Measurement, Evaluation and Educational Statistics
The unit tests scale types, criteria of test quality, evaluation distinctions, and descriptive statistics with one or two computation items.
Measurement and scales
Measurement assigns numerals to attributes according to rules. Stevens' scales: nominal (labels only), ordinal (ranks, unequal intervals), interval (equal units, arbitrary zero), ratio (true zero, such as reaction time).
Evaluation
Evaluation judges the extent to which objectives are attained. Formative evaluation occurs during teaching and gives feedback; summative evaluation comes at the end and grades. Norm-referenced tests compare a student with a group; criterion-referenced tests compare with a standard. CCE combines formative and summative assessment.
Test quality
Validity (measures what it claims), reliability (consistency), objectivity, usability and norms. Reliability is necessary but not sufficient for validity.
Statistics to compute
Mean = ΣX/N (sensitive to extreme scores); median = positional middle; mode = most frequent. Range = H − L. Quartile deviation = (Q3 − Q1)/2. Standard deviation = √(Σd²/N). Percentile rank locates a score in the distribution. Correlation ranges from −1 to +1. Normal curve: mean = median = mode at the centre; 68.26% of cases lie within ±1 SD, 95.44% within ±2 SD, 99.73% within ±3 SD.
Worked example
Scores 10, 20, 30, 40, 50: mean = 150/5 = 30, median = 30, range = 40. Now change 50 to 90: mean = 190/5 = 38, but the median remains 30. Reasoning: the mean uses every score and shifts with an outlier, while the median is positional and robust, so the median is preferred for skewed data.
Traps that cost marks
Claiming reliability guarantees validity; reading correlation as causation; confusing SD with range; using the mean for highly skewed distributions.