1. You can get a good, although not very great, statistical analysis from a sample size of 1,000/200,000,000 if you have done an excellent sampling.
2. You may get a terrible statistical analysis from 100,000/200,000,000 if you have done a horrible sampling. For instance, if you go to Nigeria, and ask 100,000 children about who would be the next US presidential elections, you will not get a healthy result. Of course, I exaggerated this example, for ease of explanation.
Those being said, if you do an excellent sampling and increase your sample size, you will have healthier results. Let’s give an example from probability. In reality, if you throw two six sided dice, you have 1/36 chance to have 6-6. However, in practice, you may throw 6-6 three times in a row even if you only throw three times. Depending on that observation, and only on that observation , you may say that throwing 6-6 is a %100 chance. However, if you throw the dice 10,000 times, you will see the factor of luck will be minimized, and in 100,000 throws, it will be further minimized (eliminated in the infinity). Since it is not optimal (for money, time, and human resources wise) to ask to all 200,000,000 eligible voters, for instance, it would be a good idea to have a sample size which is neither too small, nor too costly.
Latest Answers