Discussion: What's Simple Random Sampling? Is It Possible?

Discussionwhats Simple Random Sampling Is It Possible To Sample Dat

What's simple random sampling? Is it possible to sample data instances using a distribution different from the uniform distribution? If so, give an example of a probability distribution of the data instances that is different from uniform (i.e., equal probability). Chapter 2 Q&A: See the attachments Chapet 2 video: (Part 1) (Part 2) Chapter 3 Q&A: See the attachments Textbook : Read Tan, Steinbach, & Kumar - Chapter 3 - Exploring Data

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Simple random sampling is a fundamental technique in statistics where each individual data point in a population has an equal probability of being chosen. This method ensures that the sample is representative of the population by assigning the same likelihood to each data instance, thereby reducing selection bias. In simple terms, if a population contains N items, each item has a 1/N chance of being included in the sample, and selections are made randomly and independently. This approach is widely used because of its straightforward implementation and the statistical validity it provides for inferential analysis.

However, the question arises whether the sampling process can deviate from a uniform distribution. The answer is yes; it is entirely possible to sample data instances using a probability distribution that is not uniform. In practice, many data sampling techniques intentionally assign different probabilities to data points based on specific criteria or desired outcomes.

An example of a non-uniform probability distribution used in data sampling is the weighted sampling approach, such as probability proportional to size (PPS) sampling. In PPS sampling, each data point's probability of selection is proportional to some measure of its importance or size within the population. For instance, in market research, larger companies with more employees might have a higher probability of being sampled compared to smaller ones, reflecting their greater influence or relevance to the study's goals. This method ensures that larger or more significant data points are more likely to be included in the sample, which can lead to more efficient and informative analysis.

Another example is the application of the exponential distribution in certain sampling contexts, especially when modeling waiting times or failure rates. Here, data points associated with more extreme or rare events can be given higher or lower sampling probabilities depending on the research focus. For example, in quality control testing, products with certain defect characteristics might be sampled with probabilities weighted to detect rarer defect types more effectively.

Using non-uniform distributions in sampling has advantages and challenges. It allows researchers to focus on particular segments of a population, improve the efficiency of data collection, or ensure that rare but important data instances are captured. Nonetheless, it complicates the statistical analysis because standard assumptions ofIID (independent and identically distributed) sampling are violated, requiring adjustments in estimation techniques to account for varying probabilities.

In conclusion, while simple random sampling based on a uniform distribution is the most straightforward method, alternative techniques that employ non-uniform distributions are not only possible but often necessary for practical applications. These methods enable targeted, efficient, and more meaningful data collection, provided that the analysis appropriately accounts for the sampling design.

References

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• Tan, P.-N., Steinbach, M., & Kumar, V. (2019). Introduction to Data Mining (2nd ed.). Pearson.
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