# SOCR HTML5 PowerCalculatorProject

## Contents

- 1 SOCR Project - SOCR HTML5 Statistical Power Calculator Project
- 1.1 Background
- 1.2 Project goals
- 1.3 Project specification
- 1.3.1 One-sample t test
- 1.3.2 Paired t test for equivalence of means
- 1.3.3 Univariate one-way repeated measures analysis of variance
- 1.3.4 Univariate one-way repeated measures analysis of variance
- 1.3.5 Confidence interval for mean based on z (n large)
- 1.3.6 Confidence interval for mean based on t (with coverage probability)
- 1.3.7 One group t-test that a mean equals user-specified value in finite population
- 1.3.8 Two-sample t-test: Equivalence of two means
- 1.3.9 Two group t-test for fold change assuming log-normal distribution
- 1.3.10 Two group t-test of equal fold change with fold change threshold
- 1.3.11 Two group Satterthwaite t-test of equal means (unequal variances)
- 1.3.12 Ratio of means for crossover design (original scale)
- 1.3.13 Wilcoxon (Mann-Whitney) rank-sum test that P(X<Y) = .5 (continuous outcome)
- 1.3.14 Wilcoxon (Mann-Whitney) rank-sum test that P(X<Y) = .5 (ordered categories)
- 1.3.15 Two-group univariate repeated measures analysis of variance
- 1.3.16 t-test (ANOVA) for difference of means in 2 x 2 crossover design
- 1.3.17 Confidence interval for difference of two means (N large)
- 1.3.18 One-way analysis of variance

- 1.4 Exemplary HTML5 tools that can be employed
- 1.5 See also

## 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.

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### 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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