When two people arguing about a study, I often hear one of them talk about how a study automatically flawed and can’t be trusted. However, studies with small sample sizes regularly appear in meta-analyses. Why aren’t they automatically considered useless?
In: Mathematics
A study is only useful if its representative of the population it is meant to represent. Would you respect a study about videogame violence if all the respondents were 50 year old moms? Would you trust a new medical device thats only tested on 5 people? What if you had some weird genetics that those 5 didnt and you get hurt as a result? It is hard to represent a large population with only a few people because we are each unique in many different ways (such as gender, sexual orientation, political views, weight, height).
Say you have balls in a bag of many different colors and your goal is to grab with your eyes closed one of each color. Say there are 7 colors in total. You grab 5 balls and you get 3 red and 2 green. You see that this is not representative of the whole population which is 7 colors, so a study with this sample will only be relevant toward red and green balls. Say you increase your sample to 15 and get red, green, and blue balls. This is better than before but still not very reflective of the overall population.
The more you increase the size of the sample the better chance you have of equally representing the 7 colors in the proportion they appear in the bag.
The “best” sample size is theoretically the entire population (so a study about students will ideally need to include all the students in the world). But this is impossible so we settle with smaller samples because thats easier and cheaper to work with
Meta analysis takes many studies and combines them, and in effect combines all of their sample sizes. Do note that in meta analysis, the sample size of each study included in it plays a role in how much influence it has on the final result. So a study with 5 people in it will contribute less than one with 500.
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