`effectsize` 套件使用指南

主創者：陳紹慶 協作者：魏志名, 蕭富聲
2022/5/24 2 min read

經過第一堂課程，為了各位學員之後在各種場域教授與討論效果量的計算與解讀，提供示範用的R程式碼及說明範例是相當有用的。我們將彙整Ben-Shachar等人(2020)開發的R套件effect size，與Ellis(2010)Chapter 1,2的內容，以接力協作的方式編輯這份作業。每位學員貢獻一點成果，換取更多人在研究教學上的便利。

編輯流程：

  1. 混合純文字及Latex編碼編輯效果量公式
  2. 在R chunk內放置可執行的R程式碼
  3. 隨時按’Knit’渲染可得編輯成果
  4. 編輯完成在討論區留言提交編輯成果。

計算效果量

d family ~ difference between groups

Groups compared on dichotomous outcomes

  • The risk difference in probabilities

  • The relative risk

  • The odds ratio

Groups compared on continuous outcomes

  • Cohen’s d

比較獨立樣本平均數的效果量Cohen’s d計算公式:

$$Cohen’s \space d = \frac{M_1 - M_2}{SD_{pooled}} $$

R程式碼範例:

## 獨立樣本比較範例
## 範例資料來自`mtcars`
cohens_d(mpg ~ am, data=mtcars)

## Cohen's d |         95% CI
## --------------------------
## -1.48     | [-2.27, -0.67]
## 
## - Estimated using pooled SD.

## 輸出效果量及95%信賴區間

  • Glass’s delta( △ )

  • Hedges’ g

  • Probability of superiority

r family ~ measures of association

Correlation indexes

(Two variables are continuous)

  • The Pearson product moment correlation coefficient (r)

負責學員 魏志名(嘉義大學)

皮爾森積差相關公式:

$$Pearson’s \space r = \frac {\sum_{i=1}^{n}(X_i-\overline{X})(Y_i-\overline{Y})}{{\sqrt{\sum_{i=1}^{n}(X_i-\overline{X})^2}}{\sqrt{\sum_{i=1}^{n}(Y_i-\overline{Y})^2}}}$$

R程式碼範例:

cor_results <- cor.test(mtcars$mpg, mtcars$disp,conf.level = 0.95) 
report::report_effectsize(cor_results)

## very large (r = -0.85, 95% CI [-0.92, -0.71])
## 輸出效果量及95%信賴區間

(Two variables are ordinal)

  • Spearman’s rho or the rank correlation coefficient (ρ)

  • Kendall’s tau (τ)

(One continous and one ordinal)

  • The point-biserial correlation coefficient (rp**b)

(Contigency table)

  • The phi coefficient (ϕ)

  • Pearson’s contingency coefficient (C)

  • Cram´er’s V (V)

  • Goodman and Kruskal’s lambda (λ)

Proportion of variance indexes

  • The coefficient of determination (r2)

負責學員 蕭富聲(佛光大學)

$$r^2 = \frac{ \sum_{i=1}^{N}(\hat{y_i}-ȳ_i)^2}{ \sum_{i=1}^{N} (y_i-ȳ_i)^2 } $$

## 決定係數比較範例
## 範例資料來自`mtcars`

m1 <- lm(hp ~ disp, data = mtcars)
summary(m1)

## 輸出效果量及95%信賴區間

  • the (uncorrected) coefficient of multiple determination (R2$)

  • the coefficient of multiple determination adjusted for sample size and the number of predictor variables (adjR2$)

  • Cohen’s f (f)

  • Cohen’s f squared

  • Epsilon squared (eps2)

  • the (uncorrected) correlation ratio (η2)

  • Omega squared (ω2)

  • The squared canonical correlation coefficient (RC2)

解讀效果量

effectsize套件收錄統計學者的建議，提供使用者查詢效果量份量的建議。在此彙整解讀效果量的函式與使用方法。

參考資源

Ben-Shachar, M. S., Lüdecke, D., & Makowski, D. (2020). effectsize: Estimation of effect size indices and standardized parameters. Journal of Open Source Software, 5(56), 2815. https://doi.org/10.21105/joss.02815

Ellis, P. D. (2010). The essential guide to effect sizes: Statistical power, meta-analysis, and the interpretation of research results. Cambridge University Press.