This page is intended as a supportive tool for 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, (mean_{1} - mean_{2})

Standard Difference between means, using standardized value z = (value-common mean) / common SD

Log Ratio of mean, (Log(mean_{1} / mean_{2}))

Comparing two proportions, using two sets of N_{pos} and N_{neg}, supporting 3 commonly used versions of the effect size

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

Javascript Programs

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)

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