# Cohen’s d size effect size # Cohen’s d size effect

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## Statistically significant versus clinically relevant

In addition to discerning what is statistically significant (p-value associated with the contrast statistic less than 0.05), in Biostatistical and Biomedical research, it is considered of vital importance to take into account what is clinically relevant, through the effect size, which can be calculated using Cohen’s d, which standardises (typifies) the difference in means.

The effect size from Cohen’s d is calculated from the difference between the means of the dependent variables of the groups being compared, normally the control group and the experimental group, between (divided) the mean of their standard deviations, and whether these variables are of the ordinal Likert type, or of the continuous-scale type, such as the time of pain remission after exposure to a certain treatment/s. The effect size is independent of the sample size.

To interpret the result of this index, and bearing in mind that it is a standardised measure, the biostatistician Cohen in 1988 proposed quantifying the magnitude of the effect as small (d = 0.2), medium (d = 0.5) and large (d = 0.8 or higher).

EXAMPLE FROM PSYCHOLOGY UNIVERSITY (U.N.E.D.)

An experiment is conducted to study whether the verbalization of the process facilitates the performance of complex manual tasks.facilitates the performance of complex manual tasks. Sixty subjects are randomly selected and 30 are assigned to each of two groups. 30 are assigned to each of two groups: the experimental group, in which the subjects verbalize the task, and the control group, in which the subjects perform the task silently. control group, in which subjects perform the task silently. As a dependent variable, the time in seconds required to perform the task in silence is recorded. The time in seconds required to complete the task is recorded as the dependent variable. For the control group, the mean was equal to 237 and quasi-standard deviation equal to 38, and for the experimental group, mean equal to 205 and quasi-standard deviation equal to 35. Cohen’s d index for quantifying the improvement in speed that occurs when verbalizing the task is: Cohen’s d index for quantifying the improvement in speed that occurs when verbalizing the task is: 0.88 is the standardized distance between the means of the two groups, and its associated probability is 0.8106, indicating that 81.06% of the subjects in the experimental group take less time than the experimental group.
is 0.8106, indicating that 81.06% of the subjects in the experimental group take less time than the average of the subjects who do not verbalize.than the average of the subjects who do not verbalize. Only 18.94% of the children who do not verbalize take less time than the average of the non-verbalizing subjects take less time than the average of those who do.

## Effect size in logistic regression

### Odds Ratio (OR) and its interpretation as effect size (ES)

For the case of a binary logistic regression, with a dichotomous dependent variable, an interpretation of the ODDS RATIO is proposed based on a Cohen’s d transformation. If the OR is less than 1.68 its effect size is considered ‘insignificant‘, if it is between 1.68-3.47: ‘small‘, between 3.47-6.71: ‘moderate‘, and if it is greater than 6.7: ‘large‘. Chen H, Cohen P, Chen S. ‘How big is a big odds ratio? Interpreting the magnitudes of odds ratios in epidemiological studies’. (2010)].