C シンボルマーク一覧
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| \(a,b,c,d\) | Events in the treatment group, non-events in the treatment group, events in the control group, non-events in the control group. | \(\beta_0, \beta_1, \beta\) | Regression intercept, regression coefficient, Type II error rate. |
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| \(c_{\alpha}\) | Critical value assumed for the Type I error rate \(\alpha\) (typically 1.96). | \(\mathcal{HC}(x_0,s)\) | Half-Cauchy distribution with location parameter \(x_0\) and scaling parameter \(s\). |
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| \(\chi^2\) | Chi-squared statistic. | \(\text{Cov}(x,y)\) | Covariance of \(x\) and \(y\). |
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| \(d\) | Cohen’s \(d\) (standardized mean difference). | \(D_g\) | Regression dummy. |
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| \(\delta\) | Non-centrality parameter (non-central \(t\) distribution). | d.f. | Degrees of freedom. |
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| \(\epsilon\) | Sampling error. | \(F\) | Snedecor’s \(F\) statistic (used by the \(F\)-tests in ANOVAs). |
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| \(g\) | Small sample bias-corrected standardized mean difference (Hedges’ \(g\)). | \(I^2\) | Higgins’ and Thompson’s \(I^2\) measure of heterogeneity (percentage of variation not attributable to sampling error). |
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| \(\int f(x) dx\) | Integral of \(f(x)\). | \(k,K\) | Some study in a meta-analysis, total number of studies in a meta-analysis. |
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| \(\kappa\) | True effect of an effect size cluster. | \(MD\), \(SMD\) | (Standardized) mean difference (Cohen’s \(d\)). |
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| \(\bar{x}\) | Arithmetic mean (based on an observed sample), identical to \(m\). | \(\mu, m\) | (True) population mean, sample mean. |
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| \(n,N\) | (Total) sample size of a study. | \(\mathcal{N}(\mu, \sigma^2)\) | Normal distribution with population mean \(\mu\) and variance \(\sigma^2\). |
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| \(\Phi(z)\) | Cumulative distribution function (CDF), where \(z\) follows a standard normal distribution. | \(\pi, p\) | True population proportion, proportion based on an observed sample. |
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| \(P(\text{X}|\text{Y})\) | Conditional probability of X given Y. | \(\hat\psi\) | (Estimate of) Peto’s odds ratio, or some other binary effect size. |
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| \(Q\) | Cochran’s \(Q\) measure of heterogeneity. | \(RR\), \(OR\), \(IRR\) | Risk ratio, odds ratio, incidence rate ratio. |
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| \(\hat{R}\) | R-hat value in Bayesian modeling. | \(R^2_*\) | \(R^2\) (explained variance) analog for meta-regression models. |
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| \(\rho, r\) | True population correlation, observed correlation. | \(SE\) | Standard error |
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| \(\sigma^2\) | (True) population variance. | \(t\) | Student’s \(t\) statistic. |
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| \(\tau^2, \tau\) | True heterogeneity variance and standard deviation. | \(\theta\) | A true effect size, or the true value of an outcome measure. |
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| \(V\), \(v\), \(s^2\), \(\widehat{\text{Var}}(x)\) | Sample variance (of \(x\)), where \(s\) is the standard deviation. | \(w\), \(w^*\), \(w(x)\) | (Inverse-variance) weight, random-effects weight of an effect size, function that assigns weights to \(x\). |
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| \(z\) | Fisher’s \(z\) or \(z\)-score. | \(\zeta, u\) | ``Error’’ due to between-study heterogeneity, random effect in (meta-)regression models. |
| \(~\) |
注記: ベクトルや行列は太字で表記される。例えば、メタ分析で観測された全ての効果量をベクトルで表すと \(\boldsymbol{\hat\theta} = (\hat\theta_1, \hat\theta_2, \dots, \hat\theta_K)^\top\) となる。ここで \(K\) は総研究数である。\(\top\) 記号はベクトルが transposed であることを表している。これは、ベクトルの要素が水平方向ではなく、垂直方向に配置されていることを意味する。これは、ベクトルと別の行列を掛け合わせるなどの操作を行う際に必要な場合がある。