If you do not see this option, then use TOOLS / ADD-INS to activate the Add-In for

20

data analysis. Refer to section 41.4.

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Statistical Analysis with Excel

” Ha (Alternate hypothesis): σ12” σ 22 <> 0, Where σ12 is the variance of

sample one, and σ 22 is the variance for sample two.

The F has a one“tail test only.

The next table shows the output of a typical F-test21.

Table 33: Output for F-test tool for equality of variances

s1 s2

Mean 7.3202 7.2345

Variance 32.6754 40.1309

Observations 168 168

Df 167 167

0.8142

P (F< = f) one“tail 0.0926

F Critical one“tail 0.8747

Interpreting the output

” The row “Variance” shows the estimated variance parameters.

” Inferences from the P value of “0.0926”:

I do not supply the sample data for most of the examples in chapter 42 to chapter 46.

21

My experience is that many readers glaze over the examples and do not go through

the difficult step of drawing inferences from a result if the sample data results are

the same as those in the examples in the book.

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Chapter 11: Hypothesis Testing

” If P is less than 0.10, then the test is significant at 90%

Confidence (equivalently, the hypothesis that the variances are

equal can be rejected at the 90% level of Confidence). The P of

0.0926 implies the test is significant at the 90% Confidence level.

Being “significant” implies that the estimated F statistic lies in

the critical region and the “null hypothesis cannot be accepted.”

You are in the area represented by the alternate hypothesis ”

the variances are unequal.

” If P is less than 0.05, then the test is significant at 95%

Confidence (equivalently, the hypothesis that the variances are

equal can be rejected at the 95% level of Confidence). The

hypothesis cannot be rejected at the 0.05 level of significance.

” If P is less than 0.01, then the test is significant at 99%

Confidence (equivalently, the hypothesis that the variances are

equal can be rejected at the 99% level of Confidence). The

hypothesis of equal variances cannot be rejected at the 0.01 level

of significance.

The test is significant only at the 0.10 level of significance. The critical

estimated F of 0.81 is higher than the critical F of 0.8747 implying that

the “null hypothesis of equal variances” cannot be accepted at a 0.05 level

of Confidence.

Once you know if the null hypothesis of equal variances can be accepted,

you can resolve whether to use the “Two“Sample T-test Assuming Equal

Variances” or “Two“Sample T-test Assuming Unequal Variances.”

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11.2.B T-TEST: TWO“SAMPLE ASSUMING UNEQUAL VARIANCES

This T-test form assumes that the variances of both ranges of data are

unequal. Use this test when the groups under study are distinct. Use a

paired test (discussed in the next section) when there is one group before

and after a treatment.

Possible hypothesis for testing

u1 is the mean of sample one. u2 is the mean for sample two. The critical

regions are based on a 5% significance level (or, equivalently, a 95%

Confidence Interval)

(a) Two“tailed

The hypothesis

” H0 (Null Hypothesis): u1” u2 = 0 (or any non“zero value)

” Ha (Alternate hypothesis): u1” u2 <> 0

Critical region:

” “Fail to accept” the null hypothesis if the absolute value of the

calculated T is higher than 1.96. Examples of such Z values are:

“+2.12” and ““2.12.”

” “Fail to reject” the null hypothesis if the absolute value of the

calculated T is lower than 1.96. Examples of such T values are:

“+1.78,” “0.00” and ““1.78.”