Sampling error (also known as sampling variability) increases when

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Question: Sampling error (also known as sampling variability) increases when

Option 1: bias is present.
- This option confuses two distinct sources of error. Sampling error refers to the natural variability that comes from using a sample rather than the full population, due to random chance. Bias, on the other hand, is a systematic error that skews results in a particular direction. While both can affect study conclusions, the presence of bias does not by itself describe an increase in sampling variability; in fact, a biased design can sometimes mask or distort true variability. So this statement is not aligned with the standard definition of sampling error.

Option 2: the sample size is increased
- Increasing the sample size generally reduces sampling error because larger samples tend to yield estimates that are closer to the true population value by the law of large numbers. This option describes the opposite of what typically happens to sampling error, making it incorrect.

Option 3: the sample size is decreased
- This is the classic relationship: smaller samples produce greater random fluctuation from sample to sample, leading to higher sampling error. With fewer observations, estimates are more variable and less precise. This option correctly identifies the situation that raises sampling variability.

Option 4: the population increases
- A larger population does not inherently increase sampling error for a given sampling plan. If the sample size remains the same, more population often means the sample is a smaller fraction of the population, which can reduce the impact of finite population corrections but does not intrinsically raise sampling error. Therefore this statement is not generally valid as a description of what increases sampling error.

Option 5: the population decreases
- When the population shrinks, the structure of the population can become more influential, and the same sample size may capture less diversity, potentially increasing sampling error, especially if the sample size is not adjusted. However, the most straightforward and commonly taught driver of sampling error is sample size, not population size, so this option is less directly correct than option 3. It can be context-dependent but is not the standard answer when teaching the basic concept.

Option 6: a cluster sample is taken
- Clustering can increase sampling error relative to a simple random sample because individuals within clusters tend to be more alike, reducing the effective sample information. This is known as a design effect. While this can increase overall variability, it depends on the sampling design rather than being a universal cause of increased sampling error in the same sense as reducing sample size. So this option partially describes a scenario that can raise error, but it is not as direct or universal as option 3.

Statistics Chapters 12-13 Test

Sampling error (also known as sampling variability) increases when

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