Statistical Analysis with Excel

In short, if the T is greater than “+1.64,” then one may conclude (with 95%

Confidence) that the means of the samples differ by the hypothesized

difference.

Excel calculates the P or Significance value for each test you run.

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

Confidence (equivalently, the hypothesis that the means are

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

criterion is considered too “loose” by some.

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

Confidence (equivalently, the hypothesis that the means are

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

standard criterion used.

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

Confidence (equivalently, the hypothesis that the means are

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

strictest criterion used.

You should memorize these criteria, as nothing is more helpful in

interpreting the output from hypothesis tests (including all the tests

intrinsic to every regression, ANOVA and other analysis). The output for

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Chapter 11: Hypothesis Testing

such a test is shown in the next table28.

Table 35: Output from a T-test for Paired Samples. The text in italics has been inserted by

the author.

First Second

sampling sampling

Mean 152 145

Variance 126 114

Observations 44 44

Pearson Correlation 0.999693

Hypothesized Mean Difference 5

Df 43

26.76 is the T

T Stat 26.76 estimated from the

data

One“tailed test

P (T< = t) one“tail 0.00 1.68 is the “T cut“off

Critical Value” from

T Critical one“tail 1.68 T-Tables

Two“tailed Test

P (T< = t) two“tail 0.00 2.02 is the “T cut“off

Critical Value” from

T Critical two“tail 2.02 T-Tables

Interpretation:

One“tailed test

P (T< = t) one“tail 0.00 Thus, significant at 99%

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

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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.

203

Statistical Analysis with Excel

One“tailed test

T Critical one“tail (positive 1.68

2.02 is the “T cut“off Critical Value” from T-

for positive tail test, negative

Tables for alpha = 0.05 and Df = 43

”1.68

for negative tail)

Inferential Analysis:

” Fail to reject null (1-tailed for null hypothesizing in a negative direction: H0 (Null

Hypothesis): mean<5)

” Fail to accept null if H0 (Null Hypothesis): mean>5.

Two“tailed Test

P (T< = t) two“tail 0.00 Thus, significant at 99%

T Critical two“tail (compare

This is the “T cut“off Critical Value” from T-

absolute value of T- stat from

2.02

the data with this absolute Tables for alpha = 0.025 and Df = 43

value)

Inferential Analysis:

” For two“tailed test, fail to accept null at 99% Confidence

ANOVA

11.4

This tool performs simple analysis of variance (ANOVA) to test the

hypothesis that means from two or more samples are equal (drawn from

populations with the same mean). This technique expands on the tests for

two means, such as the T-test.

Go to the menu option TOOLS/DATA ANALYSIS29. Select the option

“ANOVA: Single Factor.” The input range must consist of two or more

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

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data analysis. Refer to section 41.4.