Anova

Question 1

Two-Way ANOVA

What is a 2-way test

Answer 1

When it is desired to test row and column effect or treatment and blocking effect,

Question 2

What is blocking in ANOVA

Answer 2

Blocking is a method used to reduce confounding (inability to separate the effects of two or more explanatory variables on the response variable. In this context, it is the inability to separate the influence of treatment from other interrupting or extraneous variables) . … In general terms, blocking compensates for situations where known factors, other than treatment group, are likely to affect what is being observed in the study.

Question 3

Here, there are two null and two alternative hypotheses:

Rows
H_0: µ_i= 0 ∀ i
i.e. the row means are the same. In other words, there is no difference (zero difference) between the means
H_1: µ_i ≠ 0 ∀i
Columns
H_0: µ_j= 0 ∀j, i.e. the Column means are the same. In other words, there is no difference (zero difference) between the means
H_1: µ_j ≠ 0 ∀j i.e. at least one of the equalities does not hold
Level of significance = 5% or 1%
Calculation of F
Rows: F_calculated =
Columns: F_calculated =

Answer 3

Rows: F_calculated = MSR/MSE
Columns: F_calculated=MSC/MSE
MSR = SSR/(r-1)
MSC = SSC/(c-1)
MSE = SSE/((r-1)(c-1))
SSR = (∑▒〖Ti .〗^2 )/nj - 〖T. .〗^2/n
Square each rows total / number of rows. - sum of rows/ no of rows
SSC = (∑▒〖T. j〗^2 )/ni - 〖T. .〗^2/n

Square each columns total / number of columns . - sum of columns / no of columns

SSE = ∑_i▒∑_j▒〖X_ij〗^2 - (∑▒〖Ti .〗^2 )/nj - (∑▒〖T. j〗^2 )/ni + 〖T. .〗^2/n

Sum of the square of all rows and columns- sum of the square of all rows- sum of squares of all columns+ total of rows/columns/number of rows and columns

Question 4

What does the table look like

Answer 4

2-Way ANOVA TABLE
Source of
Variation Df SS MS Test Ratio
Row(Treatment) r- 1 SSR MSR = SSR/(r-1) F_1 = MSR/MSE

F_2 = MSC/MSE
Column  c-1  SSC  MSC = SSC/(c-1)  
Within Means (Error)  (r-1)(c-1)  SSE  MSE = SSE/((r-1)(c-1))  
Total  n-1  SST