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Appendix C: Calculation Formulas for Analysis of Variance (Independent Sampling)

\begin{array}{l} CM & = & Correction for mean \\ = & \frac{{(Total of all observations)}^{2}}{Total number of observations} = \frac{{(Σ y_{i})}^{2}}{n} \\ SS(Total) & = & Total sum of squares \\ = & (Sum of squares of all observations) - CM = Σ y_{i}^{2} - CM \\ SST & = & Sum of squares for treatments \\ = & (\begin{matrix} Sum of squares of treatment totals with \\ each square divided by the number of \\ observations for that treatment \end{matrix}) - CM \\ = & \frac{T_{1}^{2}}{n_{1}} + \frac{T_{2}^{2}}{n_{2}} + \dots + \frac{T_{k}^{2}}{n_{k}} - CM \\ SSE & = & Sum of squares for error = SS (Total) - SST \\ MST & = & Mean square for treatments = \frac{SST}{k - 1} \\ MSE & = & Mean square for error = \frac{SSE}{n - k} \\ F & = & Test statistic = \frac{MST}{MSE} \end{array}

$\begin{array}{l} CM & = & Correction for mean \\ = & \frac{{(Total of all observations)}^{2}}{Total number of observations} = \frac{{(Σ y_{i})}^{2}}{n} \\ SS(Total) & = & Total sum of squares \\ = & (Sum of squares of all observations) - CM = Σ y_{i}^{2} - CM \\ SST & = & Sum of squares for treatments \\ = & (\begin{matrix} Sum of squares of treatment totals with \\ each square divided by the number of \\ observations for that treatment \end{matrix}) - CM \\ = & \frac{T_{1}^{2}}{n_{1}} + \frac{T_{2}^{2}}{n_{2}} + \dots + \frac{T_{k}^{2}}{n_{k}} - CM \\ SSE & = & Sum of squares for error = SS (Total) - SST \\ MST & = & Mean square for treatments = \frac{SST}{k - 1} \\ MSE & = & Mean square for error = \frac{SSE}{n - k} \\ F & = & Test statistic = \frac{MST}{MSE} \end{array}$

where

\begin{array}{l} n & = & Total number of observations \\ k & = & Number of treatments \\ T_{i} & = & Total for treatment i (i = 1, 2, \dots, k) \end{array}

$\begin{array}{l} n & = & Total number of observations \\ k & = & Number of treatments \\ T_{i} & = & Total for treatment i (i = 1, 2, \dots, k) \end{array}$

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Table of Contents for Appendix C: Calculation Formulas for Analysis of Variance (Independent Sampling)

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Table of Contents for
Appendix C: Calculation Formulas for Analysis of Variance (Independent Sampling)