* Quantile lower bounds to reliability based on locally optimal splits.
- Extending the theory of lower bounds to reliability based on splits given by Guttman (in Psychometrika 53, 63-70, 1945), this paper introduces quantile lower bound coefficients λ 4(Q) that refer to cumulative proportions of potential locally optimal "split-half" coefficients that are below a particular point Q in the distribution of split-halves based on different partitions of variables into two sets. Interesting quantile values are Q=0.05,0.50,0.95,1.00 with λ 4(0.05)≤λ 4(0.50)≤λ 4(0.95)≤λ 4(1.0). Only the global optimum λ 4(1.0), Guttman's maximal λ 4, has previously been considered to be interesting, but in small samples it substantially overestimates population reliability ρ. The three coefficients λ 4(0.05), λ 4(0.50), and λ 4(0.95) provide new lower bounds to reliability. The smallest, λ 4(0.05), provides the most protection against capitalizing on chance associations, and thus overestimation, λ 4(0.50) is the median of these coefficients, while λ 4(0.95) tends to overestimate reliability, but also exhibits less bias than previous estimators. Computational theory, algorithm, and publicly available code based in R are provided to compute these coefficients. Simulation studies evaluate the performance of these coefficients and compare them to coefficient alpha and the greatest lower bound under several population reliability structures.
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Overview of verb provide
The verb provide has 7 senses (first 4 from tagged texts)
1. (270) supply, provide, render, furnish -- (give something useful or necessary to; "We provided
the room with an electrical heater")
2. (25) provide, supply, ply, cater -- (give what is desired or needed, especially support, food or
sustenance; "The hostess provided lunch for all the guests")
3. (14) provide -- (determine (what is to happen in certain contingencies), especially by including
a proviso condition or stipulation; "The will provides that each child should receive half of the
money"; "The Constitution provides for the right to free speech")
4. (2) put up, provide, offer -- (mount or put up; "put up a good fight"; "offer resistance")
5. leave, allow for, allow, provide -- (make a possibility or provide opportunity for; permit to be
attainable or cause to remain; "This leaves no room for improvement"; "The evidence allows only one
conclusion"; "allow for mistakes"; "leave lots of time for the trip"; "This procedure provides for
lots of leeway")
6. provide, bring home the bacon -- (supply means of subsistence; earn a living; "He provides for
his large family by working three jobs"; "Women nowadays not only take care of the household but
also bring home the bacon")
7. provide -- (take measures in preparation for; "provide for the proper care of the passengers on
the cruise ship")
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