6 Educational Statistics · 6.1 Statistics for teachers
6.1.2 Testing and evaluation: kinds of tests, qualities of a good test, types of evaluation and norms
Measurement gives a number, evaluation adds a value judgement; a good test is valid, reliable, objective and usable and has norms; evaluation is placement (before teaching), formative and diagnostic (during), summative (at the end), while prognostic tests predict future success.
- APPSC Paper I
- Standard level
- 14 min read
- Free
Core facts
- Measurement = describing a trait in numbers (quantitative only). Evaluation = measurement or description plus a value judgement (quantitative + qualitative); it is wider and continuous.
- Test = a tool (set of questions or tasks) that gives a sample of behaviour; examination = a formal, usually end-of-course, test.
- Achievement test: measures what a pupil has learnt (present attainment in a subject).
- Aptitude test: measures capacity to learn a skill with training; it predicts future success, so it is prognostic. An entrance test (for example B.Ed. entrance) is best an aptitude test.
- Prognostic test = a test that forecasts a pupil's future performance.
- Diagnostic test: finds a pupil's specific weaknesses and their causes; it is followed by remedial teaching.
- Qualities of a good test: validity, reliability, objectivity, usability (practicability) and norms; also discriminating power and comprehensiveness. Subjectivity is not a quality of a good test.
- Validity = the test measures what it claims to measure (the most important quality).
- Reliability = consistency: the same pupils get about the same scores when tested again.
- Objectivity = scoring is free from the examiner's personal judgement: different examiners give the same score.
- Usability = easy and economical to give, score and interpret (time, cost, length).
- Norms = the average performance of a representative (standardisation) group, used to interpret a raw score: age, grade, percentile and standard-score norms.
- Percentile rank 70 = the pupil scored higher than 70% of the norm group (not 70% marks).
- Placement evaluation: before teaching, to check entry knowledge and place pupils in the right group.
- Formative evaluation: during teaching, to give feedback and improve learning; terms formative and summative coined by Michael Scriven (1967).
- Diagnostic evaluation: during teaching, for pupils who keep failing despite formative help; finds the cause of the difficulty.
- Summative evaluation: at the end of a unit, course or programme of study; for grading, promotion and certificates (terminal or annual examination).
- Assessment for learning = formative, part of teaching, the prerequisite for planning teaching; assessment of learning = summative, after teaching; assessment as learning = the learner assesses himself (self-monitoring).
- CCE = Continuous and Comprehensive Evaluation; required by the RTE Act, 2009, Section 29(2)(h); recommended by NCF 2005.
- Bloom's taxonomy (1956), cognitive domain, lowest to highest: knowledge, comprehension, application, analysis, synthesis, evaluation. Revised (Anderson and Krathwohl, 2001): remember, understand, apply, analyse, evaluate, create.
Explained
1. Measurement, assessment, evaluation
| Term | What it does | Example |
|---|---|---|
| Measurement | assigns a number | Ravi scored 32 out of 50 |
| Assessment | gathers evidence of learning by many tools | tests, projects, observation, portfolio |
| Evaluation | judges worth against a standard | Ravi's 32 is "good" and he needs help in fractions |
Gronlund's summary: evaluation = measurement (or description) + value judgement. Measurement is a part of evaluation, not the other way round.
2. Kinds of tests
| Basis | Kinds |
|---|---|
| Purpose | achievement, aptitude (prognostic), diagnostic, intelligence, personality, attitude scale, interest inventory |
| Who makes it | standardised (experts; tried out, has norms and a manual) vs teacher-made (informal, for one class) |
| Form of items | essay type vs objective type (MCQ, true-false, matching, completion) vs short answer |
| Reference point | norm-referenced (pupil compared with the group) vs criterion-referenced (pupil compared with a fixed standard of mastery) |
| Administration | individual vs group; verbal vs non-verbal (performance) |
| Time | speed test (many easy items, strict time) vs power test (items of rising difficulty, enough time) |
- Achievement looks at the past (what was learnt), aptitude at the future (what can be learnt), diagnostic at why a pupil fails.
- Attitude scales: Thurstone, Likert; aptitude battery: DAT (Differential Aptitude Tests).
3. Essay type and objective type
| Point | Essay type | Objective type |
|---|---|---|
| Scoring | subjective, varies with the examiner | objective, with a key |
| Coverage | few questions, small part of syllabus | many items, wide coverage |
| Tests best | organisation, expression, original thinking | recall, understanding, application |
| Weakness | low reliability, slow to mark | guessing, costly to prepare |
4. Qualities of a good test in more detail
- Validity is specific to a purpose: a good maths test is not a valid test of reading.
- Reliability is necessary but not sufficient for validity: a valid test is always reliable, but a reliable test need not be valid. A scale that always reads 2 kg too much is reliable, not valid.
- Objectivity raises reliability; a teacher who wants credibility in valuing answer scripts must be objective (same criteria for every script, no favours).
- Standardisation: the same instructions, time and scoring rules for everyone.
- Discriminating power: the test separates good and weak pupils.
5. Ways to estimate reliability (each gives a correlation coefficient; .70 or more is usually acceptable)
| Method | How | Shows |
|---|---|---|
| Test-retest | same test, same group, after a gap | stability over time |
| Parallel (alternate) forms | two equivalent forms of the test | equivalence |
| Split-half | odd and even items correlated; Spearman-Brown formula for the whole test | internal consistency |
| Rational equivalence | Kuder-Richardson (KR-20, KR-21), Cronbach's alpha | internal consistency |
- A longer test, objective scoring, clear instructions and a wide range of ability raise reliability.
- Total variance of scores = true variance + error variance.
6. Kinds of validity
| Kind | Question it answers | Example |
|---|---|---|
| Content | do the items cover the syllabus and objectives? | built in with a blueprint; key for achievement tests |
| Concurrent (criterion) | does it agree with a present criterion? | new test vs teacher's ratings now |
| Predictive (criterion) | does it forecast later success? | entrance test vs later grades |
| Construct | does it measure the trait in the theory? | an anxiety scale behaving as theory says |
- Face validity = the test only looks right to the user; it is not proof of validity.
- A validity coefficient (test vs criterion) is usually lower than a reliability coefficient.
7. Norms and derived scores
| Norm | Score is compared with | Example |
|---|---|---|
| Age norm | average score of each age | mental age 10 |
| Grade norm | average score of each class | reads at class 6 level |
| Percentile norm | percentage of the group below | PR 85 |
| Standard-score norm | distance from the mean in SD units | z, T, stanine, deviation IQ |
- Percentile: P₂₅ = Q₁, P₅₀ = median, P₇₅ = Q₃. Percentile norms are the most widely used and easy to explain, but percentile units are unequal along the scale.
- A raw score has no meaning by itself; norms or a criterion give it meaning.
8. Types of evaluation by time and purpose
| Type | When | Purpose |
|---|---|---|
| Placement | before instruction | entry behaviour, grouping |
| Formative | during instruction, often | feedback, correct and improve |
| Diagnostic | during, when difficulties persist | find causes, plan remedial teaching |
| Summative | end of unit, course or programme | grade, promote, certify |
- Prognostic use (predicting success in a course or job) runs across these: aptitude and entrance tests.
- Assessment for learning "closes the gap" between where the pupil is and where he should be; pupils get feedback and take part. Assessment of learning sums up achievement against standards at a point in time.
9. CCE and exam reform
- Continuous: regular assessment through the year (formative and summative tests), not one annual examination.
- Comprehensive: covers scholastic (subjects) and co-scholastic areas (life skills, attitudes, values, health, arts, sports).
- Aims: reduce exam stress and rote learning, find learning gaps early, give remedial help.
- RTE Act 2009 also bars any board examination for a child until elementary education is complete (Section 30(1)). NEP 2020 asks for a holistic, 360-degree progress card.
10. Bloom's taxonomy of educational objectives
| Domain | Levels (lowest → highest) | By |
|---|---|---|
| Cognitive (knowing) | knowledge, comprehension, application, analysis, synthesis, evaluation | Bloom, 1956 |
| Cognitive, revised | remember, understand, apply, analyse, evaluate, create | Anderson and Krathwohl, 2001 |
| Affective (feeling) | receiving, responding, valuing, organisation, characterisation | Krathwohl, Bloom and Masia, 1964 |
| Psychomotor (doing) | imitation, manipulation, precision, articulation, naturalisation | R.H. Dave, 1970 |
From the options understanding, applying, analysing, evaluating, the highest is evaluating.
11. Planning a test: blueprint. A blueprint (table of specifications) spreads the marks over content units × objectives (knowledge, understanding, application) and item types. It gives the test content validity and balance.
Common traps
- ✗ "Subjectivity is a characteristic of a good test." ✓ A good test is objective; subjectivity is a defect.
- ✗ "A test that predicts the future of students is an achievement test." ✓ It is a prognostic test (aptitude tests are prognostic).
- ✗ "The best B.Ed. entrance test is an achievement test." ✓ An aptitude test, because selection must predict success.
- ✗ "Diagnostic test = prognostic test." ✓ Diagnostic finds present weaknesses and causes; prognostic predicts future success. (APPSC 2019's Telugu printed రోగనిర్ధారణ పరీక్ష, "diagnosis", for prognostic; the English key is prognostic.)
- ✗ "Evaluation at the end of a programme is formative or diagnostic." ✓ It is summative.
- ✗ "Assessment of learning is the prerequisite for teaching." ✓ Assessment for learning (formative) is.
- ✗ "A reliable test is always valid." ✓ A valid test is always reliable; a reliable test may not be valid.
- ✗ "Percentile rank 80 means 80% marks." ✓ It means 80% of the group scored below the pupil.
- ✗ "Measurement and evaluation are the same." ✓ Evaluation = measurement + value judgement.
- ✗ "Synthesis (or create) is below evaluation in every version of Bloom." ✓ Original 1956: evaluation is highest; revised 2001: create is highest.
Quick revision
- Evaluation = measurement + value judgement.
- Good test: validity (most important), reliability, objectivity, usability, norms; not subjectivity.
- Validity = measures what it claims; reliability = consistency; objectivity = same score from any examiner.
- Achievement = what was learnt; aptitude = prognostic, predicts; diagnostic = finds causes → remedial teaching.
- Placement before, formative during, diagnostic when problems persist, summative at the end.
- Assessment for learning = formative (prerequisite for teaching); of learning = summative; as learning = self-assessment.
- Reliability: test-retest, parallel forms, split-half (Spearman-Brown), KR-20; validity: content, concurrent, predictive, construct.
- Norms: age, grade, percentile, standard score; PR = % of the group below.
- CCE: continuous + comprehensive (scholastic and co-scholastic); RTE 2009 Section 29(2)(h).
- Bloom 1956: evaluation highest; revised 2001: create highest.
Go deeper: Deeper (beyond what APPSC Paper I usually asks)
Deeper Advanced
1. Item analysis. Difficulty index p = proportion of pupils answering the item correctly (higher p = easier item); items near p = 0.5 (about 0.6 for four-option MCQs) discriminate best. Discrimination index D = proportion correct in the upper group − proportion correct in the lower group (top and bottom 27% are commonly used); D runs from −1 to +1; about 0.4 and above is good; a negative D marks a faulty item. The point-biserial r of an item with the total score is another index.
2. Spearman-Brown. Whole-test reliability = 2r ÷ (1 + r), where r is the correlation of the two halves: r = 0.6 gives 1.2 ÷ 1.6 = 0.75.
3. Criterion-referenced testing (term from Robert Glaser, 1963) reports mastery against a fixed cut-off; it suits mastery learning and minimum levels of learning. Norm-referenced tests spread pupils out for selection.
4. Grading. Marks are converted to grades on an absolute basis (fixed mark ranges) or a relative basis (position in the group, often on the normal curve). Grades reduce the effect of small, unreliable mark differences.
Practise this topic. Questions on Measures of central tendency, with answers explained.
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