Critical Difference Calculator

Formula

The formula to calculate the Critical Difference (CD) is:

\[ \text{CD} = \frac{|\text{M1} - \text{M2}|}{\sqrt{\left( \frac{\text{SD1}^2}{\text{N1}} \right) + \left( \frac{\text{SD2}^2}{\text{N2}} \right)}} \]

Where:

\(\text{CD}\) is the critical difference
\(\text{M1}\) is the mean of group 1
\(\text{M2}\) is the mean of group 2
\(\text{SD1}\) is the standard deviation of group 1
\(\text{SD2}\) is the standard deviation of group 2
\(\text{N1}\) is the sample size of group 1
\(\text{N2}\) is the sample size of group 2

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.

Example Calculation

Let's assume the following values:

Mean of Group 1 (M1) = 50
Mean of Group 2 (M2) = 45
Standard Deviation of Group 1 (SD1) = 5
Standard Deviation of Group 2 (SD2) = 4
Sample Size of Group 1 (N1) = 30
Sample Size of Group 2 (N2) = 25

Using the formula:

\[ \text{CD} = \frac{|50 - 45|}{\sqrt{\left( \frac{5^2}{30} \right) + \left( \frac{4^2}{25} \right)}} = \frac{5}{\sqrt{\left( \frac{25}{30} \right) + \left( \frac{16}{25} \right)}} = \frac{5}{\sqrt{0.83 + 0.64}} = \frac{5}{1.22} \approx 4.12 \]

The Critical Difference (CD) is approximately 4.12.