# Techniques Of One-way Analysis Of Variance

**Techniques of One-way Analysis of Variance:**

**1**. In One-way analysis of variance there are k samples, one from each of k normal populations with common variance σ ^{2} and means μ_{1},μ_{2}, ...μ_{n}. The number of observations n_{i} in samples may be equal or unequal i.e.

** n _{1} n_{2} ....... n_{k} = N**

**2**. Linear Model:

x_{i j} = μ αi e_{i j}

Where x_{i j }= observations i = 1,2, ....k, j = n_{i}

μ = The general mean

ai = Effect of ith factor = mi−m

e_{i j} = Effect of error or random term.

**3**. Null Hypothesis (H_{0}) and Alternative Hypothesis (H_{1}):

H_{0} : The means of the populations are equal i.e.

μ_{1} = μ_{2 }= ....,= μ_{k}

H_{1}: At least two of the means are not equal.

**4**. Computations:

(**i**) Calculate sum of observations in each sample and of all observations.

Sum of sample observations:

Sum of the squares of the sample observations:

(**ii**) Calculate correction factor CF = T^{2}/N

Where T = Square of the sum of all the observations =

N = Total number of observations

(**iv**) Calculate total sum of squares (TSS) by the formula

(**v**) Sum of squares between (SSB) samples by the formula

(**vi**) Calculate sum of squares within samples by the formula

Sum of squares may also be computed as SSW = TSS − SSB. Sum of squares within samples is also called Error Sum of Squares.