ANOVA and Least Squares - Speech or Presentation Example

MSS stands for the mean sum of squares, which is nothing but the sum of squares (of the difference between individual data points and the mean) divided by the degree of freedom. For a chosen value of the degree of significance and degree of freedom; there is a critical value of F-statistics that determines whether or not there is a significant difference between the two groups of data. 

In the present study, the given dataset was divided into two groups of the dataset by taking the first eight data points in group one and the remaining seven data points in group two. The values were inserted in two columns of the MS Office Excel worksheet. A single factor ANOVA was performed using MS Office Excel at significance level a = 0.05. The summary output of the analysis is presented in Table 1. From this analysis, it can be seen that the value of F-statistics for this pair of datasets is 0.832622 while the value of F-critical (for a = 0.05 and df = 13) is 4.667186 i.e. F-statistics is much smaller than F-critical. Therefore, it can be concluded that there is no significant difference between the two datasets.

Table 1: Output of Single Factor ANOVA (Analysis of Variance) using MS Office Excel

ANOVA: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

Column 1

8

332

41.5

136

Column 2

7

328

46.85714

120.1429

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

107.1429

1

107.1429

0.832622

0.378127

4.667186

Within Groups

1672.857

13

128.6813

Total

1780

14