A research study comparing three treatments with n=5 in each treatment produces T1=5, T2=10, T3=15 with SS1=6, SS2=9, SS3=9 and (Greek letter E)X squared =94. What is SS total? What is SS between and what is SS within?
34
To calculate the SS total, SS between, and SS within, we need some additional information. Specifically, we need the number of observations (N) and the grand mean (μ).
However, from the given information, we can calculate SS total. The SS total represents the total sum of squares and quantifies the variability in the dataset, regardless of the treatments or groups.
SS total can be calculated using the formula:
SS total = Σ(x - μ)²
where Σ represents the summation symbol, x is the individual data point, and μ is the grand mean.
The given information includes the sum of squares (SS) for each treatment (SS1, SS2, SS3) and the sum of squares for the whole dataset (ΣX²).
To calculate SS total, we can use the following formula:
SS total = ΣX² - (ΣX)² / N
Here, N represents the total number of observations.
Since (Greek letter E)X squared = 94, we have:
SS total = 94 - (ΣX)² / N
Since the sample size is n = 5 for each treatment and there are three treatments, the total number of observations is N = n * number of treatments = 5 * 3 = 15.
Substituting the values into the formula, we get:
SS total = 94 - (30)² / 15
Simplifying further:
SS total = 94 - 900 / 15
= 94 - 60
= 34
Therefore, the SS total is 34.
To calculate SS between and SS within, we need the grand mean (μ). However, the given information does not provide the mean value. Please provide the necessary information, such as the mean, so we can calculate SS between and SS within.