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?

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    $\begingroup$ I think is a question for another section of the community, the statistical one: Cross Validated $\endgroup$ – have fun Sep 10 '17 at 16:32
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    $\begingroup$ Welcome to Biology.SE. I'm voting to close this question as off-topic because it belongs to stats.SE (or at worst Medical Sciences(health.stackexchange.com) but definitely not Biology.SE). +1 to @vkehayas answer though. $\endgroup$ – Remi.b Jan 10 '18 at 23:48
  • $\begingroup$ Also, please always narrow your posts down to a single question. $\endgroup$ – Remi.b Jan 10 '18 at 23:50

Regarding your first question, the effect size is not invalid if the confidence interval (CI) crosses 0. The effect size is a point estimate. When the CI -a range estimate of the coverage probability- includes 0, the probability that the range of the effect size can include 0 cannot be rejected at the $1-\alpha$ level of confidence.

Regarding your second question, from the definition of Hedge's g:

$$g = \frac{\bar{x_1} - \bar{x_2}}{sd_{pooled}}$$

we can see that if $\bar{x_2}$ is larger than $\bar{x_1}$ then $g$ will be negative. So, the sign only determines which of the estimates is larger and that will depend on which estimate is considered as the reference.


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