Appendix 2 - List of data sources used in analyses

Reference list for sources of data used in the analyses

Appendix 1 - Standardized mean effect sizes used in analyses

Data that was used in all analyses. See appendix 2 for list of references from which data were collected

The average of the probabilities of Type I and Type II error, ω (a) and the cost-weighted probability of errors, ω_c (b).

<p>The combined probabilities of Type I and Type II error, <i>ω</i> (a), and the cost-weighted probability of errors, <i>ω</i>_c (b). The <i>α</i> level at i) minimizes average error (assuming a Type I/Type II error cost ratio of 1), while the <i>α</i> level at ii) minimizes the cost-weighted probability of errors at a Type I/Type II error cost ratio of 4.</p

The non-linear relationship between <i>α</i> and <i>β</i>.

<p>The relationship between <i>α</i> and <i>β</i> for an independent 2-sample, 2-tailed <i>t</i>-test with n₁ = n₂ = 10, and critical effect size = 1 <i>σ</i>.</p

Determination of optimal <i>α</i> from the <i>a priori</i> combined probabilities of Type I and Type II error.

<p><i>α</i> and <i>ω</i> (the average of Type I and Type II error) for independent, 2-tailed, 2-sample <i>t</i>-tests (n₁ = n₂). Data are for 3 (dotted line), 10 (solid line), and 30 (double line) samples per group, with critical effect sizes of 1 SD of either group. Drop lines indicate the minimum average of Type I and Type II error and its associated value of <i>α</i>.</p

Probabilities of Type I (<i>α</i>), Type II (<i>β</i>) and average error (<i>ω</i>), with corresponding test conclusions for large, medium and small effect sizes (<i>δ</i>) using standard <i>α</i> levels and by setting <i>α</i> to minimize combined probabilities of Type I and Type II error.

a<p><i>p</i>-value used for significance testing is 0.0012 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032734#pone.0032734-Mootha1" target="_blank">[11]</a>.</p><p>Probabilities are calculated for a simple linear regression with <i>N</i> = 43, from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032734#pone.0032734-Mootha1" target="_blank">[11]</a>.</p

Probabilities of Type I (<i>α</i>), Type II (<i>β</i>) and average error (<i>ω</i>), with corresponding test conclusions for large, medium and small effect sizes (<i>δ</i>) using standard <i>α</i> levels and by setting <i>α</i> to minimize combined probabilities of Type I and Type II error.

a<p><i>p</i>-value used for significance testing is 0.14 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032734#pone.0032734-Vredenburg1" target="_blank">[10]</a>.</p><p>Probabilities are calculated for a two-sample <i>t</i>-test (two-tailed) with n₁ = 3, n₂ = 8, and <i>σ</i>_p = 17.27, from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032734#pone.0032734-Vredenburg1" target="_blank">[10]</a>.</p

Probabilities of Type I (<i>α</i>), Type II (<i>β</i>) cost-weighted average error (<i>ω</i>_c), and average error (<i>ω</i>), with corresponding test conclusions for Type I/Type II error cost ratios of 4, 1, and 0.25 using standard <i>α</i> levels and by setting <i>α</i> to minimize cost-weighted average of probabilities of Type I and Type II error.

a<p><i>p</i>-value used for significance testing is 0.02495 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032734#pone.0032734-Crawley1" target="_blank">[12]</a>.</p><p>Probabilities are calculated for a one-way ANOVA with <i>N</i> = 30, <i>k</i> = 3, and <i>σ</i>_{p (within groups)} = 3.4, and critical effect size = <i>σ</i>_{p (within groups)} from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032734#pone.0032734-Crawley1" target="_blank">[12]</a>.</p