Errors of Measurement: Ceiling and Floor Effects

Definitions

One example of ceiling and floor effects is the measurement of an attitude toward the use of the death penalty for convicted serial killers using a 1–5 scale surveying 100 persons where 90 persons in the sample select a value of 5 and another 10 persons select a value of 4. The impact of the indications creates a distribution that would not be considered normally distributed and generates an average value so close to the limits of the scale (maximum value 5 and the mean is 4.90). As a result, the estimation of variance and standard deviation produces a value so low that relative to the scale (1 to 5 is a four points of potential range) the values become very small. The floor effect is simply the reverse, where the choice would be 90 persons selecting 1 and 10 persons selecting a value of 2. Mathematically, the impact remains the same; the reference to floor or ceiling simply indicates whether the restriction is at the top or the bottom of the scale.

Ceiling and floor effects are important when the desired informational use for the data involves comparison of groups or use in statistical analysis. If the evaluation involves measuring the achievement of a threshold, such as a communication apprehension evaluation, then the fact that 90% of students score perfect on an exam does not constitute a problem. However, if one seeks to assess the relative level of mathematical knowledge possessed by a group of persons, failure to achieve some minimal distribution indicates an inability to provide relative assessment of knowledge and essentially all persons appear equal in knowledge.

Causes

The cause for such distributions can be related to several factors: (a) scale construction limitations, (b) sample selection issues, or (c) content issues in the variable of interest. Identifying the source of the effect provides some clues about a means of recommending a solution or way to address the particulars of the error of measurement.

When designing scales, a distribution of responses needs to be provided. If a scale is constructed so that it generates a set of responses that are shared or in common, the goal of providing measurement (the separation of persons on the basis of scores) does not become achieved. For example, if one wants to evaluate the ability to tell a joke, measured by whether other persons laugh out loud and in intervals of 15 seconds, may produce results with no person laughing after the first 15 second interval. Using this scale would have every person scored at the same value. As such, the goal, differentiating persons on the basis of ability, represents failure. Another technique might be to shorten the measurement to measure in seconds the longest laugh, which may provide differentiation among abilities.

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