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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 ...
Scale analysis is an effective shortcut for obtaining approximate solutions to equations often too complicated to solve exactly. The object of scale analysis is to use the basic principles of convective heat transfer to produce order-of-magnitude estimates for the quantities of interest.
It is a special case of Cronbach's α, computed for dichotomous scores. [2] [3] It is often claimed that a high KR-20 coefficient (e.g., > 0.90) indicates a homogeneous test. However, like Cronbach's α, homogeneity (that is, unidimensionality) is actually an assumption, not a conclusion, of reliability coefficients.
The values are ordered in a logical way and must be defined for each variable. Domains can be bigger or smaller. The smallest possible domains have those variables that can only have two values, also called binary (or dichotomous) variables. Bigger domains have non-dichotomous variables and the ones with a higher level of measurement.
The point-biserial correlation is mathematically equivalent to the Pearson (product moment) correlation coefficient; that is, if we have one continuously measured variable X and a dichotomous variable Y, r XY = r pb. This can be shown by assigning two distinct numerical values to the dichotomous variable.
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.
In set theory, a dichotomous relation R is such that either aRb, bRa, but not both. [1] A false dichotomy is an informal fallacy consisting of a supposed dichotomy which fails one or both of the conditions: it is not jointly exhaustive and/or not mutually exclusive. In its most common form, two entities are presented as if they are exhaustive ...
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.