I used an internet calculator for Hedges g, and the result was 1.69. as I was going through the internet to understand what this means I realized this is a Z score. how do I convert this to an effect size score?
Remember that Hedges' g measures the effect size, which tells you the difference between any two groups such as an experimental group and a control group. Its formula is:
g = (mean of group A - mean of group B)/pooled standard deviation
On the other hand, z-score is a standard score used usually in two contexts
1. When the population mean and population standard deviation are known
z = (raw score x - population mean)/population standard deviation
2. When the population mean and population standard deviation are unknown
z = (raw score x - sample mean)/sample standard deviation
From the formulas you can clearly see the difference between hedges' g and z-score.
Two major differences:
z-score measures the difference between a test or observed score (a value not a mean) and a mean of population/sample, while the hedges' g is the measurement of difference between two means.
z-score involves simple standard deviation either sigma (population sd) or S (sample sd), while hedges' g involves a pooled standard deviation. There is a difference between the simple and pooled standard deviations' formulas.
Hedges D is like Cohens D, it is already an effect size and you report it as such, see my article cited below for how to interpret it.
It is a group difference effect size, similar in many ways to t tests, z test scores, and pair wise t test scores. However, Hedges D of G is the coefficient of variation between groups, the difference between group means divided by their deviation. A really simple way to make this a unit free effect size percent in a Excel spread sheet or similar software is
(M1 - M2) / pooled SD x 100
The M1 is first group mean, M2 is second group mean, and just average the two standard deviations (SD) then convert to a percent. This becomes relative difference effect size units free and anything over 10% is a small effect, refer to Cohen for effect size interpretations. Hope that helps?
See also,
Strang, K.D. (2021). General analytics limitations with coronavirus healthcare big data. International Journal of Healthcare Technology and Management 18(1), 1-11. doi:10.1504/IJHTM.2020.111964 Inderscience
Strang, K.D. (2021). Which organizational and individual factors predict success versus failure in procurement projects. International Journal of Information Technology Project Management, 12(3), 21-43. IGI