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ESCI (Pronounced "esky") is a set of interactive simulations that run under Microsoft Excel

With ESCI you can:

Dr Geoff Cumming
Professor Geoff Cumming
School of Psychological Science,
La Trobe University, Bundoora, Melbourne, Australia
explore many Confidence Interval (CI) concepts
calculate and display CIs for your own data, for some simple designs
calculate CIs for Cohen’s standardised effect size d
explore noncentral t distributions and their role in statistical power
use CIs for simple meta-analysis, using original or standardised units
explore all these concepts via vivid interactive graphical simulations
 

New ESCI modules
The following ESCI modules go with published articles. (There is information about these and other articles, including abstracts and/or downloads of the articles themselves, at my School page.) These ESCI modules are free downloads, for non-commercial use, and were developed in Microsoft Excel 2003 or XP. (They may also run in earlier versions of Excel.) Sorry, no Mac versions yet.

ESCI PPS p intervals (downloads) is a module that allows you to explore three of the figures in:
Cumming, G. (2008). Replication and p intervals: p values predict the future only vaguely, but confidence intervals do much better. Perspectives on Psychological Science, 3, 286-300.

NOTE: Excel 2007 The above module runs in Excel 2007, as well as Excel 2003. The modules below probably will not run properly in Excel 2007. (Excel 2007 runs much more slowly that Excel 2003, has many display bugs, and does not support smooth interactivity. If you still have Excel 2003, preserve it carefully!)

ESCI IBI levels of confidence (downloads) is a module that allows you to explore figures in this Teaching Statistics article, and to adjust levels of confidence:
Cumming, G. (2007). Inference by eye: Pictures of confidence intervals and thinking about levels of confidence. Teaching Statistics, 29, 89–93.

ESCI CInext PM (downloads) is a module that allows you to explore confidence intervals and replication. If an experiment is replicated, what is the average probability that an initial confidence interval will capture a replication mean? How does this vary for various initial confidence intervals? It accompanies:
Cumming, G., & Maillardet, R. (2006). Confidence intervals and replication: Where will the next mean fall? Psychological Methods, 11, 217-227.

ESCI Inference by eye (downloads) is a module that allows you to explore the figures in our ‘Inference by eye’ article, and to adjust the confidence level C for a single CI. It accompanies:
Cumming, G., & Finch, S. (2005) Inference by eye: Confidence intervals and how to read pictures of data. American Psychologist, 60, 170-180.

ESCI APR Simulation and ESCI APR Figures (downloads) are modules that allow you to run a simulation to explore the ideas of PR, the probability of replication, and APR, the average probability of replication. They accompany:
Cumming, G. (2005). Understanding the average probability of replication. Comment on Killeen (2005). Psychological Science, 16, 1002-1004.

ESCI JSMS (downloads) is a module that allows you to calculate and display CIs for a two independent group design. It accompanies:

Wolfe, R., & Cumming, G. (2004) Communicating the uncertainty in research findings: Confidence intervals. Journal of Science and Medicine in Sport, 7, 138-143.

ESCI Ustanding Stats (downloads) is a module that allows you to simulate replication of an experiment and see where replication means fall in relation to an initial CI. It also gives information about mean capture percentages of replication means, for a CI of a chosen level of confidence. It accompanies:

Cumming, G., Williams, J., & Fidler, F. (2004) Replication, and researchers’ understanding of confidence intervals and standard error bars. Understanding Statistics, 3, 299-311.

Classic ESCI
The original ESCI is the ESCI-delta set of modules, developed in Microsoft Excel 97.

The rationale for ESCI-delta
Statistics reform requires wider use of confidence intervals (CIs) and effect size measures, in original and standardised units. We therefore need CIs for standardised effect sizes. Unfortunately in many cases these are not easily calculated, and require use of noncentral distributions. ESCI-delta enables you to find the CI for Cohen’s d for your own data, which requires use of noncentral t. ESCI-delta also allows you to explore noncentral t itself, and its most familiar application, the calculation of statistical power.

Statistics reform also encourages meta-analysis. The best way to explore (and teach) simple meta-analysis may be via CIs, graphically presented. ESCI-delta supports the development of ‘meta-analytic thinking’ in original measurement units and in standardised units using Cohen’s d. (You may know that d is simply a mean, or mean difference, divided by a standard deviation. So d is in units of standard deviations, like a z score.)

The Confidence Interval primer
The following CI primer article explains confidence intervals for Cohen’s d. It gives an introduction to noncentral t distributions and discusses related concepts including power and simple meta-analysis. It is illustrated with part-images from ESCI-delta.

Cumming, G., & Finch, S. (2001). A primer on the understanding, use and calculation of confidence intervals based on central and noncentral distributions. Educational and Psychological Measurement, 61 (August). (Abstract)

ESCI-delta is the set of six simulation workbooks mentioned in the Cumming & Finch article. (Further ESCI simulations are planned. Bookmark this site.)

The simulations that make up ESCI-delta


NonCentral t NonCentral t
Explore NonCentral t distributions and calculate accurate probabilities. |More|Downloads|

Power Power
Explore statistical power, which in most cases requires NonCentral t calculations. |More|Downloads|

 
CIjumping CIjumping
Repeated sampling, to illustrate basic concepts of confidence intervals (CIs). |More|Downloads|

CIoriginal CIoriginal
Calculate and display CIs for your data, for three simple experimental designs. |More|Downloads|

CIdelta CIdelta
Calculate and display CIs for standardised effect sizes (Cohen's d), for One and Two Group designs. Requires use of NonCentral t distributions. |More|Downloads|

MAthinking MAthinking 
Explore simple Meta-analysis, based on graphical display of CIs, for effect sizes in original measurement units, and for standardised effect sizes (Cohen's d). |More|Downloads|

Images may not match ESCI precisely.

*ESCI and the CI primer article use d for the sample statistic of Cohen’s effect size, and [lowercase Greek delta] for the poulation parameter. On this site we cannot display the symbol delta reliably, so we use d instead.

Interesting links
You may care to visit the websites of the following researchers:

Rodney Carr: Excel workbooks (XLStatistics) for many statistics teaching and analysis functions

Michael Smithson: SPSS scripts for confidence intervals based on noncentral distributions. Textbook Statistics with Confidence

James Steiger: Various software, including CI and power calculations

Bruce Thompson: Statistical references and links, with an emphasis on statistics reform

Acknowledgements
Michael Smithson raised noncentral distributions as a topic of interest.
Bruce Thompson prompted the Cumming & Finch paper, and advised at every stage.
Rodney Carr showed what Excel can do.
Fiona Fidler, Sue Finch and Neil Thomason collaborated and advised.
Joanna Leeman advised, and suggested the name ESCI.
Geoff Robinson provided the routines for calculating noncentral t.
David Walsh developed the graphics, built this site and advised.

 

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