The design effect The design effect (deff) quantifies the extent to which the expected sampling error in a survey departs from the sampling error that can be expected under simple random sampling .
My question is 


*

*Why do we compare expected sampling design with simple random sampling instead of other sampling method such as , systematic sampling , stratified sampling ?

 A: Sampling designs are often compared to simple random sampling, mainly because formulas for estimators and variances (and variance estimators) are very simple for SRS :
$
\begin{align*}
\mathbb{V}(\hat{Y}_{HT, SRS}) &= (1-\dfrac{n}{N}) \dfrac{S^2}{n} \\
\text{with : } S^2 &= \dfrac{1}{N-1} \sum_{k \in pop} (y_k - \bar{Y})^2
\end{align*}
$
It'd be impratical to compare the sampling variance of a particular sampling design with :


*

*Stratified sampling, because sampling error depends very much on sample allocation between strata and how strata are designed (imagine badly designed strata and allocation : you could end up with a much higher error than SRS with same sample size, whereas wisely designed strata and Neyman allocation can spectacularly improve precision compared to SRS)

*Systematic sampling, because its variance is very hard to compute. Very often, people using systematic sampling consider that the sampling variance is roughly equal to the variance of a stratified sampling using proportional allocation and strata formed by the variable on which the sample frame was sorted before the draw.

