A study is surveying basketball players and are interested in making inference on their mean height. After measuring and recording all of their heights, the researchers find out that the ruler that was used to assess their heights was warped/stretched. Thus, all of the recorded heights are underestimates of the actual heights.

What is this an example of?

Question

A study is surveying basketball players and are interested in making inference on their mean height. After measuring and recording all of their heights, the researchers find out that the ruler that was used to assess their heights was warped/stretched. Thus, all of the recorded heights are underestimates of the actual heights.

What is this an example of?

BlackTom AI · Accepted Answer

In this scenario, the researchers are using a measuring instrument (a ruler) that is not accurate because it is warped or stretched. This means every height measurement recorded will be systematically lower than the true height. Such a consistent, instrument-based distortion is a classic example of measurement bias, where the data collected deviate from the truth in a predictable, non-random way due to flaws in the measurement process.

Because the instrument causes all measurements to be artificially low, the study’s estimate of the mean height will also be biased downward, leading to underestimation of the true average height of the players. This is different from random error, which would cause measurements to be sporadically high or low around the true value without a consistent direction.

If there were answer choices, the incorrect options would typically represent other error types or biases, such as:
- Sampling bias: bias introduced by how participants are chosen, not by measurement tools.
- Random error: variability that is random and averages out with a large sample, not a consistent under- or overestimation.
- Systematic bias due to participant behavior: bias arising from participants' responses rather than from an instrument flaw.
- Instrument reliability issues that cause inconsistent readings: this would be more about precision (consistency) rather than the consistent underestimation caused by a warped ruler.

In short, the warped/stretched ruler skews all measurements in a single direction, which is the hallmark of measurement bias affecting the study’s mean height estimation.

STA304H1 S Module 2 - Quick (15 min) Quiz

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