In statistics, simple random samples are part of an individual (sample) selected from a larger set (population). Each individual is randomly selected and completely coincidental, so that each individual has the same probability to be chosen at any stage during the sampling process, and each part of the k individual has the same probability to be selected for the sample as other parts of the k individual. These processes and techniques are known as simple random sampling , and should not be equated with systematic random sampling. A simple random sample is an unbiased survey technique.
Simple random sampling is a basic type of sampling, as it can be a component of other more complex sampling methods. The simple random sampling principle is that each object has the same probability to choose from. For example, suppose N student wants to get tickets for basketball games, but there is only X & lt; N tickets for them, so they decided to have a fair way to see who should go. Then, everyone is numbered in the range from 0 to N -1, and a random number is generated, either electronically or from a random number table. Figures outside range from 0 to N -1 are ignored, as are the numbers previously selected. The first X number will identify the lucky ticket winner.
In small and often large populations, such sampling is usually done " without replacement ", that is, one deliberately avoids selecting any population member more than once. Although simple random sampling can be done with replacements instead, this is less common and will usually be described more fully as simple random sampling with replacement . Sampling done without replacement is no longer independent, but still meet the ability of exchange, so many results still apply. Furthermore, for small samples of large populations, sampling without replacement is approximately the same as sampling with replacement, since the chances of selecting the same individual are twice lower.
An unbiased selection of random from an individual is important so that if a large number of samples is taken, the average sample will accurately represent the population. However, this does not guarantee that a particular sample is a perfect representation of the population. Simple random sampling only allows one to draw valid conclusions externally about the entire population based on the sample.
Conceptually, simple random sampling is the simplest of the probability sampling techniques. This requires a complete sampling frame, which may not be available or feasible to build for large populations. Even if a complete framework is available, a more efficient approach is possible if other useful information is available about units in the population.
The advantage is that it is free from misclassification, and it requires a minimum initial knowledge of the population apart from the frame. Its simplicity also makes it relatively easy to interpret the data collected in this way. For this reason, simple random sampling best suits situations where little information is available about the population and data collection can be efficiently performed on items that are randomly distributed, or where the sampling cost is small enough to make efficiency less important than simplicity. If this condition does not apply, stratified sampling or cluster sampling can be a better choice.
Video Simple random sample
Algorithm
Several efficient algorithms for simple random sampling have been developed. The naive algorithm is a draw-by-draw algorithm in which at each step we remove the item in that step from the set with the same probability and place the item in the sample. We continue until we have the desired size sample k. The disadvantage of this method is that it requires random access on the set.
The selection-rejection algorithm was developed by Fan et al. in 1962 required a single passing data; However, this is a sequential algorithm and requires knowledge of the total number of items n, which is not available in a streaming scenario.
A very simple random sorting algorithm proved by Sunter in 1977 that only gives random numbers taken from a uniform distribution (0, 1) as the key for each item, sorting all items using the key and selecting the smallest k item.
J. Vitter in 1985 proposed a widely used reservoir sampling algorithm. This algorithm requires no initial knowledge of n and uses constant space.
Random sampling can also be accelerated by sampling from the gap distribution between the samples, and jumping over the gap.
Maps Simple random sample
Difference between systematic random sampling and simple random sample
Consider a school with 1,000 students, and suppose that a researcher wants to select 100 of them for further research. All their names may be put in a bucket and then 100 names may be pulled out. Not only does everyone have the same opportunity to choose, we can also easily calculate the probability of P from the chosen person chosen, because we know the sample size ( n ) and the population ( N ):
2. Dalam hal bahwa setiap orang yang dipilih dikembalikan ke kolam pilihan (yaitu, dapat dipilih lebih dari satu kali):
This means that every student in the school has the possibility of about 1 in 10 possibilities to be selected using this method. Furthermore, all combinations of 100 students have the same selection probability.
If a systematic pattern is entered into random sampling, it is referred to as "systematic (random) sampling". An example would be if students at school have numbers attached to their names ranging from 0001 to 1000, and we choose a random starting point, e.g. 0533, and then selects every 10 names afterwards to give us a sample 100 (starting with 0003 after reaching 0993). In this sense, this technique is similar to cluster sampling, since the choice of the first unit will determine the rest. This is no longer simple random sampling, since some combinations of 100 students have a greater probability of choice than others - for example, {3, 13, 23,..., 993} have 1/10 chance of selection, while {1, 2 , 3,..., 100} can not be selected based on this method.
Taking a sample of dichotomous population
If a member of the population comes in three types, say "blue" "red" and "black", the number of red elements in a given size sample will vary based on the sample and hence a random variable whose distribution can be studied. The distribution depends on the number of red and black elements in the full population. For a simple random sample with a replacement, the distribution is binomial distribution . For a simple random sample without a replacement, one obtains a hypergeometric distribution .
See also
- Multistage sampling
- Nonprobability sampling
- Polls
- Quantitative marketing research
References
Source of the article : Wikipedia
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