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Example 1: Dichotomous variables A Guttman scale may be hypothesized for the following five questions that concern the attribute "acceptance of social contact with immigrants" (based on the Bogardus social distance scale), presented to a suitable population:
Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. [1] Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio.
It is possible, for example, to have a high KR-20 with a multidimensional scale, especially with a large number of items. Values can range from 0.00 to 1.00 (sometimes expressed as 0 to 100), with high values indicating that the examination is likely to correlate with alternate forms (a desirable characteristic).
Scaling of data: One of the properties of the tests is the scale of the data, which can be interval-based, ordinal or nominal. [3] Nominal scale is also known as categorical. [6] Interval scale is also known as numerical. [6] When categorical data has only two possibilities, it is called binary or dichotomous. [1]
A categorical variable that can take on exactly two values is termed a binary variable or a dichotomous variable; an important special case is the Bernoulli variable. Categorical variables with more than two possible values are called polytomous variables ; categorical variables are often assumed to be polytomous unless otherwise specified.
A specific case of biserial correlation occurs where X is the sum of a number of dichotomous variables of which Y is one. An example of this is where X is a person's total score on a test composed of n dichotomously scored items. A statistic of interest (which is a discrimination index) is the correlation between responses to a given item and ...
Figure 2: Graph showing histograms of person distribution (top) and item distribution (bottom) on a scale. For dichotomous data such as right/wrong answers, by definition, the location of an item on a scale corresponds with the person location at which there is a 0.5 probability of a correct response to the question.
The item-total correlation approach is a way of identifying a group of questions whose responses can be combined into a single measure or scale. This is a simple approach that works by ensuring that, when considered across a whole population, responses to the questions in the group tend to vary together and, in particular, that responses to no individual question are poorly related to an ...