IQ 128, a Failed Maths Test, and a Streaming Proposal
A group test of mental ability, printed in English, is given to 300 Class 8 students in a rural Karnataka block; most children speak Kannada at home and the school has no science laboratory. Kiran scores IQ 128 but fails the Maths unit test and cannot solve a two-step word problem. His father wants him moved to a 'science special batch' in the city; his teacher says the score 'must be wrong'. A second child, Shalini, scores 94 and is the best problem-solver in the class. The block education officer proposes using the same test next year to stream all Class 9 students into science, commerce and arts sections.
1. Is the teacher right that the score 'must be wrong'? Explain what an IQ of 128 does and does not tell you about Kiran.
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The teacher is half right.
What 128 means. The score is norm-referenced: Kiran performed about two standard deviations above the mean of the norm group, roughly the top 2–3% on this test's reasoning items.
What it does not mean.
- It is not a measure of all ability and says nothing directly about classroom Maths performance; an IQ test samples analogies, vocabulary, patterns and reasoning, not syllabus content.
- A single score has a standard error of measurement; the true score lies in a band of a few points, so one administration is not a stable estimate.
- The test was in English for a Kannada-home-language child in a school without a lab, so the score may partly reflect language and test-wiseness.
- The two facts are not contradictory: a specific gap (a missing prerequisite, a language-loaded word problem) can coexist with high general reasoning.
Conclusion: the score is not 'wrong', but it cannot carry the decision alone. Examine the error pattern, ask him to solve the same problem in Kannada, and check prerequisites before concluding anything about his ability.
2. Identify two features of this testing situation that threaten validity for this group, and state what would reduce each.
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- Cultural and language bias (construct validity). The test is in English while most children's home language is Kannada; verbal items then measure English proficiency rather than mental ability. The group's scores are systematically depressed and individual rankings distorted. Reduction: translate and back-translate, pilot with local children, use non-verbal/figural items, and give instructions in Kannada.
- Norm and standardisation problems (interpretive validity). The norms presumably come from a different population (urban, English-medium, lab-equipped), so comparing this block's scores against them is meaningless; unfamiliar format and an untrained administrator further depress scores. Reduction: build local norms or report within-block percentiles, standardise instructions and practice items, and train the administrator.
A third point worth credit: a group test is less reliable than individual administration, so scores near any cut-off must be verified individually before being acted upon. Validity is not a property of the test in the abstract - it is a property of the test used with a particular group for a particular purpose.
3. Evaluate the officer's streaming proposal using concepts of intelligence and of test use.
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Streaming on this test would be indefensible.
Test use. A test should be used only for the purpose for which it was validated. Allocating children to three streams for years on the basis of one biased, error-prone group score is a clear misuse; the decision is high-stakes and effectively irreversible.
The concept of intelligence. Intelligence is not one thing perfectly captured by one number. Even on a general-factor view, scores carry measurement error and profile variation; Gardner's and Sternberg's approaches point to spatial, practical and interpersonal abilities that this paper test does not sample. Shalini - 94, best problem-solver in the class - is the proof inside this very data set that the ranking and the ability do not coincide.
Consequences. Streaming on a biased test creates a self-fulfilling prophecy: labelled children receive lower expectations, weaker peers and less teacher attention, so the prediction comes true (Pygmalion effect). Kiran would be streamed upward and Shalini downward largely on language.
Better: use the test as one screening input alongside classroom work and teacher judgement, assess individually in Kannada, provide a bridge course, and re-assess after a year.