23-Ind-B5 Ergonomics · December 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — Dec. 2015 — 98-Ind-B5 Ergonomics. Three-hour, open-book exam (all notes, books and any non-communicating calculator permitted); the paper requires 4 of its 5 questions (Part A mandatory, any two of Part B's Questions 2–4, and Part C mandatory) — all five are solved below for completeness.
Reference texts: Sanders & McCormick, Human Factors in Engineering and Design (7th ed.) — controls/displays, anthropometry, workplace and computer-workstation design; Waters, Putz-Anderson & Garg, NIOSH Applications Manual for the Revised NIOSH Lifting Equation (1994) — the RWL/LI formula and multiplier tables reproduced on the exam's own pages 6–7.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Fitts' Law states that the time to move to and acquire an on-screen target increases with the distance to the target and decreases with the target's size: $MT=a+b\log_2\!\left(\dfrac{2A}{W}\right)$, where $MT$ is movement time, $A$ is the distance (amplitude) from the starting point to the target, $W$ is the target's width along the movement axis, and $a,b$ are empirical constants. The term $\log_2(2A/W)$ is the index of difficulty: a target that is far away and narrow is slow to hit; a target that is close and wide is fast.
Hick's Law (the Hick–Hyman Law) states that the time to decide among a set of alternatives increases with the number of equally likely choices: $RT=a+b\log_2(n+1)$, where $RT$ is reaction/decision time and $n$ is the number of alternatives. Unlike Fitts's Law, Hick's Law is not about the hand's physical travel – it is about how long the mind takes to discriminate between options before the hand ever starts moving, and that time can be reduced by organizing choices into meaningful groups rather than presenting them as one large undifferentiated set.
Fitts' Law favours Menu A (the radial/pie menu). Every item sits at nearly the same distance $A$ from the centre where the cursor starts, so the movement distance is short and uniform regardless of which item is chosen — unlike a linear list, where the last item is much farther from the cursor's landing point than the first. A radial layout can also give each item a wide angular wedge as its effective target width $W$, whereas a stacked list is constrained to narrow, fixed-height rows. Both effects (smaller $A$, larger $W$) reduce the index of difficulty $\log_2(2A/W)$, so average movement time to any item is lower on the pie menu — the empirical finding (Callahan et al., 1988) that pie menus outperform linear menus in selection speed is a direct consequence of this Fitts's-Law geometry.
Hick's Law favours Menu B (the linear/list menu), because of how it is organized, not because it has fewer items. The list menu actually shows more items (ten, one greyed out/disabled) than the radial menu's eight, but it groups them into four visually separated clusters using whitespace — navigation commands, page actions, view commands, and developer tools. This lets the user first recognize the relevant cluster, then discriminate among only the two or three items within it, rather than evaluating all ten items as one flat, equally-weighted set. Chunking a large choice set into smaller, meaningfully labelled groups is exactly what Hick's Law recommends to keep decision time down, since the effective number of alternatives compared at any one moment is the size of a cluster, not the size of the whole menu. The radial menu, by contrast, presents all eight functions in one homogeneous ring with no grouping cue, so the user must discriminate the full set at once — the faster motor access Fitts's Law predicts for it does not translate into a faster decision under Hick's Law.
The two laws therefore point in different directions here: Fitts's Law rewards a layout that minimizes travel distance and maximizes target size (the pie menu), while Hick's Law rewards a layout that minimizes the number of alternatives evaluated at each decision step through grouping (the categorized list) — a well-designed interface for a menu of this size would combine both, e.g., a categorized radial menu with items grouped into sub-rings or a first-level ring of categories.
