ANOVA & Least Squares – Speech or Presentation Example

ANOVA ANALYSIS ANOVA stands for Analysis of Variance. This analysis compares a pair of dataset to examine whether or not there a significant difference between the pair of dataset under investigation. The cause of variance is present within a group of data as well as between the groups of data. The relative magnitude of variance between the groups to that within the groups is given by F-statistics which is defined as

Here MSS stands for mean sum of squares, which is nothing but sum of squares (of the difference between individual data points and the mean) divided by the degree of freedom. For a chosen value of 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. If F-statistics for a pair of dataset is less than the critical value of F-statistics, then there is no significant difference between the two dataset and vice versa.
In the present study the given dataset was divided in two groups of dataset by taking first eight data points in group one and the remaining seven data points in group two. The values were inserted in two columns of MS Office Excel worksheet. Single factor ANOVA was performed using MS Office Excel at significance level  = 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 dataset 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 dataset.
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