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ExcelF-Test, t-Tests

You will need to have installed the Data Analysis Toolpak in Excel to utilize thesefunctions.

Excel can perform anF-test on two series of data to determine whether the variances ofthe two series are equal. Based on the result, you can determine which Case 2 t-test (aspresented in class) to perform on your data. This handout illustrates these Excel

functions.

F-Test: Two-Sample for Variances

Suppose you want to compare two types of structural steel using measured strength data(in 1000 lbs./sq. in.) to determine if the types are significantly (statistically) different. To

know which t-test to perform, you must first perform anF-test.

1.

Type your strength data into two lists, one for each steel type:

2. In the Data tab, select Data Analysis and selectF-Test Two-Sample for Variancesfrom the list of analysis tools. A dialog box appears.

3. Variable 1 Range will be your first column of data (do not include the heading) and

Variable 2 Range is the second column of data.

4. For Alpha, input 0.05, since you want a 95% significance level (the convention).

5. Click the New Worksheet Ply radio button to create a new tabbed sheet for yourresults.

6. Click OK to close the dialog box.

A new tabbed sheet (ply) opens, displaying theF-test results.

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Mean and variance (!2) for each data set. Also calculated:

Observations: N

df: Degrees of Freedom

F: Excel calculatesFthe way we did it in class with one major difference: itputs thesmallervariance in the numerator. Thus Excel calculatesFas the

reciprocalofFcalcfrom class.

P: probability that the observed difference in variance between the two sets ofdata results from random error. If P < 0.05, variances are statistically different.

FCritical one-tail: Excel calculatesFCritical as the reciprocalof the value we

found in class asFtable.

Because Excel calculates bothFandFCritical as reciprocalsof the way we determinedthem in class, to interpret the results of ExcelsF-test, you must make the following

comparison:

IfF

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As before, we want to compare tcalc(tStat above) with ttable(tCritical two-tail

above).

The comparison is the same as presented in class. That is:

If tcalc< ttable(as it is here, with 1.35 < 2.10), the means are not statistically different.