Question

While conducting a one-way ANOVA comparing 6 treatments with 10 observations per treatment, computed value for SST = 290 and MSE = 5. Find the value of F and also construct the ANOVA table.

Answer 1

There are 60 observations. N = 60 and k = 6 treatments

Source of variation	SS(Sum of square)	Df	MS(Mean Square)	F
Treatment	SST = 290	k -1 = 5	MST = 58	11.6
Error	SSE = 270	n-k = 54	MSE = 5
Total	TSS = 560	n-1 = 59

Here number of treatments k = 6

Total number of observations N = 60

The degrees of freedom for total = N-1 = 60 – 1 = 59

The degrees of freedom for treatments = k-1 = 6 – 1 = 5

The degrees of freedom for Error = N – k = 54

MSE = 5

MSE = SSE / N – K

SSE = 5*54 = 270

SST = 290

MST = SST / k-1 = 290/5 = 58

SS(Total) = SST + SSE

TSS = 290 + 270 = 560

F = MST /MSE = 58 / 5 = 11.6

F = 11.6