# What does it mean when a 95% confidence interval includes zero for Hedges' g?

https://www.medicaljournals.se/jrm/content/html/10.2340/16501977-2210

I understand the difference between statistical significance and effect size, but I am having trouble interpreting the data on Table III in the article linked above. I am evaluating the WOMAC scores. My first question is can effect size confidence intervals cross zero and still be valid? My second question is about the negative and positive values of the Hedges'g. The first study scores the WOMAC in a way where the higher the score, the better the outcome. The second two studies score the WOMAC in a way where the lower the score, the better the outcome. Does this mean that in the first study a positive Hedges'g indicate larger effect for the treatment group and a negative Hedges' g for the other two studies indicate larger effect for the treatment group?

## 2 Answers

Confidence Interval

...can effect size confidence intervals cross zero and still be valid?

Yes. There is no rule about the validity of numbers in a confidence interval. All a confidence interval means is that if we would repeat this experiment many times and construct 95% CI every time, then 95% of those intervals contain the true value.

Whether such an interval contains zero is only meaningful in the context of hypothesis testing. If there is a hypothesis $\text{H}_0: \mu_1 - \mu_2 = 0$, then at $\alpha = 0.05$, we cannot conclude a significant difference between $\mu_1$ and $\mu_2$ if the 95% confidence interval contains zero.

Hedge's g

My second question is about the negative and positive values of the Hedges'g. ...

Hedges' g is the observed difference divided by the pooled standard deviation: $\frac{\bar{y}_1 - \bar{y}_2}{s_{\text{pooled}}}$. If it is positive, then $\bar{y}_1>\bar{y}_2$. If it is negative, then $\bar{y}_1<\bar{y}_2$.

Positive or negative sign for Hedges g has no connection with the scoring system of question items or subscales used for measuring the outcome because the outcome or scores are measured in a similar way for both treatment as well as control groups . g depends on difference between groups' scores and standard deviation of each ot two groups - treatment group and control group.

Further you may structure your question about confidence interval separately with detailed problem that you are facing . This concerns inferential statistics.