Aside from their difference that quota sampling is a type of non probability sampling and stratified sampling is a type of probability sampling , haw can I determine which type to use as a sampling method?
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Quota sampling method and Stratified sampling method are similar in practice except like you said Quota sampling method is non-probabilistic while Stratified sampling method is probabilistic.
In sampling, both Quota and Stratified sampling are not used in isolation, they are used in addition to another sampling method such as judgemental for Quota and SRS for Stratiified sampling methods.
The choice of whether to use Quota or Stratified sampling method depends on the sampling method you use with them. When you segment your population and then select your sample based on judgment, then we call it Quota sampling method. However, when you segment your population and then select your sample based on any of the probabilistic sampling methods like the simple random sampling (SRS), then we call it Stratified sampling method.