# SOCR HTML5 PowerCalculatorProject

### From Socr

(Created page with '== SOCR Project - SOCR HTML5 Statistical Power Calculator Project== ===Background=== [[Image:SOCR_Activities_MotionCharts_HPI_070109…') |
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===Background=== | ===Background=== | ||

- | [[Image: | + | [[Image:SOCR_Analyses_NormalPower_CompareCurves_RawData_Annie_20061026_1.jpg|350px|thumbnail|right| SOCR Power Calculator Web-app]] |

- | + | ... | |

===Project goals=== | ===Project goals=== | ||

- | The goal of this project is to redesign the Java-based [[ | + | 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 | + | 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. | ||

+ | * 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

## SOCR Project - SOCR HTML5 Statistical Power Calculator Project

### Background

...

### 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.

- 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).

#### 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) 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) 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.

...

### Exemplary HTML5 tools that can be employed

- JSXGraph HTML5/JS Mathematical Functions Charts and graphs
- D3
- See the JavaScript InfoVis Toolkit
- Manual Graphics Paint canvas in HTML5
- RGraph HTML5 Charts and Graphs
- Rendera: Interactive HTML5/CSS3/JS web-page Editor

### See also

- SOCR Power Analysis for Normal Distribution Activity and Applet
- Power Java Calculator
- nQuery Advisor Power calculator User Guide

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