Figure 149: CORRELATION

The output is reproduced in the next table.

Table 31: Output from Correlation Analysis tool

s1 s2 x1 x2 x3 x4

s1 1.00000

s2 “0.75973 1.00000

x1 “0.13434 0.13226 1.00000

x2 0.21423 0.47238 0.01658 1.00000

x3 0.20122 “0.08459 “0.15748 0.14568 1.00000

x4 “0.13567 0.12935 0.99998 0.01040 “0.15839 1.00000

Interpreting the output

” A high level of correlation is implied by a correlation coefficient

that is greater than 0.5 in absolute terms (that is, greater than

0.5 or less than “0.5).

” A mid level of correlation is implied if the absolute value of the

coefficient is greater than 0.2 but less that 0.5.

” A low level of correlation is implied if the absolute value of the

coefficient is less than 0.2.

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Chapter 10: Statistics Tools

10.3.A COVARIANCE TOOL AND FORMULA

The options are same as for the CORRELATION TOOL. The covariance

is dependent on the scale of measurement of the data series. Therefore,

there is no standard scale from which to infer if a covariance value is

“high” or “low.” Thus, use the correlation tool that provides a uniform

scale of ““1 to 1.”

The coefficient of determination can be roughly interpreted as the

proportion of variance in a series that can be explained by the values of

the other series. The coefficient is calculated by squaring the correlation

coefficient.

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Statistical Analysis with Excel

180

Page for Notes

Statistical Analysis with Excel

CHAPTER 11

HYPOTHESIS TESTING

This chapter teaches:

” Z-TESTING FOR POPULATION MEANS WHEN POPULATION

VARIANCES ARE KNOWN

” PAIRED SAMPLE T-TESTS

” T-TESTING MEANS WHEN THE TWO SAMPLES ARE FROM

DISTINCT GROUPS

” THE PRETEST” F-TESTING FOR EQUALITY IN VARIANCES

” T-TEST: TWO“SAMPLE ASSUMING UNEQUAL VARIANCES

” T-TEST: TWO“SAMPLE ASSUMING EQUAL VARIANCES

” ANOVA

The statistics Add-In provides some procedures for hypothesis testing.

(see 7.1) and

The “Inverse Functions” in Excel

other statistics software can be used to build Confidence Interval™s that

provide the values for the “Critical Regions” for conducting hypothesis

tests. The use of the functions opens up a much wider range of possible

hypothesis tests limited only by the Inverse functions available in Excel.

I include a set of “testing rules” in several of the examples. These rules

will blow your mind ” it will make hypothesis testing a readily

comprehensible step“by“step process. The rules will assist you in all

hypothesis tests” in Excel or otherwise.

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Chapter 11: Hypothesis Testing

This chapter requires the Analysis ToolPak Add-Ins; chapter 9

shows how to learn how to launch the Add-Ins.

Z-TESTING FOR POPULATION MEANS WHEN

11.1

POPULATION VARIANCES ARE KNOWN

This tool performs a two“sample Z-test for means with known variances.

This tool is used to test hypotheses about the difference between two

population means.

Possible hypothesis for testing