What is the intuition behind Cohen's d? Can anyone please help me in understanding what does the result of Cohen's d gives us? Like how do we interpret the results and what does the positive and negative sign mean?
 A: Cohen’s D
Cohen's d is an effect size used to indicate the standardized difference between two means.
Cohen’s D is one of the most common ways to measure effect size. An effect size is how large an effect of something is. For example, medication A has a better effect than medication B.
The formula for Cohen’s D is:
$d = \frac{M_{1}-M_{2}}{S_{pooled}}$
Where:


*

*$M_{1}$ = mean of group 1

*$M_{2}$ = mean of group 2

*$S_{pooled}$ = pooled standard deviations for the two groups. 


Interpreting Results
A d of 1 indicates the two groups differ by 1 standard deviation, a d of 2 indicates they differ by 2 standard deviations, and so on. Standard deviations are equivalent to z-scores (1 standard deviation = 1 z-score).
The below figure is an example of the overlap between two normally distributed groups for different Cohen d values. The mean of the pink population is 50. The standardizer (i.e., the standard deviation) of the between-group difference is 15. Thus, for a standardized between-group difference of 0.5, the between-group difference (effect size; ES) in original units will be $0.5 = ES/15$, which gives 7.5. So the difference between the mean of the two distributions is 1/2 a standard deviation, or 7.5

As you can see, there is considerable overlap between the two distribution even when Cohen’s d indicates a large effect. This means that even for large effects there will be many individuals that go against the population-level pattern. Always keep these types of figures in mind when trying to interpret effect size measures.
Rule of Thumb Interpretation
If you aren’t familiar with the meaning of standard deviations and z-scores or have trouble visualizing what the result of Cohen’s D means, use these general “rule of thumb” guidelines (which Cohen said should be used cautiously):
Small effect = 0.2
Medium Effect = 0.5
Large Effect = 0.8

“Small” effects are difficult to see with the naked eye. For example, Cohen reported that the height difference between 15-year-old and 16-year-old girls in the US is about this effect size. “Medium” is probably big enough to be discerned with the naked eye, while effects that are “large” can definitely be seen with the naked eye (Cohen calls this “grossly perceptible and therefore large”). For example, the difference in heights between 13-year-old and 18-year-old girls is 0.8. An effect under 0.2 can be considered trivial, even if your results are statistically significant.
Bear in mind that a “large” effect isn’t necessarily better than a “small” effect, especially in settings where small differences can have a major impact. For example, an increase in academic scores or health grades by an effect size of just 0.1 can be very significant in the real world. Durlak (2009) suggests referring to prior research in order to get an idea of where your findings fit into the bigger context.
There is no straight forward way to interpret standardized effect size measures. While they are increasingly being reported in published manuscripts, Cohen’s d and other such measures should not have glanced over.
In simple Cohen's d is frequently used in estimating sample sizes for statistical testing. A lower Cohen's d indicates the necessity of larger sample sizes, and vice versa, as can subsequently be determined together with the additional parameters of desired significance level and statistical power
