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Sensitivity of the Range to Outliers
Although the range is easy to compute, it can provide a misleading impression of a distribution's variability when outliers are present. Because the range relies solely on the absolute highest and lowest values, a single extreme score will drastically inflate the range, giving the false appearance that the entire dataset is widely spread out.
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Research Methods in Psychology - 4th American Edition @ KPU
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Sensitivity of the Range to Outliers
Example of Calculating the Range
Which measure of variability is calculated as the difference between the highest and lowest scores in a distribution?
A researcher is studying the variability in the number of social interactions participants have in a single day. Match each participant's set of scores with its calculated range.
A researcher finds that a sample of social anxiety scores ranges from to . After discovering a technical glitch that added points to every participant's score, the researcher subtracts points from each score to correct the data. The range of the corrected anxiety scores will be smaller than the range of the original, uncorrected scores.
An undergraduate researcher is evaluating how effectively the range describes the variability of different datasets. Rank the following research scenarios from the one where the range is the most misleading (least representative of the typical spread) to the one where the range is the most accurate (most representative of the spread).
Match each term related to the range with its correct definition in the context of psychological data analysis.
A clinical psychologist compares the number of panic attacks experienced by patients in two different treatment groups over a month. If Group A has a range of and Group B has a range of , how should the researcher interpret the difference between these two groups?
A psychologist records the reaction times of five participants: 250ms, 280ms, 310ms, 350ms, and 420ms. The value 170ms represents the _____ of this dataset.
A developmental psychologist records the ages (in years) of a sample of toddlers: , , , , and . Applying the calculation for the range as the difference between the highest and lowest scores in the distribution, the researcher determines the range of toddler ages to be years.
A cognitive psychologist studies participant reaction times and obtains the following scores: ms, ms, ms, and ms. After adding a new participant with a reaction time of ms to this distribution, the range increases by _____ ms.
A researcher is evaluating the stability of the range as a measure of variability across different participant groups. Rank the following reaction-time distributions (in milliseconds) from the one where the range is the most stable and representative measure of variability to the one where it is the least stable and representative (most heavily distorted by a single outlier).
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Example of the Range's Sensitivity to Outliers
What is the primary reason the range can provide a misleading impression of a distribution's variability when outliers are present?
A researcher collects reaction-time scores (in milliseconds) from 10 participants: 220, 230, 225, 240, 235, 228, 232, 226, 238, and 812. The last participant's unusually high score was caused by a distraction during testing. If the researcher computes the range for this dataset, the resulting value will accurately reflect how spread out the typical participants' scores are.
A researcher is examining three small datasets representing student stress levels (measured on a scale of 1 to 100). Match each dataset with the description that best captures the resulting range and its sensitivity to any outliers present.
Rank the following research scenarios from the least misleading use of the range to the most misleading use, based on the sensitivity of the range to outliers.
Suppose you are constructing a demonstration for a psychology lab to show how the range can provide a misleading impression of spread. Your goal is to design a dataset of five participants where the 'typical' spread (the range of the first four participants) is exactly , but the inclusion of a fifth participant (an outlier) inflates the total range to exactly . Which of the following datasets successfully meets these design criteria?
Match each conceptual aspect of the range () to the explanation of why it can provide a misleading impression of a distribution's variability when outliers are present.
Although the range is easy to compute, it is often a misleading measure of spread because it is highly sensitive to _____, which can disproportionately inflate the result.
In a cognitive psychology experiment, a researcher records reaction times (in milliseconds) for two conditions. Condition A scores are {200, 205, 210, 215, 220} and Condition B scores are {200, 205, 210, 215, 400}, where the last value is an outlier caused by a distracted participant. The range for Condition B is _____ times larger than the range for Condition A.
A developmental psychologist measures the number of words spoken by two-year-olds in a 10-minute play session. Group A: {12, 15, 14, 16, 13} (Range = words). Group B: {12, 15, 14, 16, 84} (Range = words). True or False: Concluding that the enriched environment generally causes children's word counts to be widely spread out across a 72-word span is an analytical error because a single extreme outlier in Group B has inflated the range, giving a misleading impression of the distribution's typical variability.
A research methods class is evaluating how well the range reflects the overall variability of different datasets. Rank the following datasets from the one where the range provides the least misleading (most representative) reflection of the distribution's general variability to the one where it provides the most misleading (least representative) reflection.