Speed-Accuracy Trade off

Speed-Accuracy Trade off

• Occurs in situations where the goal is to move a limb as fast as possible to reach a target or intercept an object with minimal error

  • Typing, hitting a ball, moving your foot

• Important in many tasks from sports to controlling machinery

• 3 different models with sepcific speed-accuracy trade-off relations

  • Logarithmic (fitt's paradigm)

  • Linear

  • Temporal

Fitt’s Experiment

• Person moves a stylus back and forth between 2 targets as fast and accurately as possible

• Movement time is measure

  • Manipulates the target width and amplitude

    • Amplitude is distance between targets

  • Changing the variables changes the index of difficulty

  • ID is related to the movement distance of the limb and to the target width which is aimed form

• ID = log_2(2A/W)

Logarithmic Speed-Accuracy Trade off

• Function between speed and accuracy when graphed in a log function produces a straight lime

• Movement time = a+b(log_2(2A/W))

  • A and b = constants

  • MT=a+b(ID)

Inverse relationship between "difficulty" of movement and speed

• Movement time must be traded-off to maintain accuracy under values of ID

• a = intercept. When accuracy is not required when ID = 0. ID is = when target width overlaps

• B is the add MT caused by increase the ID

  • The body part/effector that is moving can effect b, only the arm, wrist or fingers can be used in this experiment and each have their own sensitivity to changes in ID and have different slopes

  • The slope is steeped for larger effectors. Larger and awkward limbs are more sensitive to changes in ID. Fingers are more precise so it has a lower slope

  • Older groups have higher slows. Lower and upper limb movements have different slopes

Linear Speed-Accuracy Trade-Off

• During rapid single aiming movements

• Person reaches with stylus from starting position to target 10-60cm away

• MT is constrained by the experimenter, width is maintained

• Accuracy measured as variability in end-point

• Error is measured as standard deviation of movement amplitude, called variation in movement end points

• We=a+b(A/Mt​)

  • a/b are constants, A is movement amplitude and MT is movement time

• Movement Amplitude on Movement variability

  • We increase for a given amplitude as MT decrease

• Movement velocity vs  Movement variability (Velocity is A/MT)

  • Velocity of movement increases for a given amplitude, We also increase

 

Comparison with Ftt's paradigm

• Fitt's uses a continuous task, Linear is discrete

• MT is constrained for Linear but it is a dependent variable in Fit's

  • We is the dependent variable for this

• In Fitt's paradigm, there are no error (within 5% margin), Accuracy is enforced or you do trial again

Feedback Hypothesis

• Logarithmic trade-off occurs for movement controlled by feedback-based corrections

• Linear trade-offs occur for tasks that are entirely preprogrammed (no feedback used) like rapid reaching task

Movement time Goal Hypothesis

• Single-aiming paradigms used controlled MTs, encourage participants to adopt a non-corrective rapid control strategy

• In Fitts task, the movement goal is to be as fast as possible but corrections are allowed

• Both argue in the end that to increase accuracy must move slower

Temporal Speed-Accuracy Trade off

• Tasks that require anticipation and timing

  • Anticipate the flight of the ball, internal movement processes and limb movement to swing in baseball

  • Paradigm, must move a slider to intercept a target moving along a track

    • Accuracy is measured in terms of errors of time (early/late arrival)

  • The more forceful the movement (smaller MT/larger velocity) the more accurate the timing

  • Opposite of spatial accuracy trade-offs

• Whe performing a discrete movement-timing task, goal is to produce a specific MT, dependent variable is variable error in timing (Vet) or SD of MTs

  • The smaller MTs within the same distance produced improved MT consistency. Movement duration is more consistent (VE) is lower with decreasing MT. MT consistency is increase as velocity is increase

  • Holds for discrete and repetitive timing tasks

  • Easier to estimate 2 seconds than 20 seconds. Easier to estimate shorter time intervals

In temporal accuracy tasks (like hitting a baseball at the right moment). The opposite happens:

• Faster (shorter movement time, bigger velocity) movements → more consistent timing.

• Why? Because:

  1. Reduced timing uncertainty: Shorter intervals are easier for the brain to measure precisely (like estimating 2 seconds is easier than 20).

  2. Less room for drift/error: Longer movements give more opportunity for variability in planning or execution to accumulate.

  3. Stronger motor commands: Faster, forceful movements rely on more “all-or-none” neural firing, which is less variable than weak, drawn-out commands.

In spatial accuracy tasks (like pointing to a target)

Moving faster makes you less accurate because there’s less time for corrections → so accuracy goes down with speed.