Estimating Mean and SD Using Wan’s Method for Meta-Analysis

---

🎯 Purpose

In meta-analyses, especially of clinical studies, researchers often encounter studies reporting medians, ranges, and quartiles instead of means and SDs. Wan et al. (2014) developed a validated approach to estimate the sample mean and SD from incomplete summary data, allowing inclusion in meta-analysis.

Wan’s Calculator automates three estimation scenarios depending on available statistics.

---

🧩 Scenario 1: Minimum, Median, Maximum, Sample Size

📌 Required Inputs:

• Minimum (a)

• Median (m)

• Maximum (b)

• Sample size (n)
  

📘 Estimation Formulas:

Example (n = 20):

• Min = 40, Median = 60, Max = 100 →Mean ≈ (40 + 2×60 + 100) / 4 = 65 →SD ≈ (100 − 40) / 4.06 = 14.78

Note: The calculator automates lookup or computes C(n) using default functions.

---

🧩 Scenario 2: Minimum, Q1, Median, Q3, Maximum, Sample Size

📌 Required Inputs:

• Minimum (a)

• First quartile (Q1)

• Median (m)

• Third quartile (Q3)

• Maximum (b)

• Sample size (n)

📘 Estimation Formulas:

Example (n = 40):

• a = 30, Q1 = 45, m = 50, Q3 = 55, b = 70 →Mean ≈ (30 + 2×45 + 2×50 + 2×55 + 70)/8 = 50 →SD ≈ √[ ((70−30)² + (55−45)²) / (2 × 4.21) ] ≈ 12.02
  

---

🧩 Scenario 3: Q1, Median, Q3, Sample Size

📌 Required Inputs:

• First quartile (Q1)

• Median (m)

• Third quartile (Q3)

• Sample size (n)

📘 Estimation Formulas:

Where A(n) is another adjustment factor depending on n:

• For n ≥ 25, A(n) ≈ 1.35
  

Example (n = 50):

• Q1 = 40, m = 50, Q3 = 60 →Mean ≈ (40 + 50 + 60)/3 = 50 →SD ≈ (60 − 40)/1.35 ≈ 14.81
  

---

🧠 Key Notes

• Wan’s method assumes that data follow roughly symmetric distributions.

• Use Scenario 2 when all five summary statistics are available (most precise).

• The calculator handles small and large n with different correction constants.

• Always specify which estimation method you used when reporting meta-analysis inputs.