Question

An experiment was run to determine whether four specific firing temperatures affect the density of a certain type of brick. A completely randomized experiment was conducted with 5 replications and led to a MSE =35.26. Use α=0.05. Calculate the Least Significant Difference value to compare two means.

Answer 1

To calculate the Least Significant Difference (LSD) value to compare two means, use the formula LSD = t * sqrt(MSE / replications). Substitute the values for MSE and replications, and find the critical value for the desired significance level. Multiply the critical value by the square root of MSE divided by replications to get the LSD value.

Step-by-step explanation:

To calculate the Least Significant Difference (LSD) value to compare two means, we need to know the Mean Square Error (MSE) and the number of replications. In this case, the MSE is 35.26 and there are 5 replications. The formula to calculate the LSD value is LSD = t * sqrt(MSE / replications), where t is the critical value for the desired significance level.Since the significance level is α=0.05, and there are 5 replications, the critical value can be found using a t-table or t-distribution calculator with a degrees of freedom equal to 5 - 1 = 4. Using the t-table, the critical value for α=0.05 and 4 degrees of freedom is approximately 2.776.Substituting the values into the formula, the LSD value is calculated as LSD = 2.776 * sqrt(35.26 / 5) ≈ 4.5434. Therefore, the Least Significant Difference value to compare two means is approximately 4.5434.