ABSTRACT
The one-way ANOVA is carried out for data in completely randomized design (CRD). The layout of CRD is as given below:
10.1.2 HYPOTHESES
The one-way ANOVA is applied to test for homogeneity of several population means. The null hypothesis states that the population means are homogenous (equal). That is,
10.1.3 TECHNIQUE
The technique consists in estimating two population variances: one is based on between-sample variance called the mean sum of squares between groups or samples (MSSB) and the other is based on within-sample variance called mean sum of squares within samples (MSSw). Then, the two estimators are compared with the F-ratio. When the samples come from identical population, these two estimates of the population variances are comparable; any difference observed between them is expected to be within the range of their sampling error. When the populations from which
the samples are drawn have different means, the MSSB is expected to provide a higher value. Symbolically, the technique of ANOVA is given as follows:
10.1.4 TEST STATISTIC
The test statistic is given by F = B
ANOVA table: It is given by
where MSSB = BSS
Example: Let us suppose that the improvement scores of 15 patients
from three different treatments are given below:
For this data, the one-way ANOVA computations are as given below:
Hence,
SSW = (65 + 100 + 265) − 370 = 430 − 370 = 60
Since the calculated value of F is more than the table value of F (2, 12) = 3.89, we reject the null hypothesis at 5 percent level of significance (P < 0.05, significant).
