This page is intended as a supportive tool for the meta-analysis program. It contains algorithms to produce the effect size and its Standard Error, which are used in meta-analysis. It includes the following types of comparisons

• Comparing two means, using two sets of n, mean, and SD, supporting 3 commonly used versions of the effect size
  • Difference between means, (mean₁ - mean₂)
  • Standard Difference between means, using standardized value z = (value-common mean) / common SD
  • Log Ratio of mean, (Log(mean₁ / mean₂))
• Comparing two proportions, using two sets of N_pos and N_neg, supporting 3 commonly used versions of the effect size
  • Risk Difference (risk₁ - risk₂), where risk = N_Pos / (N_Pos+N_Neg)
  • Log(Risk Ratio) (Log(risk₁ / risk₂))
  • Log(Odds Ratio) (log(odd₁ / odd₂)), where odd = N_Pos / N_Neg
• Correlation Coefficient ρ, using sample size N and ρ. As ρ is not normally distributed thoughout its range, the effect size requires Fisher's Z transformation to convert sample size and ρ to normally distributed Z and its Standard Error (se), so they can be used in meta-analysis. The formulae are
  Z = 0.5 * log((1 + ρ) / (1 - ρ)), and
  SE = 1 / sqrt(n - 3), where n is the sample size
• Reverse Transformation from Fisher's Z to Correlation Ciefficient ρ is the reverse transformation of Fisher's Z back to Correlation Coefficient ρ. the Formula is
  ρ = exp(2 * Z) - 1) / (exp(2 * Z) + 1)
  This is useful to transform the combined summary Z and its 95% confidence intervals back into Correlation Coefficient (ρ) values after meta-analysis

Data for Difference Between Means, Standard Difference Between Means, and Log(Ratio of Means)
Data a table with 6 columns
    - Each row from a separate study
    - All rows have 6 columns
    - Column 1, 2, and 3 = n, mean, Standard Deviation of index (treatment) group
    - Column 4, 5, and 6 = n, mean, Standard Deviation of reference (control) group

Difference Between Means:
Standard Differences Between Means:
Log(Ratio of Means):

Data for Risk Difference, Log(Risk Ratio), and Log(Odds Ratio) :
Data a table with 6 columns
    - Each row from a separate study
    - All rows have 4 columns
    - Column 1 and 2 = numbers with positive attributes in index and reference group (pos1,pos2)
    - Column 3 and 4 = numbers with negative attributes in index and reference group (neg1,neg2)

Risk Difference:
Log(Risk Ratio):
Log(Odds Ratio):

Data for Correlation Coefficients :
Data a table with 2 columns
    - Each row from a separate study
    - All rows have 2 columns
    - Column 1 = sample size (n)
    - Column 2 = Correlation Coefficient (ρ)

Correlation Coefficients:

Reverse Transformation from Fisher's Z to Correlation Ciefficient ρ
    - Data a single column of Z values