# Sources of Variation

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Average time it takes to process applications

Office 1 Office 2 Office 3

Employee 1 15 11 17

Employee 2 17 21 15

Employee 3 14 12 17

Employee 4 16 27 16

Excel Output -

Anova: Single Factor

SUMMARY

Groups Count Sum Average Variance

Column 1 4 62 15.5 1.666667

Column 2 4 71 17.75 58.25

Column 3 4 65 16.25 0.916667

ANOVA

Source of Variation SS df MS F Between Groups 10.5 2 5.25 0.258904 P-value 0.777455

F crit 4.256492

Within Groups 182.5 9 20.27778

Total 193 11

1) What does the F crit mean?

2) What numbers represent the SST, SSE and SS Total?

3) What does the P-value number mean?

4) How do the F and F crit relate to each other? What do these numbers mean?

5) Re-run an ANOVA in Excel and determine if the average processing times between workers (employees are in rows) are the same or different.

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##### Solution Summary

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1) The F statistic is formed from the ratio of the two data-model variances. It is possible to compute critical values, Fcrit, for specific levels of confidence and degrees of freedom.

2) SST will compute a wide variety of descriptive statistics on your data set. These include means, standard deviations, ranges, correlations, one-way and multi-way cross-tabulations. These procedures are useful for checking data entry and exploring simple relationships between variables. AutoSignal uses four common goodness of fit statistics. In the following descriptions, SSM is the sum of squares about the mean, SSE is the sum of squared errors (residuals), n is the total number of data values, and m is the number of coefficients in the model. DOF, the degree of freedom, is n-m.

Coefficient of Determination (r-squared)

r² = 1 - SSE/SSM

Degree of Freedom Adjusted Coefficient of Determination

DOF r² = (1 - SSE*(n-1))/(SSM*(DOF-1))

Fit Standard Error (Root MSE)

StdErr = ...

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