“Laws” of Human Performance ECE 695 Alexander J. Quinn January 24, 2018

Miller’s Law Memory span is limited to 7 ± 2 chunks “Memory span” is the number of items a person can remember for short periods of time and repeat back correctly “Chunks” are the mental units we use to remember things. You saw this previously in the Model Human Processor paper.

Miller’s Law 765 494 3483 ↓ 765 494 3 4 8 3

(depends on the person) Miller’s Law 346 789 2102 ↓ ???? (depends on the person)

Miller’s Law relates to short-term memory (Memorizing digits of PI is long-term memory.) Miller’s Law 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388235378759375195

Short-term memory (not long-term) Chunks may be person-specific Miller’s Law Short-term memory (not long-term) Chunks may be person-specific May vary depending on… kind of chunk age person trial

How long does it take to choose among n choices? Hick’s Law How long does it take to choose among n choices? Credit: https://www.zomato.com/toronto/five-guys-brampton-gta/menu

Hick’s Law dbultiores utiongernh iterephyar hervajoycl ailludietf liginaterr ydompefula andrefusen mpustinicu calorincus aryondiend onteredrax dibloganto coliterity oureashall larithanex ctaindroar rashinesgr lopremites egookerlin riveyeator oryphardic endesomale somporthem rcillouste fertiveruc sycedreadl rflethochn groafterig triyanatep trisopanam ialtsonett untibberna Credit: https://www.zomato.com/toronto/five-guys-brampton-gta/menu

Hick’s Law kadandicon minianetil nobsonoedy opoilimpad rfressisha scantontra Credit: https://www.zomato.com/toronto/five-guys-brampton-gta/menu

Hick’s Law for making choices 𝑅𝑇=𝑎+𝑏 log⁡(𝑛) RT is the the reaction time to make a choice a, b depends on the type of task and is determined experimentally n is the number of choices

Hick’s Law Credit: https://www.zomato.com/toronto/five-guys-brampton-gta/menu

Fitts’ Law A W

W A Fitts’ Law Credit: Paul M Fitts, Journal of Experimental Psychology, Vol 47 No 6, June 1954

W A Fitts’ Law 𝑀𝑇=𝑎+𝑏 log 2 2𝐴 𝑊

𝑀𝑇=𝑎+𝑏∙𝐼𝐷 𝐼𝐷= log 2 2𝐴 𝑊 Fitts’ Law MT is the average time to point to a task a, b depend on the input device and are determined experimentally ID is the index of difficulty for a target 𝐼𝐷= log 2 2𝐴 𝑊

𝐼𝐷= log 2 2𝐴 𝑊 Fitts’ Law ID is the index of difficulty for a target A = amplitude (distance to move) W = width, relative to the axis of motion 2 is to ensure that the ID is always positive

W A Fitts’ Law, derivation In time duration t, you move a fixed proportion (1-r) of the remaining distance After 1t, the distance remaining is rA. After 2t, the distance remaining is r2A. After nt, the distance remaining is rnA. Solve for n. 𝑟 𝑛 𝐴= 𝑊 2 𝑛= log 𝑟 𝑊 2𝐴 𝑛= 1 log 2 𝑟 log 2 𝑊 2𝐴 𝑛= 1 log 2 𝑟 − log 2 2𝐴 𝑊 n is the number of time steps needed to complete the full movement. Credit: http://www.inf.ed.ac.uk/teaching/courses/hci/1011/lecs/fitts.pdf

See resources page on web site More… Power Law of Practice Forgetting curve Sensitivity to delay See resources page on web site