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

Release 4.5 contains the following new features:

**Time series analysis**

In this release we initiate support for time series analysis. This work will continue in the next release as well. New functions that are available in this release are:

**ACF**(R1, *k*) – autocorrelation function of order *k* for the data in the column range R1

**ACVF**(R1, *k*) – autocovariance function of order *k* for the data in the column range R1

**PACF**(R1, *k*) – partial autocorrelation function of order *k* for the data in column range R1

**ACOV**(R1, *k*) – autocovariance matrix for the data in column range R1

**ACORR**(R1, *k*) – autocorrelation matrix for the data in column range R1

**Bland-Altman**

Bland-Altman is a method for comparing two measurements of the same variable. A **Bland-Altman** data analysis tool is now available, which can be accessed via the **Reliability** menu option.

**Correlation Exact Test**

The Correlation Exact Test can be used in place of the Fisher transformation approach to testing the value of the correlation coefficient. The following functions have been added:

**CORRDIST**(*r, n, rho*) – correlation distribution function (cdf) for a sample of size *n* with sample correlation* r* and population correlation *rho*

**CORRINV**(*alpha, n, rho*) – inverse of the correlation distribution function

**CORRETEST**(R1, R2*, rho, tails*) – p-value for the correlation exact test for the data in ranges R1 and R2, with population correlation *rho* and *tails* = 1 or 2

**CORRELETEST**(R1, R2*, rho, lab, alpha, tails*) – array function similar to CORRETEST, except that a 1-alpha confidence interval is also output

Thanks to António Teixeira who suggested this topic and contributed greatly to its development.

**Skewness and Kurtosis Testing**

The following array functions test whether sample data comes from a distribution which has zero skewness and/or kurtosis.

**SKEWTEST**(R1, *lab, alpha*) – array function which tests whether the skewness of the sample data in range R1 is zero (consistent with a normal distribution). The output consists of sample skewness, standard error, test statistic, p-value and 1-alpha confidence interval

**KURTTEST**(R1, *lab, alpha*) – array function which tests whether the kurtosis of the sample data in range R1 is zero (consistent with a normal distribution). The output consists of sample kurtosis, standard error, test statistic, p-value and 1-alpha confidence interval

**D’Agostino-Pearson Test for Normality**

The D’Agostino-Pearson test is yet another test to determine whether data comes from a population which is normally distributed. Generally, Shapiro-Wilk will give more accurate results, but this test can be useful where the sample data has a number of repetitions.

**DAGOSTINO**(R1) – the test statistic *s*^{2} + *k*^{2} where *s* is the test statistic for skewness testing and *k* is the test statistic for kurtosis testing (described above).

**DPTEST**(R1) – p-value for the D’Agostino-Pearson test. When the data comes from a population with a normal distribution, the D’Agostino-Pearson test statistic has a chi-square distribution with 2 degrees of freedom.

**Population skewness and kurtosis functions**

The follow functions have been added:

**SKEWP**(R1) – skewness of the distribution for the population in range R1. This is equivalent to the Excel 2013/2016 function SKEW.P, and can be useful to users with prior versions of Excel.

**KURTP**(R1, *excess*) – kurtosis of the distribution for the population in range R1. If *excess *= TRUE then 3 is subtracted from the result (the usual approach so that a normal distribution has kurtosis of zero).

**Adjusted Correlation Coefficient and Coefficient of Determination**

The following function output the usual adjusted *R*^{2} value:

**RSQ_ADJ**(*r, n*) – adjusted *R*^{2} value = 1-(1-*r*^{2})(*n*-1)/(*n*-2) where *r* = the sample correlation and *n* = the size of the sample

**RSQ_ADJ**(R1, R2) – adjusted *R*^{2} value for the data in ranges R1 and R2

The following function outputs a relatively unbiased value for the population correlation coefficient. Note that this value is not the square root of the adjusted *R*^{2} value described above, and provides a better estimate of the population correlation coefficient.

**CORREL_ADJ**(*r, n*) – estimated population correlation coefficient = *r*[1 +(1 –*r*^{2}) /2(*n* -3)] where* r* = the sample correlation and *n* = the size of the sample

**CORREL_ADJ**(R1, R2) – estimated population correlation coefficient for the data in ranges R1 and R2

Thanks to António Teixeira who suggested this topic.

**Matrices raised to a Power**

For any square matrix* A, A*^{0} = the identity matrix and *A*^{n+1} = *A*^{n}A. The following function calculates *A*^{n} where *A* is the matrix contained in the* k × k* range R1.

**MPOWER**(R1, *n*) = *A*^{n} where* A* consists of the data in range R1.

We use this function with Markov chains.

**Bug Fixes**

The results for the **Scheirer Ray Hare Test** data analysis tool had an error, which produced incorrect results. This has now been corrected. Thanks for Kevin Bluxome for identifying this error.

The values for the adjusted means in the **ANCOVA** data analysis tool were in error. This has now been corrected. Thanks to Bill G. for identifying this error.