2.7.1. Sampling Errors

A population consisting of numerical values has two important characteristics which are of relevance here. First, Central Tendency which may be measured by the mean, the median or the mode. Second, Dispersion, which can be measured by calculating the “standard deviation”, “mean deviation”, “range”, etc.

Sampling errors arise when we measure a characteristic of a sample rather than the entire population. The population includes all items from which a sample can be drawn, and important characteristics of this population can be described through central tendency (like mean, median, or mode) and dispersion (how spread out the values are). Central tendency gives us a 'central' value from the dataset, while measures of dispersion tell us how much the data points differ from that central value.

Imagine you are trying to estimate the average height of students in a large school. Instead of measuring every single student, you decide to measure just 30 students from a randomly selected class. The average height of those 30 students represents your sample, but it may not perfectly reflect the average height of the entire school. If the selected students happen to be mostly tall, your estimate will be higher than the actual average, showcasing a sampling error.

Sampling bias occurs when the sampling plan is such that some members of the target population could not possibly be included in the sample.

Sampling bias happens when certain groups within the population are systematically excluded from the sample, making the sample unrepresentative. This can lead to inaccurate results and generalizations to the whole population, as the data collected might over-represent or under-represent certain views or characteristics.

Consider you want to know about the average spending habits of a city. If you only survey people in wealthy neighborhoods, you might conclude that everyone in the city spends a lot on luxury items. However, residents in poorer areas, who would spend differently, are not represented, leading to a skewed perspective of the overall spending habits of the city.

Non-response occurs if an interviewer is unable to contact a person listed in the sample or a person from the sample refuses to respond. In this case, the sample observation may not be representative.

Non-response errors occur when individuals chosen for the sample do not provide data, either because they cannot be reached or choose not to participate. This can skew the results if the non-respondents differ significantly from those who do respond. If a portion of your sample refuses to answer questions, the resulting data can misrepresent the entire population.

Suppose you're conducting a survey to understand how students feel about school lunches. If only those who love school lunches respond, while students who dislike them do not participate, your results will suggest that most students are happy with the lunches when, in reality, many are not. Thus, the absence of responses from a segment of the population affects the integrity of your findings.

This type of error arises from the recording of incorrect responses. For example, if a teacher asks a student to measure the length of a table, the measurements may vary due to different measuring techniques or carelessness.

Errors in data acquisition can occur due to mistakes during the collection or recording of data. This can include mishearing a response, writing down incorrect data, or using faulty measurement tools. Such inaccuracies can lead to flawed analyses and conclusions.

Imagine a scenario where students are measuring the height of plants in a science experiment. If some students use a ruler while others use a tape measure and do not convert their measurements to the same units, the average height calculated from these mixed-up reports would be incorrect. This illustrates how crucial accuracy is during data collection to maintain the integrity of results.

Non-sampling errors are more serious than sampling errors because a sampling error can be minimized by taking a larger sample. It is difficult to minimize non-sampling errors, even by taking a large sample.

Non-sampling errors encompass all other types of errors that can occur during the survey and data collection process that are not related to the sample size. These errors can have significant impacts on the validity of the data and can lead to inaccurate conclusions. They can occur from poor survey design, respondent misunderstandings, or errors made by data collectors.

Think of a restaurant survey asking patrons to rate their experience. If the survey is poorly phrased or confusing, diners might misinterpret the questions and give feedback that does not reflect their true experience. This misrepresentation would be a non-sampling error, affecting the restaurant’s ability to understand customer satisfaction accurately.

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