Whit percentiles are IQ scores o 115, 130 and 145?

The calculation uises z = (score − 100) / 15 and the cumulative standard normal distribution, rounded tae twa decimal places. Mean 100 and SD 15 are common scale conventions. Actual test manuals decide the suitable norms, score ranges and interpretation; a mathematical normal curve disna validate a new test. Neisser et al., 1996 Pearson, 2020

A percentile isnae a percentage richt

A percentile is aboot whaur ye staun in a reference distribution. It disna say that a body answered that percentage o items richt or has that percentage o aa intelligence. Guidance on test uise requires a justified reference group and evidence for the intended score interpretation. Without thae, a percentile can luik mair precise than its basis gies grounds for. International Test Commission, 2001

Whit changes wi age?

IQ is age-normed: on the conventional scale, the reference mean is 100 in ilka age group. A bairn and an adult can get the same age-adjusted score while answerin different items or gettin different raw totals. Sae the normal-model arithmetic disna describe an unadjusted performance curve across a lifetime. Neisser et al., 1996 Pearson, 2020

Norms depend an the test, population and period an aa. Raven's review records variation in matrix-test norms across settings and time. A score frae ae instrument shouldnae be treatit as though ilka test and historical norm table haed identical measurement properties. Raven, 2000

Why the extreme tail needs extra care

Small norm samples haud little direct information aboot very rare scores. Sae an appealin tail percentile can depend on model assumptions as weel as observations. Guidance on test uise asks for evidence that suits the inference, and a score report's uncertainty tells ye mair than treatin the last decimal place as exact. International Test Commission, 2001 Pearson, 2020

Does a matrix puzzle score define overall IQ?

Carpenter and colleagues analyse the reasoning processes in Raven matrices. That gies a theoretical account o an important faimily o tasks, no a licence tae turn onie hame-made puzzle total intae a normed overall IQ. Wark on the structure o cognitive performance warns an aa against assummin that ilka task measures ae identical aspect o ability. Carpenter et al., 1990 Hampshire et al., 2012

Whit aboot retests and measurement error?

A meta-analysis finds systematic retest gains in tests o cognitive ability. Sae a repeated test result may reflect familiarity as weel as ither differences. Reliability research adds that task scores and differences need measured stability afore they can be treatit as individual traits. Neither issue is fixed by showin mair percentile digits. Scharfen et al., 2018 Hedge et al., 2017

For an established assessment, uise its ain report, age norms and confidence interval. For an exploratory online task, keep the result at the level its validation supports. Thir mathematical examples explain a common scale; they dinnae justify tellin a player they're smarter than a particular percentage o fowk. International Test Commission, 2001 Pearson, 2020

The useful distinction is atween understandin hou a percentile is calculated and haein evidence that a particular score belangs on that curve. Baith are needed afore makin a personal comparison. Neisser et al., 1996 International Test Commission, 2001