SOCR HTML5 PowerCalculatorProject

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(Created page with '== SOCR Project - SOCR HTML5 Statistical Power Calculator Project== ===Background=== [[Image:SOCR_Activities_MotionCharts_HPI_070109…')
 
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===Background===
===Background===
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[[Image:SOCR_Activities_MotionCharts_HPI_070109_Fig6_9_Animation.gif|350px|thumbnail|right| SOCR MotionChart Web-app]]
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[[Image:SOCR_Analyses_NormalPower_CompareCurves_RawData_Annie_20061026_1.jpg|350px|thumbnail|right| SOCR Power Calculator Web-app]]
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The amount, complexity and provenance of data have dramatically increased in the past five years. Visualization of observed and simulated data is a critical component of any social, environmental, biomedical or scientific quest. The [[SOCR_MotionCharts|SOCR MotionCharts]] provide an interactive infrastructure for discovery-based exploratory analysis of multivariate data. This dynamic data visualization tool enables the displaying of high-dimensional longitudinal data. SOCR Motion Charts allows mapping of ordinal, nominal and quantitative variables onto time, 2D axes, size, colors, glyphs and appearance characteristics, which facilitates the interactive display of multidimensional data.
+
...
===Project goals===
===Project goals===
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The goal of this project is to redesign the Java-based [[SOCR_MotionCharts]] applet using only [http://en.wikipedia.org/wiki/HTML5 HTML5], [http://www.w3schools.com/css3 CSS3] and [http://www.w3schools.com/js/ JavaScript], and in the process introduce some useful and powerful expansions of this web-app.
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The goal of this project is to redesign the SOCR Java-based [[Power_Analysis_for_Normal_Distribution]] applet using only [http://en.wikipedia.org/wiki/HTML5 HTML5], [http://www.w3schools.com/css3 CSS3], [https://developer.mozilla.org/en/AJAX AJAX]/[http://www.json.org JSON], and [http://www.w3schools.com/js/ JavaScript], and in the process introduce some useful and powerful expansions of this web-app.
===Project specification===
===Project specification===
-
The HTML5/JavaScript implementation of the new SOCR MotionCharts Web-App es expected to lower the device and software barriers for users. There are three specific extensions to the Motion Charts application that are necessary in this redesign process
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The HTML5/JavaScript implementation of the new SOCR Power Calculator Web-App es expected to lower device, software and statistical-expertise barriers for all users. The following list of designs and analysis are expected to be included in the new SOCR Power Web-app, according to the power calculations included in the provided references.
-
[[Image:SOCR_HTML5_Expansion_MotionCharts_Fig1.png|350px|thumbnail|right| SOCR MotionChart Color Spectrum Web-app Improvement]]
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The basic classification of all power/sample analysis calculations depends on:
 +
* Parameters: Means, Proportions, Survival, Agreement, or Regression
 +
* Design/Goals: One, Two, or more groups
 +
* Type of analysis: Test, Confidence Interval, or Equivalence
 +
 
 +
====One-sample t test====
 +
Paired t test for difference in means: Power, sample size, or effect size are computed using central and non-central t distribution.
 +
* O’Brien, R.G., Muller, K.E. (1993) [http://www.bios.unc.edu/~mhudgens/bios/662/2008fall/OBrienMuller1993.pdf Unified Power Analysis for t-tests through Multivariate Hypotheses], in Edwards, L.K. (Ed.), Applied Analysis of Variance in Behavioral Science, Marcel Dekker, New York. Chapter 8 (pp 297-344).
 +
 
 +
====Paired t test for equivalence of means====
 +
Power, sample size, or effect size are computed using central and non-central t distribution.
 +
* Machin, D., Campbell, M.J. (1987) Statistical Tables for Design of Clinical Trials, Blackwell Scientific Publications, Oxford.
 +
* Cohen, J (1988) [http://books.google.com/books?hl=en&lr=&id=Tl0N2lRAO9oC Statistical Power Analysis for the Behavioral Sciences], Psychology Press, 1988
 +
 
 +
====Univariate one-way repeated measures analysis of variance====
 +
One-way repeated measures contrast - Power, sample size, or effect size are computed using central and non-central F.
 +
* Dixon, W.J., Massey, F.J. (1983) Introduction to Statistical Analysis. McGraw-Hill. Chapter 14.
 +
* Overall, J.E., Doyle, S.R. (1994) Estimating Sample Sizes for Repeated Measures Designs, Controlled
 +
Clinical Trials 15:100-123.
 +
 
 +
====Univariate one-way repeated measures analysis of variance====
 +
* Muller, KE, Barton CN (1989) [http://www.jstor.org/stable/10.2307/2289941 Approximate Power for Repeated-Measures ANOVA lacking Sphericity], Journal of the American Statistical Association, 84:549-555.
 +
 
 +
====Confidence interval for mean based on z (n large)====
 +
* Confidence interval for difference in paired means (n large)
 +
* Confidence interval for repeated measures contrast
 +
* Dixon, W.J., Massey, F.J. (1983) Introduction to Statistical Analysis. 4th Edition. McGraw-Hill. Pages 80-85.
 +
* Overall, J.E., Doyle, S.R. (1994) Estimating Sample Sizes for Repeated Measures Designs, Controlled Clinical Trials 15:100-123.
 +
 
 +
====Confidence interval for mean based on t (with coverage probability)====
 +
* Confidence interval for difference in paired means (coverage probability)
 +
* Kupper, L.L. and Hafner, K.B. (1989) How appropriate are popular sample size formulas? The American Statistician 43:101-105.
 +
* Hahn GJ, Meeker WQ (1991) Statistical Intervals. A guide for practitioners. John Wiley & Sons, Inc. New York.
 +
 
 +
====One group t-test that a mean equals user-specified value in finite population====
 +
* Paired t-test of mean difference equal to zero in finite population
 +
* Confidence interval for mean based on z (n large) adjusted for finite population
 +
* Confidence interval for mean based on t (with coverage probability) finite population
 +
* Confidence interval for difference in paired means based on z (n large) adjusted for finite population
 +
* Confidence interval for difference in paired means based on t (with coverage probability) finite population
 +
* Cochran, G. (1977) Sampling Techniques 3rd Edition. John Wiley & Sons Inc. New York, pages 23-28.
 +
 
 +
====Two-sample t-test: Equivalence of two means====
 +
* Dixon, W.J., Massey, F.J. (1983) Introduction to Statistical Analysis. McGraw-Hill.
 +
* O’Brien, R.G., Muller, K.E. (1993) “Unified Power Analysis for t-tests through Multivariate Hypotheses”, in Edwards, L.K. (Ed.), Applied Analysis of Variance in Behavioral Science, Marcel Dekker, New York. Chapter 8 (pp 297-344).
 +
 
 +
====Two group t-test for fold change assuming log-normal distribution====
 +
* Diletti, E., Hauschke D., Steinijans, V.W. "Sample size determination for bioequivalence assessment by means of confidence intervals" Int. Journal of Clinical Pharmacology 29(1991) p. 7.
 +
 
 +
====Two group t-test of equal fold change with fold change threshold====
 +
* Diletti, E., Hauschke D., Steinijans, V.W. "Sample size determination for bioequivalence assessment by means of confidence intervals" Int. Journal of Clinical Pharmacology 29(1991), p. 7.
 +
 
 +
====Two group Satterthwaite t-test of equal means (unequal variances)====
 +
* Moser, B.K., Stevens, G.R., Watts, C.L. "The two-sample t test versus Satterthwaite’s approximate F test" Commun. Statist.-Theory Meth. 18(1989) pp. 3963-3975.
 +
 
 +
====Two one-sided equivalence tests (TOST) for two-group design
 +
* Chow, S.C, Liu, J.P. Design and Analysis of Bioavailability and Bioequivalence Studies, Marcel Dekker, Inc. (1992)
 +
* Schuirmann DJ (1987) A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability, J. Pharmacokinet Biopharm 15:657-680.
 +
* Phillips KE (1990) Power of the two one-sided tests procedure in bioequivalence, J. Pharmacokinet Biopharm 18:137-143.
 +
* Owen DB (1965) A special case of a bivariate non-central t distribution. Biometrika 52:437- 446.
 +
 
 +
====Ratio of means for crossover design (original scale)====
 +
* Hauschke D, Kieser M, Diletti E, Burke M (1999) Sample size determination for proving equivalence based on the ratio of two means for normally distributed data. Statistics in Medicine 18: 93-105.
 +
 
 +
====Wilcoxon (Mann-Whitney) rank-sum test that P(X<Y) = .5 (continuous outcome)====
 +
* Noether GE (1987) Sample size determination for some common nonparametric statistics. J. Am Stat. Assn 82:645-647.
 +
 
 +
====Wilcoxon (Mann-Whitney) rank-sum test that P(X<Y) = .5 (ordered categories)====
 +
* Kolassa J (1995) A comparison of size and power calculations for the Wilcoxon statistic for ordered categorical data. Statistics in Medicine 14: 1577-1581.
 +
 
 +
====Two-group univariate repeated measures analysis of variance====
 +
* Muller, KE, Barton CN (1989) Approximate Power for Repeated-Measures ANOVA lacking Sphericity. Journal of the American Statistical Association 84:549-555.
 +
 
 +
====t-test (ANOVA) for difference of means in 2 x 2 crossover design====
 +
* Senn, Stephen. Cross-over Trials in Clinical Research, Wiley (2002) Page 285.
 +
 
 +
====Confidence interval for difference of two means (N large)====
 +
* Confidence interval width for one-way contrast
 +
* Dixon, W.J., Massey, F.J. (1983) Introduction to Statistical Analysis. 4th Edition. McGraw-Hill. Pages 80-85 and 130-131.
 +
* Confidence interval for difference of two means (coverage probability)
 +
* Kupper, L.L. and Hafner, K.B. (1989) How appropriate are popular sample size formulas? The American Statistician, 43:101-105.
 +
 
 +
====One-way analysis of variance====
 +
* Single one-way contrast
 +
* O’Brien, R.G., Muller, K.E. (1993) “Unified Power Analysis for t-tests through Multivariate Hypotheses”, in Edwards, L.K. Appendix — 7-9, (Ed.), Applied Analysis of Variance in Behavioral Science, Marcel Dekker, New York. Pages 297-344.
 +
 
 +
...

Current revision as of 23:14, 6 July 2012

Contents

SOCR Project - SOCR HTML5 Statistical Power Calculator Project

Background

SOCR Power Calculator Web-app

...

Project goals

The goal of this project is to redesign the SOCR Java-based Power_Analysis_for_Normal_Distribution applet using only HTML5, CSS3, AJAX/JSON, and JavaScript, and in the process introduce some useful and powerful expansions of this web-app.

Project specification

The HTML5/JavaScript implementation of the new SOCR Power Calculator Web-App es expected to lower device, software and statistical-expertise barriers for all users. The following list of designs and analysis are expected to be included in the new SOCR Power Web-app, according to the power calculations included in the provided references.

The basic classification of all power/sample analysis calculations depends on:

  • Parameters: Means, Proportions, Survival, Agreement, or Regression
  • Design/Goals: One, Two, or more groups
  • Type of analysis: Test, Confidence Interval, or Equivalence

One-sample t test

Paired t test for difference in means: Power, sample size, or effect size are computed using central and non-central t distribution.

Paired t test for equivalence of means

Power, sample size, or effect size are computed using central and non-central t distribution.

Univariate one-way repeated measures analysis of variance

One-way repeated measures contrast - Power, sample size, or effect size are computed using central and non-central F.

  • Dixon, W.J., Massey, F.J. (1983) Introduction to Statistical Analysis. McGraw-Hill. Chapter 14.
  • Overall, J.E., Doyle, S.R. (1994) Estimating Sample Sizes for Repeated Measures Designs, Controlled

Clinical Trials 15:100-123.

Univariate one-way repeated measures analysis of variance

Confidence interval for mean based on z (n large)

  • Confidence interval for difference in paired means (n large)
  • Confidence interval for repeated measures contrast
  • Dixon, W.J., Massey, F.J. (1983) Introduction to Statistical Analysis. 4th Edition. McGraw-Hill. Pages 80-85.
  • Overall, J.E., Doyle, S.R. (1994) Estimating Sample Sizes for Repeated Measures Designs, Controlled Clinical Trials 15:100-123.

Confidence interval for mean based on t (with coverage probability)

  • Confidence interval for difference in paired means (coverage probability)
  • Kupper, L.L. and Hafner, K.B. (1989) How appropriate are popular sample size formulas? The American Statistician 43:101-105.
  • Hahn GJ, Meeker WQ (1991) Statistical Intervals. A guide for practitioners. John Wiley & Sons, Inc. New York.

One group t-test that a mean equals user-specified value in finite population

  • Paired t-test of mean difference equal to zero in finite population
  • Confidence interval for mean based on z (n large) adjusted for finite population
  • Confidence interval for mean based on t (with coverage probability) finite population
  • Confidence interval for difference in paired means based on z (n large) adjusted for finite population
  • Confidence interval for difference in paired means based on t (with coverage probability) finite population
  • Cochran, G. (1977) Sampling Techniques 3rd Edition. John Wiley & Sons Inc. New York, pages 23-28.

Two-sample t-test: Equivalence of two means

  • Dixon, W.J., Massey, F.J. (1983) Introduction to Statistical Analysis. McGraw-Hill.
  • O’Brien, R.G., Muller, K.E. (1993) “Unified Power Analysis for t-tests through Multivariate Hypotheses”, in Edwards, L.K. (Ed.), Applied Analysis of Variance in Behavioral Science, Marcel Dekker, New York. Chapter 8 (pp 297-344).

Two group t-test for fold change assuming log-normal distribution

  • Diletti, E., Hauschke D., Steinijans, V.W. "Sample size determination for bioequivalence assessment by means of confidence intervals" Int. Journal of Clinical Pharmacology 29(1991) p. 7.

Two group t-test of equal fold change with fold change threshold

  • Diletti, E., Hauschke D., Steinijans, V.W. "Sample size determination for bioequivalence assessment by means of confidence intervals" Int. Journal of Clinical Pharmacology 29(1991), p. 7.

Two group Satterthwaite t-test of equal means (unequal variances)

  • Moser, B.K., Stevens, G.R., Watts, C.L. "The two-sample t test versus Satterthwaite’s approximate F test" Commun. Statist.-Theory Meth. 18(1989) pp. 3963-3975.

====Two one-sided equivalence tests (TOST) for two-group design

  • Chow, S.C, Liu, J.P. Design and Analysis of Bioavailability and Bioequivalence Studies, Marcel Dekker, Inc. (1992)
  • Schuirmann DJ (1987) A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability, J. Pharmacokinet Biopharm 15:657-680.
  • Phillips KE (1990) Power of the two one-sided tests procedure in bioequivalence, J. Pharmacokinet Biopharm 18:137-143.
  • Owen DB (1965) A special case of a bivariate non-central t distribution. Biometrika 52:437- 446.

Ratio of means for crossover design (original scale)

  • Hauschke D, Kieser M, Diletti E, Burke M (1999) Sample size determination for proving equivalence based on the ratio of two means for normally distributed data. Statistics in Medicine 18: 93-105.

Wilcoxon (Mann-Whitney) rank-sum test that P(X<Y) = .5 (continuous outcome)

  • Noether GE (1987) Sample size determination for some common nonparametric statistics. J. Am Stat. Assn 82:645-647.

Wilcoxon (Mann-Whitney) rank-sum test that P(X<Y) = .5 (ordered categories)

  • Kolassa J (1995) A comparison of size and power calculations for the Wilcoxon statistic for ordered categorical data. Statistics in Medicine 14: 1577-1581.

Two-group univariate repeated measures analysis of variance

  • Muller, KE, Barton CN (1989) Approximate Power for Repeated-Measures ANOVA lacking Sphericity. Journal of the American Statistical Association 84:549-555.

t-test (ANOVA) for difference of means in 2 x 2 crossover design

  • Senn, Stephen. Cross-over Trials in Clinical Research, Wiley (2002) Page 285.

Confidence interval for difference of two means (N large)

  • Confidence interval width for one-way contrast
  • Dixon, W.J., Massey, F.J. (1983) Introduction to Statistical Analysis. 4th Edition. McGraw-Hill. Pages 80-85 and 130-131.
  • Confidence interval for difference of two means (coverage probability)
  • Kupper, L.L. and Hafner, K.B. (1989) How appropriate are popular sample size formulas? The American Statistician, 43:101-105.

One-way analysis of variance

  • Single one-way contrast
  • O’Brien, R.G., Muller, K.E. (1993) “Unified Power Analysis for t-tests through Multivariate Hypotheses”, in Edwards, L.K. Appendix — 7-9, (Ed.), Applied Analysis of Variance in Behavioral Science, Marcel Dekker, New York. Pages 297-344.

...


Exemplary HTML5 tools that can be employed

See also





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