Enter the means, standard deviations, and sample sizes for two groups into the calculator to determine the critical difference. The critical difference is a statistical measure used to determine if the difference between two group means is significant.
Critical Difference Formula
The following formula is used to calculate the critical difference between two groups:
CD = |M1 - M2| / √((SD1² / N1) + (SD2² / N2))
Variables:
- CD is the critical difference
- M1 is the mean of group 1
- M2 is the mean of group 2
- SD1 is the standard deviation of group 1
- SD2 is the standard deviation of group 2
- N1 is the sample size of group 1
- N2 is the sample size of group 2
To calculate the critical difference, subtract the mean of group 2 from the mean of group 1, take the absolute value of that difference, and then divide by the square root of the sum of the squared standard deviation of group 1 divided by its sample size and the squared standard deviation of group 2 divided by its sample size.
What is Critical Difference?
The critical difference is a value used in statistics to determine whether the difference between two means is statistically significant. It takes into account the variability within each group and the size of each group. A larger critical difference suggests that the observed difference between group means is less likely to be due to random chance and more likely to be significant.
How to Calculate Critical Difference?
The following steps outline how to calculate the critical difference:
- First, determine the means of both groups (M1 and M2).
- Next, determine the standard deviations of both groups (SD1 and SD2).
- Then, determine the sample sizes of both groups (N1 and N2).
- Use the formula to calculate the critical difference (CD).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge.
Mean of Group 1 (M1) = 80
Mean of Group 2 (M2) = 85
Standard Deviation of Group 1 (SD1) = 10
Standard Deviation of Group 2 (SD2) = 12
Sample Size of Group 1 (N1) = 30
Sample Size of Group 2 (N2) = 30
