# Release 4.1 of Real Statistics Resource Pack

The Real Statistics website is in the process of being updated to reflect the new features. These changes will be made over the next few days.

Thanks to all of you who have made suggestions for new capabilities and have identified bugs.

Release 4.1 contains the following new features:

Fligner Killeen test for homogeneity of variances

The FKTEST function outputs the p-value for the Fligner Killeen test for homogeneity of variances.

Two-sample Runs Test

The RUNS2TEST array function is now available. This function performs the two-sample runs test. A similar capability has been added to the Non-parametric Tests data analysis tool. A special option is included to handle the case where there are many tied values.

Enhancement to the One-sample Runs Test

A new capability has been added to the one sample runs test. When range R1 contains only two distinct values and these values are characters then RUNSTEST(R1, lab, tails) is equivalent to in RUNSTEST(s, lab, tails) where s = the string consisting of the values contained in R1.

ICC Power and Sample Size Requirements

The ICC_POWER and ICC_SIZE functions are now available. These functions calculate the statistical power and sample size required for the ICC(1,1) version of the intraclass correlation. A similar capability has been added to the Power and Sample Size data analysis tool.

Jarque-Barre test for normality

The JBTEST and JARQUE functions have been added. JBTEST outputs the p-value for the Jarque-Barre test for normality and JARQUE calculates the test statistic.

Identification of potential outliers

Two commonly used criteria for identifying potential outliers are to flag data elements x such that (1) x >  + 2.5*s or x − 2.5*or (2) x > Q3 + 1.5*IQR or x < Q1 − 1.5*IQR.

Using the new STANDARD function, a potential outlier occurs when (1) STANDARD(x,R1) > 2.5 or STANDARD(x,R1) < -2.5 or (2) STANDARD(x, R1,1,exc) > 1.5 or STANDARD(x, R1,1,exc) < -1.5, where STANDARD is defined as follows.

if type = 0 (default) then

STANDARD(x, R1, type, exc) = STANDARDIZE(x, x̄, s)

while if type = 1 then

STANDARD(x, R1, type, exc) = (x − Q3)/IQR if x > Q3, (x − Q1)/IQR if x < Q1 or 0 otherwise (i.e. when Q1 ≤ x ≤ Q3)

where

x̄ = AVERAGE(R1)
s = STDEV(R1)
Q1 = QUARTILE.EXC(R1,1) if exc = TRUE and Q1 = QUARTILE(R1,1) otherwise
Q3 = QUARTILE.EXC(R1,3) if exc = TRUE and Q3 = QUARTILE(R1,3) otherwise
IQR = IQR(R1, exc)

New Logistic Regression function

The resource pack adds a new array function LogitCoeff2 for the calculation of the logistic regression coefficients and related parameters. The function takes the form

LogitCoeff2(R1, R2, lab, head, alpha, iter)

This function is similar to the existing LogitCoeff function. In particular, the lab, head, alpha and iter arguments are the same, as is the output of the new function. The differences are as follows:

(1) In LogitCoeff(R1, lab, raw, head, alpha, iter), R1 contains all the data, where the data for the independent variables precede the data for the dependent variable. In LogitCoeff2, R1 contains the data for the independent variables and R2 contains the data for the dependent variable. If R2 contains one column then this indicates that the data is in raw format, while if R2 contains two columns then the data is in summary format

(2) The data in R1 and R2 for LogitCoeff2 can contain non-numeric values. These are treated as missing data and are not included in the analysis

Delete error values data analysis tool

A Remove error cells option has been added to the Reformatting a Data Range data analysis tool. When this option is selected any cell in the input data range which contains an error value (#N/A, #DIV/0!, etc.) is replaced by an empty cell. This is the same functionality provided by the DELErr function.

Changes to the noncentral distribution functions

All the functions that calculate or use the noncentral t, F and chi-square distributions (NT_DIST, NF_INV, ANOVA1_POWER, etc.) have been revised so that if you specify a value for the parameter m (which limits the number of terms in the infinite sum used to estimate the distribution value) that is higher than the limit for this parameter, then the software will automatically reduce the value to the highest usable value.

The default value for m has also been revised from 40 to 80.

Bug fix for the Mann-Whitney and Signed Ranks tests with ties

A bug has been fixed in the SRANK_TEST and MANN_TEST functions as well as in the equivalent capabilities in the data analysis tools. The bug resulted in a negative variance when the ties option is chosen.

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### 2 Responses to Release 4.1 of Real Statistics Resource Pack

1. Rich says:

Hi, Charles
Congratulations on yet another release of additional tools to your ever-growing statistical analysis suite.

When you see this, you may have already discovered that the potential outlier description above may require a wording change for flagging low-end outliers using the IQR.

Regards, Rich

• Charles says:

No, I hadn’t discovered the error, but thanks Rich very much for bringing it to my attention. I have just corrected the description, replacing Q3 by Q1 for the low-end outliers. Charles