# Data Analytic Resources -- developed by MML

**Note to Users:** Researchers using these tools for any of their analyses and reporting results in presentations, papers, books are requested to appropriately **cite** their use of the tools as indicated at the end of each coresponding tool description section. The specific shiny links are not stable and may change, however, this web-page is stable and will continually link to the indicated data analytic resource.

**MMLR2 (2017): https://shiny.rcg.sfu.ca/u/zrauf/MML-R2/
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R2 (a predecessor to MMLR2) was developed by Steiger and Fouladi (1992) to advance the practice of multiple regression analysis planning and results reporting. The original R2 program is an MSDOS program which implements procedures not generally available in commonly used statistical software, and provides an early illustration of the application of the use of principles of non-centrality interval estimation discussed in the chapter by Steger and Fouladi (1997) in the widely cited book *What if there were no significance tests (Harlow, Mulaik, & Steiger, eds., 1997)*. R2 provides exact confidence intervals for the squared multiple correlation coefficent based on a random regressor model, varied power calculations, distributional probability calculations, and non-standard hypothesis tests of the squared multiple correlation.

MMLR2 implements some of the key features of R2 but also uses the more commonly used fixed regressor model framework (e.g., GPower) for some the procedures. In addition to the base features of R2, MMLR2 provides capabilities for 2ndary multiple regression analyses based on reported correlations, including standardized regression coefficents and corresponding confidence intervals based.

MMLR2 provides a web-based interface permitting users to perform:

- Calculation of confidence intervals and lower confidence bounds for the squared multiple correlation, using either
- a fixed regressor method or
- the random regressor method,

similar to those implemented in GPower and R2 respectively, which can then in turn be used for CI on differences between independent squared multiple correlation values as described by Zou (2007) .

Using a fixed regressor model framework, MMLR2 also permits

- Power calculation for tests of significance of the squared multiple correlation
- Calculation of the sample size necessary to achieve a desired level of power for testing a hypothesis of zero multiple correlation

For the above functionality (CIs, Power, Sample, users make their selection of interest, input the required values for the calculation (e.g, N) into textboxes, and click submit to obtain the value(s) of interest.

*Additionally,* using a fixed regressor framework, MMLR2 permits calculation of:

- squared multiple correlations and
- standardized regression coefficents
- estimated standard errors and confidence intervals for standardized regression coefficients, as well as t-values and p-values, based on estimated SEs/CIs from Jones & Waller, 2013

using raw data, inputted correlation, or covariance matrices. After input the necessary data file, users can flexibily identify **any** variable as the criterion variable and **any **of the remaining variables as the regressor set. For this functionality, the users make their selection of interest (e.g., calculate "R2 from sample data") and load the csv file for their "sample". Note: Your data can either be raw data (row = observation, column = variable), a correlation matrix, or a covariance matrix. It should be in headerless, .csv file format. You can use **MML CSV generator** (see below) for assistance on setting up an appropriately formatted *.csv correlation matrix file.

Documentation page for MML-R2 is still under developement/in preparation.

**Researchers using any of the functions in MML-R2 should reference their use of the tool for their analyses and results by citing: Fouladi, R.T., Serafni, P.E., & Mustapha, A. (2018). MML-R2. Retrieved from http://www.sfu.ca/psychology/research/mml/resources.html**

**MMLWBCORR (2018):https://shiny.rcg.sfu.ca/u/zrauf/MML-WBCORR/**

WBCORR (Within-Between CORRelational tests) is correlation pattern hypotheis test program developed for Mathematica by Steiger (2004). WBCORR can handle raw or correlation data, in one or more samples, with or without equal sample sizes, and with or without the assumption of multivariate normaltiy. The program implements GLS, TSGLS, ADF, and TSADF chi-square statistics. See Steiger (2004) for a discussion of the methods employed by WBCORR.

MMLWBCORR provides a web-based interface permitting users to perform analyses similar to those analyzable using Steiger's WBCORR, using the GLS, TSGLS, ADF, and TSADF chi-square statistics. However, MLWBCORR differs from the Steiger's Mathematica WBCORR (2004) in its implementation of tests of correlation patterns for common specified values, and its treatment of missing data. In particular, MLWBCORR draws on work presented in Yuan, Lambert, Fouladi (2004) for tests of multivariate normality under conditions of missing data conditions.

In additon to provision of a test of the overall *within/between* correlation pattern model; additionally confidence intervals on parameter estimates are provided; confidence interval widths are corrected for the number of unique parameters in the correlation pattern model under estimation as appropriate.

Please be sure to read the information in the MML-WBCORR tabs for formatting input files, etc., as appropriate.

**Researchers using any of the functions in MML-WBCORR should reference their use of the tool for their analyses and results by citing: Fouladi, R.T., & Serafni, P.E. (2018). MML-WBCORR. Retrieved from http://www.sfu.ca/psychology/research/mml/**

**MMLMULTICORR (2018):https://shiny.rcg.sfu.ca/u/zrauf/MML-Multicorr/**

MULTICORR (Within-Matrix CORRelational tests) is correlation pattern hypotheis test program developed by Steiger (1980). The program implements normal theory procedures based on Fisher transforms of correlations to provide chi-square statistics to address research questions concerning correlation patterns within a single correlation matrix. GLS, TSGLS, ADF, and TSADF chi-square statistics. See Steiger (1980) for a discussion of the methods employed by MULTICORR.

MML-MULTICORR provides a web-based interface permitting users to address the same research qusestions as with Steiger's MULTICORR; However MML-MULTICORR (2018) uses the GLS, TSGLS, ADF, and TSADF chi-square statistics based on correlation distribution theory. Additionally, MML-MULTICORR differs from the Steiger's 1980 implementations in terms of its implementation of tests of correlation patterns for common specified values, as well as its treatment of missing data. In particular, MML-MULTICORR draws on work presented in Yuan, Lambert, Fouladi (2004) for tests of multivariate normality under conditions of missing data conditions.

In additon to provision of a test of the overall within-matrix correlation pattern model; confidence intervals on parameter estimates are provided; confidence itnerval widths are corrected for the number of unique parameters in the correlation pattern model under estimation as appropriate.

Please be sure to read the information in the MML-MULTICORR tabs for formatting input files, etc., as appropriate.

**Researchers using any of the functions in MML-MULTICORR should reference their use of the tool for their analyses and results by citing: Fouladi, R.T., & Serafni, P.E. (2018). MML-MULTICORR. Retrieved from http://www.sfu.ca/psychology/research/mml/**

**MML CSV Generator (2017):**https://shiny.rcg.sfu.ca/u/zrauf/csv-generator/

MML CSV Generator was created to facilitate the construction of appropriately formatted csv correlation matrix and hypothesis matrix files for MMLWBCORR and MMLMULTICORR. The Correlation Matrix tab of MML CSV Generator can also be used to create appropriately formatted csv files to make use of MMLR2's flexible capabability to calculate squared multiple correlations and standardized regression coefficients based on input correlation matrices.

**Researchers wanting to cite use of MML-CSV Generator should reference their use of the tool for their analyses and results by citing: Fouladi, R.T., Serafni, P.E. , & Mustapha, A. (2017). MML-CSV Generator. Retrieved from http://www.sfu.ca/psychology/research/mml/**

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