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- ANOVA and Least Squares

The paper "ANOVA and Least Squares" is an excellent example of a speech or presentation on statistics. ANOVA stands for Analysis of Variance. This analysis compares a pair of a 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. Here MSS stands for the mean sum of squares, which is nothing but a sum of squares (of the difference between individual data points and the mean) divided by the degree of freedom. For a chosen value of a 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 a dataset is less than the critical value of F-statistics, then there is no significant difference between the two datasets and vice versa. 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 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 the 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 datasets.