Space Relations – Paper Puzzles

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Appropriate For New Applicants
Existing Employees
Comprehensiveness Basic
Administration Time - 30 min
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Scoring Options hand icon
Language English
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Space Relations (Paper Puzzles) was developed by Thustone for use in a factorial and validation study of mechanical aptitude (Thurstone, 1951). It was one of several tests used in this study which differentiated individuals with high mechanical interest and experience from those with low mechanical interest and experience. While other uses may be found for the test based on the information listed under Basic Technical Data, its primary validation at the present is for assessing mechanical aptitude.


The test consists of one page of instructions, practice exercises, and three pages of test items. There are 30 items in the test proper. The subject's task is to determine which one of several flat pieces will be left over if all the other pieces are assembled so as to correspond with a given two¬dimensional form. Paper Puzzles is a paper-and-pencil test which can be administered individually or to groups. It gives a single score: the number right minus one-third of the number wrong.

Background Research

Paper Puzzles was designed for use in a factorial study of mechanical aptitude conducted by L.L. Thurstone and others (Thurstone, 1951). It was specifically designed as a test of the space factor found in earlier studies (Thurstone, 1944; Thurstone & Thurstone, 1941).


The reliability of a test is the extent to which the scores are stable, that is, the extent to which the same score will result if the test is administered to the same subject at two different times. There are at least three general methods of estimating the reliability: the split-half method, the test-retest method, and the use of parallel forms of the test. A test as simple and homogeneous as Paper Puzzles lends itself well to the split-half method. In Thurstone's study of mechanical aptitude the corrected split-half reliability of the test was .68.


Paper Puzzles was included in the battery of 32 group tests which Thurstone administered to 350 high school juniors in his study of mechanical aptitude (Thurstone, 1951). The study indicated which of these several tests differentiated a criterion group of high mechanical interest and experience from a criterion group of low mechanical interest and experience. These criterion groups were selected from the total group on the basis of criterion measures used in the Navy and elsewhere. Paper Puzzles was one of the tests on which subjects with high mechanical interest and experience did better than did subjects of low mechanical interest and experience. Its specific validity for this study was a p-value of less than .001 which means that this differentiation could have occurred by chance less than 1 in 1,000 times.

A factorial analysis of the results of the 32 group tests for the 350 subjects was also undertaken by Thurstone. Five clearly defined factors were found. Paper Puzzles had loadings (correlations) on two of these factors. These were the second space factor and the second closure factor (closure flexibility). Because Paper Puzzles has about equal loadings (correlations) on two factors, it is not factorially pure; that is, it measures both factors rather than just one. The second space factor is defined as the ability to visualize a flexible configuration, that is, to visualize a diagram, drawing, or figure of some kind in which there is internal movement or displacement of the parts. It is this factor which appears to be the essential characteristic of mechanical aptitude. In this research, all of the criterion measures of mechanical aptitude showed up strongly on this factor. The closure flexibility factor is defined as the ability to keep in mind a configuration against distraction, that is, to see a given configuration which is "hidden" or embedded in a larger drawing, diagram, or figure. It is the ability to retain a complex figure or idea despite distraction. It is worthwhile noting that factorially pure tests of the closure flexibility factor also differentiated between the high and low criterion groups on mechanical aptitude. It is recommended that Space Relations (Paper Puzzles) be included in mechanical aptitude test batteries for these reasons.

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