Observations are classified into groups on the basis of single criterion.In such classification there are k samples ,one from each k normal populations with common variance
MSE N-k SSE Within samples N-1 SST Total MSC K-1 SSC Between samples Mean square Degree of freedom Sum of Squares Source of variation
ANOVA table for two way analysis of variance N-1 SST Total F R MSE (C-1)(r-1) SSE Residual F C MSR r-1 SSR Between rows MSC C-1 SSC Between columns F ratio Mean square Degree of freedom Sum of squares Sources of variation
In a bivariate distribution the data are fairly large ,they must be summarized in the form of a two way table. Here for each variable the values are grouped into various classes( not necessarily the same for both the variable) keeping in view the same consideration as in the case of univariate distribution.
Eg. If there are m classes for the x variable series and n classes for the y variable series then there will be m*n cells in the two way table. By going through the different pairs of the values(x,y) and using tally marks we can find the frequency for each cell and thus obtained the so called bivariate frequency table .