Introduction to Dependent and Independent Variables in Motor Control Research

Foundations of Motor Behavior Research: Variables and Measurement

• Fundamental Role of Variables in Research:
  • Precise variable definition is required to analyze human movement, just as specific core concepts are required across scientific disciplines:
  • Physics cannot be discussed without the concept of force.
  • Mathematics cannot function without basic operations such as addition, subtraction, multiplication, and division.
  • Cardiovascular physiology cannot be studied without referencing the heart.
  • Empirical research cannot be conducted or interpreted without defining Dependent Variables (DVs) and Independent Variables (IVs).

Experimental Research Design and Statistical Capture

• Experimental Paradigm Example:

  • Objective: Evaluate the impact of feedback on pointing movement accuracy as a function of age.
  • Motor Task: Pointing with eyes closed at a $5\,\text{cm}$ target embedded within a larger target.
  • Sample Groups:
  • Group 1: KINE 2035 university students.
  • Group 2: Grade 9 students.
  • Feedback Protocol: Verbally provided after each trial for $5$ consecutive attempts (e.g., "too high but off by just a little", or "too low by a lot").
  • Error Calculation: Mean Constant Error (Mean CE) computed across the $5$ trials.

• Mathematical Formula for Mean Constant Error:   $\text{Mean CE} = \frac{\sum (X_i - T)}{n}$

  • Where $X_i$ represents individual trial performance scores, $T$ represents the target location, and $n$ represents the total number of trials.

• Statistical Dataset Representation:

  • Participant 1: Group $1.00$, MCES $16.00$
  • Participant 2: Group $1.00$, MCES $14.00$
  • Participant 3: Group $1.00$, MCES $15.00$
  • Participant 4: Group $1.00$, MCES $13.00$
  • Participant 5: Group $1.00$, MCES $14.00$
  • Participant 6: Group $2.00$, MCES $7.00$
  • Participant 7: Group $2.00$, MCES $8.00$
  • Participant 8: Group $2.00$, MCES $5.00$
  • Participant 9: Group $2.00$, MCES $4.00$
  • Participant 10: Group $2.00$, MCES $5.00$

• Descriptive Statistics Summary:

  • Group $1.00$ ($N = 5$): Mean = $14.4000\,\text{cm}$, Standard Deviation = $1.14018$, Standard Error Mean = $.50990$
  • Group $2.00$ ($N = 5$): Mean = $5.8000\,\text{cm}$, Standard Deviation = $1.64317$, Standard Error Mean = $.73485$

• Inferential Statistics Output (Independent Samples T-Test):

  • Levene's Test for Equality of Variances: $F = 1.600$, $\text{Sig.} = .242$
  • Equal Variances Assumed: $t = 9.615$, $\text{df} = 8$, One-Sided $p < .001$, Two-Sided $p < .001$, Mean Difference = $8.60000$, Standard Error Difference = $.89443$
  • $95\%$ Confidence Interval of Difference: Lower Limit = $6.53745$, Upper Limit = $10.66255$
  • Equal Variances Not Assumed: $t = 9.615$, $\text{df} = 7.127$, One-Sided $p < .001$, Two-Sided $p < .001$, Mean Difference = $8.60000$, Standard Error Difference = $.89443$
  • $95\%$ Confidence Interval of Difference: Lower Limit = $6.49263$, Upper Limit = $10.70737$

• Interpretation of Main Effects:
  • Group 2 (older participants) exhibits significantly lower Mean Constant Error ($5.8\,\text{cm}$) compared to Group 1 (younger participants, $14.4\,\text{cm}$), demonstrating superior movement accuracy.

Complex Experimental Designs and Interaction Effects

• Multi-Factorial Research Setup:

  • Dependent Variable ($1$ DV): Mean Constant Error ($\text{cm}$).
  • Independent Variables ($2$ IVs):
  1. Group (Level 1: Group 1 / Younger; Level 2: Group 2 / Older)
  2. Type of Feedback (Level 1: General Feedback; Level 2: Specific Feedback)

• Interaction Patterns Across Conditions:

  • Younger Group (Group 1): Displays consistent, high inaccuracy ($\text{Mean CE} \approx 14\text{--}16\,\text{cm}$) regardless of whether feedback is general or specific.
  • Older Group (Group 2):
  • Under General Feedback conditions, performance exhibits high error levels comparable to the younger group.
  • Under Specific Feedback conditions, performance accuracy drastically improves, resulting in a pronounced reduction in Mean CE.

Dependent Variables (DV) and Performance Measures

• Definition and Functionality:

  • A Dependent Variable is any metric measured, observed, or quantified to evaluate emerging motor behavior.
  • Dependent variables operationalize theoretical constructs into measurable quantitative units:
  • Power (Construct) $\rightarrow$ Vertical jump height (DV)
  • Agility (Construct) $\rightarrow$ Time to complete a T agility test or Movement Time (DV)
  • Accuracy (Construct) $\rightarrow$ Absolute Error (DV)
  • Range of Motion (Construct) $\rightarrow$ Angular displacement of a joint (DV)
  • Decision Making (Construct) $\rightarrow$ Choice Reaction Time (DV)

• Conceptual Properties of DVs:

  • Termed "dependent" because their values depend upon and change in response to differences across individuals, movement tasks, or environmental settings.
  • Precise operational definitions are mandatory to ensure standardization, repeatability, and accurate interpretation.

• Detailed Operational Definitions of Key DVs:

  • Movement Time ($\text{s}$): The elapsed duration between movement initiation and movement completion.
  • Angular Displacement ($^\circ$): The numerical difference between the final position and the initial position of a joint.
  • Reaction Time ($\text{ms}$): The interval between stimulus onset and the initiation of a movement.
  • Absolute Error ($\text{ms}$): The cumulative duration spent outside a specified target zone.
  • Mean Path Length Velocity ($\text{cm/s}$): The average velocity of the Center of Pressure (COP) recorded throughout a trial.

• Categorization of Motor Skill Performance Measures:

• Performance Outcome Measures:

  • Time to complete a task ($\text{s}$, $\text{min}$, $\text{hr}$): e.g., Time taken to run a mile or type a word.
  • Reaction Time (RT) ($\text{s}$, $\text{ms}$): e.g., Duration between starter's signal and motion commencement.
  • Error magnitudes ($\text{AE}$, $\text{CE}$, $\text{VE}$): e.g., Distance ($\text{cm}$) off-target in limb positioning.
  • Percentage or frequency of errors: e.g., Count of missed free throws.
  • Successful trial frequencies: e.g., Number of target hits in beanbag throwing.
  • Target maintenance time: e.g., Seconds cursor remains on target in tracking tasks.
  • Balance duration: e.g., Seconds standing in stork stance.
  • Linear or vertical displacement: e.g., Height reached in a vertical jump.
  • Repetitions to mastery: e.g., Number of practice attempts needed to achieve error-free performance.

• Performance Production Measures:

  • Kinematic Displacement: Distance traveled by a limb during goal-directed cursor movements.
  • Kinematic Velocity: Movement speed of a limb moving toward a specified target.
  • Kinematic Acceleration: Acceleration and deceleration profile trajectories during movement.
  • Joint Angle: Angular configuration of joints at specific events (e.g., impact phase during ball striking).
  • Joint Torque: Net rotational force exerted around a joint (e.g., knee joint torque during vertical jump takeoff).
  • Electromyography (EMG): Precise timing of muscular activation (e.g., onset of biceps firing during rapid arm flexion).
  • Electroencephalography (EEG): Neural activity patterns recorded during skill execution (e.g., archery aiming phase).
  • Positron Emission Tomography (PET): Cerebral metabolic activation during motor tasks (e.g., keyboard typing).
  • Functional Magnetic Resonance Imaging (fMRI): Regional brain activation patterns during repetitive movements (e.g., finger tapping to a metronome).

Independent Variables (IV), Manipulation, and Experimental Levels

• Definition and Scientific Control:

  • An Independent Variable is any factor systematically manipulated, selected, or controlled by a researcher to determine its causal effect on motor behavior.
  • Manipulation refers to controlling and stratifying conditions or participant groups (e.g., controlling group selection by comparing $12\text{-year-olds}$ versus $18\text{-year-olds}$).

• Levels of Independent Variables:

  • Levels represent specific discrete sub-categories or conditions within a single IV.
  • Identification procedure: First enumerate the total number of distinct IVs, then list all discrete levels contained within each IV.

Empirical Examples of Independent Variables in Motor Control

• Single IV Design (Age):
  • $1$ Independent Variable: Age ($3$ Levels: $8\,\text{years}$, $12\,\text{years}$, $24\,\text{years}$).
  • Key Finding (Henry & Rogers, 1960): Reaction time (RT) and movement variability both decrease systematically as age increases.

• Single IV Design (Clinical Diagnosis Group):
  • $1$ Independent Variable: Group ($2$ Levels: Boys with Developmental Coordination Disorder [DCD] vs Typically Developing Control Boys).
  • Experimental Task: Catching a ball moving at a stable speed of $2.0\,\text{m/s}$.

• Data Summary across Clinical and Control Groups:

  • Moment of grasp onset ($\text{ms}$): DCD = $-238 \pm 41.8\,\text{ms}$; Control = $-251 \pm 31.4\,\text{ms}$

  • Moment of hand closure ($\text{ms}$): DCD = $-74 \pm 37.9\,\text{ms}$; Control = $-57 \pm 23.0\,\text{ms}$

  • Moment of completion ($\text{ms}$): DCD = $220 \pm 56.3\,\text{ms}$; Control = $160 \pm 34.8\,\text{ms}$ ($p < .05$

  • Total movement time ($\text{ms}$): DCD = $458 \pm 74.8\,\text{ms}$; Control = $411 \pm 49.7\,\text{ms}$

  • Maximal hand aperture ($\text{mm}$): DCD = $111 \pm 8.4\,\text{mm}$; Control = $117 \pm 5.5\,\text{mm}$

  • Relative maximal hand aperture ($\%$): DCD = $72 \pm 5.6\%$; Control = $76 \pm 6.4\%$

  • Hand opening at completion ($\text{mm}$): DCD = $51 \pm 5.3\,\text{mm}$; Control = $53 \pm 5.2\,\text{mm}$

  • Closing distance ($\text{mm}$): DCD = $60 \pm 6.2\,\text{mm}$; Control = $64 \pm 7.5\,\text{mm}$

  • Maximal closing velocity ($\text{mm/s}$): DCD = $669 \pm 65.3\,\text{mm/s}$; Control = $808 \pm 105.5\,\text{mm/s}$ ($p < .05$

  • Note: Negative time values represent millisecond durations prior to initial ball-hand contact.

  • Single IV Design (Motor Task Type):

• $1$ Independent Variable: Task ($2$ Levels: Pointing vs Grasping).

• Kinematic Profile Findings (Jeannerod, 1990):

  • Grasping movements display an acceleration phase shorter than the deceleration phase.
  • Pointing movements display an acceleration phase longer than the deceleration phase.

• Two IV Design (Group and Training Time):

  • $2$ Independent Variables:
  1. Group ($2$ Levels: Young vs Elderly)
  2. Time ($2$ Levels: Pre-practice vs Post-practice)
  • Dependent Variable: Primary Submovement Distance ($^\circ$).

• Three IV Design (Surface, Stance, Group):

  • $3$ Independent Variables:
  1. Surface Condition ($2$ Levels: Firm Surface [FS] vs Compliant Surface [CS])
  2. Stance Condition ($2$ Levels: Single Stance vs Dual Stance)
  3. Population Group ($2$ Levels: Control Group vs DCD Group)
  • Dependent Variable: Mean Path Length Velocity ($\text{cm/s}$).

• Longitudinal Single IV Design (Intervention Phase):

  • $1$ Independent Variable: Evaluation Stage ($4$ Levels: Initial Evaluation, Pre-Training, Post-Training, Follow-Up).
  • Dependent Variable: Ground Reaction Force (GRF) Breaking Force expressed in Body Weight units ($\text{BW}$).

• Practice Variability Design (McCracken & Stelmach, 1977):

  • Task: Ballistic-timing accuracy measured in Absolute Error ($\text{ms}$).
  • Independent Variables:
  1. Practice Condition ($2$ Levels: Constant Practice vs Variable Practice)
  2. Test Stage ($3$ Levels: Last 30 Training Trials, Immediate Transfer, Delayed Transfer)
  • Performance Findings:
  • Constant practice achieves lower absolute error ($15\,\text{ms}$) during the final 30 training trials compared to variable practice.
  • Variable practice achieves superior absolute error reduction during both immediate transfer and delayed transfer testing phases.

• Epidemiological Risk Factor Design:

  • Independent Variables:
  1. Activity Domain ($2$ Levels: Transportation vs Recreation)
  2. Safety Equipment Usage ($2$ Levels: No Helmet Use vs Helmet Use)
  • Outcome Metric: Injury percentage reported over a 2-year period (2012 National Survey of Bicyclist and Pedestrian Attitudes and Behaviors).
  • Domain Odds Ratios:
  • Transportation: Odds Ratio $\text{OR} = 2.81\,\text{(95\% CI: 1.14, 6.94)}$
  • Recreation: Odds Ratio $\text{OR} = 2.81\,\text{(95\% CI: 0.56, 14.02)}$

• Development and Target Complexity Design:

  • Independent Variables:
  1. Age Group ($2$ Levels: Children vs Adolescents)
  2. Practice Group Target Quantity ($4$ Levels: No Target, 1 Target, 4 Targets, 5 Targets)
  • Dependent Variable: Absolute Error ($\text{cm}$).
  • Pattern: Absolute error decreases progressively across target quantities, with adolescents maintaining consistently lower error than children.

Special Case: Correlational Research Architecture

• Distinguishing Correlational Variables:

  • Correlational designs do not apply active experimental manipulation; instead, they compute the association between two naturally occurring dependent variables.
  • Terminology adaptation:
  • Predictor Variable: The variable used to predict performance (analogue to an independent variable; plotted on the horizontal X-axis).
  • Criterion Variable: The primary focus of research about which information is sought (analogue to a dependent variable; plotted on the vertical Y-axis).

• Examples of Correlational Relationships:

  • Simulation Score (Predictor / X-axis) vs Road Test Score (Criterion / Y-axis).
  • Response Time in seconds (Predictor / X-axis) vs Movement Time in seconds (Criterion / Y-axis) ($R^2 = 0.669$).

• Empirical Exercise Comparison (Pull-Ups vs Chin-Ups):

  • Biomechanical Distinctions:
  • Pull-Up: Execution with palms facing away from the participant (pronation).
  • Chin-Up: Execution with palms facing toward the participant (supination).
  • Sample Dataset ($N = 10$ Subjects):
  • Subject 1: Body Weight = $130\,\text{lbs}$, Chin-Ups = $10$, Pull-Ups = $8$
  • Subject 2: Body Weight = $130\,\text{lbs}$, Chin-Ups = $9$, Pull-Ups = $7$
  • Subject 3: Body Weight = $140\,\text{lbs}$, Chin-Ups = $15$, Pull-Ups = $12$
  • Subject 4: Body Weight = $150\,\text{lbs}$, Chin-Ups = $9$, Pull-Ups = $10$
  • Subject 5: Body Weight = $150\,\text{lbs}$, Chin-Ups = $7$, Pull-Ups = $6$
  • Subject 6: Body Weight = $160\,\text{lbs}$, Chin-Ups = $5$, Pull-Ups = $3$
  • Subject 7: Body Weight = $160\,\text{lbs}$, Chin-Ups = $3$, Pull-Ups = $4$
  • Subject 8: Body Weight = $160\,\text{lbs}$, Chin-Ups = $8$, Pull-Ups = $7$
  • Subject 9: Body Weight = $170\,\text{lbs}$, Chin-Ups = $4$, Pull-Ups = $5$
  • Subject 10: Body Weight = $170\,\text{lbs}$, Chin-Ups = $6$, Pull-Ups = $3$

Guidelines and Constraints for Assignment 1

• Mandatory Exclusions:
  • Correlational studies must NOT be selected or utilized for Assignment 1.
  • Systematic reviews must NOT be selected or utilized for Assignment 1.