Question

Explain how each of the three types of sums of squares relate to your research hypothesis and/or observations.

Answer 1

1) variance between the samples
The variance between samples measures the difference between the sample mean of each group and the overall mean. It also measures the difference from one group to another. The sum of squares between the samples is denoted by SSB. For calculating variance between the samples, take the total of the square of the deviations of the means of various samples from the grand average and divide this total by the degree of freedom, k-1 , where k = no. of samples.

$SSB=\sum_{j=1}^{n}n_{j}(\bar{X_{j}}- \bar{\bar{X}})^{2}$

2) variance within samples
The variance within samples measures the inter-sample or within sample differences due to chance only. It also measures the variability around the mean of each group. The sum of squares within the samples is denoted by SSW. For calculating variance within the samples, take the total sum of squares of the deviation of various items from the mean values of the respective samples and divide this total by the degree of freedom, n-k, where n = total number of all the observations and k = number of samples.

$SSE=\sum_{j=1}^{n}(X_{j}- \bar{X}_{j})^{2}$

3) the total variance
The total variance measures the overall variation in the sample mean.The total sum of squares of variation is denoted by SST. The total variation is calculated by taking the squared deviation of each item from the grand average and dividing this total by the degree of freedom, n-1 where n = total number of observations.

$TSS=\sum_{j=1}^{n}(X_{ij}- \bar{\bar{X}})^{2}$