1. What is Standard Mean Difference?

The Standard Mean Difference (SMD) is a measure of effect size that compares the difference between two group means relative to their variability. It's commonly used in meta-analyses and research studies to quantify the magnitude of differences between groups.

2. How Does the Calculator Work?

The calculator uses the SMD formula:

Where:

• \( Mean1 \) — Mean of group 1
• \( Mean2 \) — Mean of group 2
• \( SD_{pooled} \) — Pooled standard deviation of both groups

Explanation: The SMD expresses the difference between group means in standard deviation units, allowing comparison across studies with different measurement scales.

3. Interpretation of SMD Values

Guidelines:

• 0.2 - Small effect
• 0.5 - Medium effect
• 0.8 - Large effect

Negative values indicate the second group has higher values than the first group.

4. Using the Calculator

Tips: Enter means for both groups and the pooled standard deviation. All values must be valid (SD_pooled > 0). The units should be consistent across all inputs.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between SMD and Cohen's d?
A: Cohen's d is a specific type of SMD that uses pooled standard deviation. The terms are often used interchangeably.

Q2: How is pooled standard deviation calculated?
A: \( SD_{pooled} = \sqrt{\frac{(n1-1)SD1^2 + (n2-1)SD2^2}{n1+n2-2}} \), where n1 and n2 are sample sizes.

Q3: When should I use SMD?
A: Use SMD when comparing continuous outcomes between groups, especially when combining results from different studies in meta-analyses.

Q4: What are the limitations of SMD?
A: SMD can be difficult to interpret clinically and may be affected by differences in baseline variability between studies.

Q5: How does SMD relate to t-tests?
A: The t-statistic from an independent samples t-test is related to SMD by: \( t = SMD \times \sqrt{\frac{n1 \times n2}{n1+n2}} \).