Question

The marketing department of a company has designed three different boxes for its product. It wants to determine which box will produce the largest amount of sales. Each box will be test marketed in five different stores for a period of a month. Information on sales is provided below.

Store 1 Store 2 Store 3 Store 4 Store 5
Box 1 210 230 190 180 190
Box 2 195 170 200 190 193
Box 3 295 275 290 275 265

I know the treatments sum of squares is meant to be 24,467.2, however, whenever I calculate it I always get 25,682.2

The error sum of squares is meant to be 2022.14, but I always get 2733.2.

So can someone give me the specific calculations as to how I'm supposed to get 24,467.2 and 2022.14? Because I can't see anything that I've done incorrectly.

Answer 1

Answer on Question #56748 – Math – Statistics and Probability

The marketing department of a company has designed three different boxes for its product. It wants to determine which box will produce the largest amount of sales. Each box will be test marketed in five different stores for a period of a month. Information on sales is provided below.

I know the treatments sum of squares is meant to be 24,467.2, however, whenever I calculate it I always get 25,682.2

The error sum of squares is meant to be 2022.14, but I always get 2733.2.

So can someone give me the specific calculations as to how I'm supposed to get 24,467.2 and 2022.14? Because I can't see anything that I've done incorrectly.

Solution

$$\begin{array}{l} CM = \\ = \frac{(210 + 230 + 190 + 180 + 190 + 195 + 170 + 200 + 190 + 193 + 295 + 275 + 290 + 275 + 265)^2}{15} \\ = 747273.6 \end{array}$$

The treatments sum of squares is

$$\begin{array}{l} SST = \frac{(210 + 230 + 190 + 180 + 190)^2}{5} + \frac{(195 + 170 + 200 + 190 + 193)^2}{5} \\ + \frac{(295 + 275 + 290 + 275 + 265)^2}{5} - 747273.6 = 24467.2 \end{array}$$

The total sum of squares is

$$\begin{array}{l} Total SS = 210^2 + 230^2 + 190^2 + 180^2 + 190^2 + 195^2 + 170^2 + 200^2 + 190^2 + 193^2 + 295^2 + 275^2 \\ + 290^2 + 275^2 + 265^2 - 747273.6 = 27200.4 \end{array}$$

Thus, the error sum of squares is

$$SSError = Total SS - SST = 27200.4 - 24467.2 = 2733.2$$

So, your answer for SSError is correct, but one for SST is false.

I also check this by means of analysis tool "Anova: Single Factor" from Data Analysis Add-in in Microsoft Excel, and results are the same.

Anova: Single Factor

SUMMARY

ANOVA

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