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Statistical Testing in Excel


Installing the functionality

Install the Analysis Tools Add-in

This adds a data analysis wizard and some excel functions to your installation.Tools>Data Analysis>

This add in is part of a basic Microsoft Office package.


T-tests

Excel includes three t-tests in the Analysis tool pack

PairedTwo sample – Equal varianceTwo sample – unequal variance

The variance assumption is tested with the f-test function discussed later


T-test: Test of means with equal Variances

Data Format for test:Each set of data must be in a single column or a rowSet the mean distance to 0 to evaluate the difference

Determine if you have a one or two sided hypothesis test

Use the appropriate p-value to judge the result.


T-test: Test of means with unequal variances





Paired t-test of two means





T-test with a function

The t-test is also available with a single function

=ttest(array1,array2,tails,type)

Array1 and array2 are each a row (or column) of data

If tails = 1, TTEST uses the one-tailed distribution. If tails = 2, TTEST uses the two-tailed distribution.

If type = 1, the paired t-test is usedIf type = 2, the two sample, equal variance test is usedIf type = 3, the two sample, unequal variance test is used

The function returns the p-value of the

specified test.


F-test: Test for Equal Variance




F-test: with a formula

The f-test is available as an Excel Formula=FTEST(array1,array2)

Array1 and array2 are each in a single row or column.

The result of the formula is the p-value for the test.


Regression:

Data formatThe Y data is in a single column of dataThe x data must be in a column of data. One or multiple x columns are allowed.If multiple x terms are used, all columns of x data must be adjacent.

This procedure provides multiple diagnostic charts as options.

Line fit chartResidual plotsProbabiloity plot


Regression Numeric Output

Note the standard regression output values. They are interpreted as they would be from any statistical software package.

R-square, standard error, and the number of observations.ANOVA table for the entire regression.Coefficient table to evaluate each term’s significance


Regression graphical outputs

B Residual Plot

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Resi

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B Line Fit Plot

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APredicted A

Normal Probability Plot

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Sample Percentile

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Three general plots are available. The normal probability plot has the axis flipped from the minitab format.All others are as expected, but you may want to change the backgrounds or modify the charts to have trend or regression lines.


Regression with formulas

Excel provides specific formulas to calculate some regression parameters.

Slope: =slope(yvalues,xvalues)Intercept: =intercept(yvalues,xvalues)R-square: =rsq(yvalues,xvalues)Standard Error: =steyx(yvalues,xvalues)Full regression output: linest(yvalues,xvalues,const,stats)

This is an array function that is entered into a range with “ctrl-shift-enter”. Read help function before using.


ANOVA:

Three ANOVA methods are provided

Single factor Allows multiple levels

Two factor with replicationMultiple readings of the same combination

Two factor without replicationOne reading per combination

The format of the data for the two factor methods is very unforgiving. If difficulties arise, read the help menus.


One way ANOVA

This is to compare multiple groups of data from the same factor.

Each group must be in adjacent columns or rows.All groups must have the same number of values.

The p-value is used to

evaluate the significance


Two way ANOVA with replications

In this case the data format is critical

One factor must be in rows.The second factor is in adjacent columns

With a single row for each replication before the next factor level is listed.

You must enter an input range that includes the labels in the format show to the right.

A B CAA 3 1 3

2 1.5 2BB 2 2 3

1 3 2


Two-way ANOVA with replications –output.

The output of the ANOVA includes information of every combination of each factor being evaluated.The ANOVA table is included which includes an interaction and within group error estimates.

Note that all F tests are a comparison of the within group variance estimate.

Anova: Two-Factor With Replication

SUMMARY A B C TotalAA

Count 2 2 2 6Sum 5 2.5 5 12.5Average 2.5 1.25 2.5 2.083333Variance 0.5 0.125 0.5 0.641667

BBCount 2 2 2 6Sum 3 5 5 13Average 1.5 2.5 2.5 2.166667Variance 0.5 0.5 0.5 0.566667

TotalCount 4 4 4Sum 8 7.5 10Average 2 1.875 2.5Variance 0.666667 0.729167 0.333333

ANOVASource of Variation SS df MS F P-value F critSample 0.020833 1 0.020833 0.047619 0.834492 5.987374Columns 0.875 2 0.4375 1 0.421875 5.143249Interaction 2.541667 2 1.270833 2.904762 0.131146 5.143249Within 2.625 6 0.4375

Total 6.0625 11


Descriptive Statistics

Data Format: all data needs to be in single columns or rows.

Multiple data sets can be done at one time.

Provides many statistics along with a confidence interval of the mean (mean +/- value listed)Note1: the interval assumes a normal distribution.Note2: Each of these statistics can also be generated with a function.

Date post:	22-May-2018
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