation of the difference between two means

To find the standard deviation of the difference between two means, you can follow these steps:

1. Understand the formula: The standard deviation of the difference between two means can be calculated using the formula:

SD_diff = √(SD_X²/n_X + SD_Y²/n_Y)

2. Identify the necessary values: You will need the standard deviations (SD) of both samples (SD_X and SD_Y) and the number of observations in each sample (n_X and n_Y).
3. Plug in the values: Insert the values you have into the formula. For example, if SD_X = 5, n_X = 30, SD_Y = 3, and n_Y = 40, then:

SD_diff = √((5²/30) + (3²/40))

4. Calculate the variances: Compute the squared standard deviations divided by their respective sample sizes. In our example:

5²/30 = 25/30 = 0.8333

3²/40 = 9/40 = 0.225

5. Add the results: Sum the values obtained from the previous step:

0.8333 + 0.225 = 1.0583

6. Take the square root: Finally, take the square root of the sum to get the standard deviation of the difference:

SD_diff = √1.0583 ≈ 1.03

This result indicates the expected variability of the difference between the two sample means. It’s a crucial step in various statistical analyses, especially in hypothesis testing.