Comprehensive Guide to Variables, Measurement Scales, and Descriptive Analysis in JASP

Software Installation and System Requirements for JASP

Accessing the Installer:
- The installation link is located on Canvas within the Lab 4 module.
- Download times vary significantly by network and hardware; installation can take anywhere from $5\,\text{minutes}$ to over $40\,\text{minutes}$ (for example, showing $35\,\text{minutes}$ remaining after $5\,\text{minutes}$ of downloading).
Operating System Specifications:
- Windows:
- The most direct installation path is downloading directly through the Microsoft Store.
- macOS:
- Installation depends on the underlying processor architecture:
  - Intel Architecture: Requires the installer designed for Intel processors.
  - Apple Silicon: Requires the installer designed for Apple chips.
- Identification procedure for macOS hardware:
  - Navigate to the Apple icon in the top-left corner of the primary display.
  - Select About This Mac from the drop-down menu.
  - Inspect the hardware line item: if labeled Processor with "Intel", install the Intel package; if labeled Chip with "Apple" (e.g., Apple Silicon), install the Apple Silicon package.
- Hardware Incompatibilities and Workarounds:
- Tablet operating systems such as iPadOS are incompatible with JASP.
- Users without compatible personal laptops must utilize on-campus computer laboratory workstations where JASP is pre-installed.

Core Scientific Variables: Independent and Dependent Variables

Independent Variables ( $IV$ ):
- Definition: Variables introduced into an experimental design or observational model to explain, predict, or cause variations in the dependent variable.
- Alternative Terminology: Often designated as predictors, factors, or the explanatory $x$ variable.
- Directionality and Exogeneity:
- Other variables within the statistical model exert no influence over the independent variable.
- The independent variable functions as the primary influencer within the model.
- The model does not attempt to explain the underlying mechanisms that cause the independent variable itself to vary.
Dependent Variables ( $DV$ ):
- Definition: The specific outcome factor that the study seeks to predict, quantify, or explain as a function of the independent variable.
- Alternative Terminology: Frequently referred to as the outcome variable, criterion variable, or the response $y$ variable.
Experimental Scenarios and Variable Identification:
- Agricultural Plant Growth Study:
- Objective: Determine the biological response of plants under varying conditions.
- Independent Variables ( $IV$ ): Soil moisture levels and fertilizer types.
- Dependent Variable ( $DV$ ): Plant growth metrics.
- University Student Satisfaction Study (Biola University Context):
- Objective: Determine whether academic discipline relates to overall program satisfaction.
- Independent Variable ( $IV$ ): Student's declared academic major.
- Dependent Variable ( $DV$ ): Level of student satisfaction.
Levels of an Independent Variable:
- Definition: Specific mutually exclusive subgroups, treatments, or operationalized categories that constitute a single variable.
- Illustrative Examples:
- Variable Gender: Contains two levels (Male, Female).
- Variable Anxiety: Operationalized into three qualitative levels (Low, Medium, High).
- Variable Soil Moisture: Operationalized into three moisture tiers (Dry, Damp/Moist, Wet).
- Variable Student Satisfaction: Measured across discrete response categories (e.g., Dissatisfied, Somewhat Satisfied, Very Satisfied; or Strongly Disagree, Somewhat Disagree, Somewhat Agree, Strongly Agree).

Levels of Measurement and Variable Classifications

Broad Variable Classifications:
- Discrete Variables:
- Variables constrained to a countable, finite set of distinct numeric properties or isolated categories.
- Characterized by exact numerical counts without fractional approximations.
- Examples: Number of motor vehicles owned, total headcount of enrolled students in a lecture hall.
- Continuous Variables:
- Variables that theoretically possess an infinite set of possible values within any given interval.
- Values are inherently approximations determined by the precision of the measuring instrument, never absolute exact values.
- Examples: Height, weight, ambient temperature, chronological duration.
The Four Levels of Measurement:
- Measurement scales establish the mathematical properties of the recorded data, thereby dictating which statistical operations and parametric analyses can be legitimately performed.
- 1. Nominal Scale (Discrete):
- Represents purely qualitative, categorical classification without intrinsic hierarchy, magnitude, or rank order.
- Numerical assignments serve solely as arbitrary labels (e.g., assigning $1 = \text{Male}$ and $2 = \text{Female}$ ).
- Examples: Biological sex, marital status, academic major, ABO blood group.
- Permissible Mathematical Operations: Frequency distributions, counts, mode, percentage allocations.
- 2. Ordinal Scale (Discrete):
- Classifies observations into discrete groups exhibiting a defined, natural sequence, rank, or direction of magnitude.
- The exact mathematical distance or interval between adjacent ranks is non-uniform or mathematically unknown.
- Examples: Highest educational level attained, competitive placement in an athletic race (e.g., first place, second place, third place), Likert-type preference scales.
- Permissible Mathematical Operations: Frequency distributions, median determination, rank-order statistics, percentile ranks, interquartile range.
- 3. Interval Scale (Continuous):
- Ordered numerical values with standardized, equal, and meaningful mathematical distances separating adjacent score units.
- Lacks a true or absolute zero point; zero represents an arbitrary calibration point rather than the complete absence of the underlying construct.
- Examples: Temperature measured in Celsius or Fahrenheit (where $0^\circ$ does not signify the total absence of thermal energy), chronological calendar dates.
- Permissible Mathematical Operations: Addition, subtraction, mean calculation, standard deviation calculation, parametric comparative analyses.
- 4. Ratio Scale (Continuous):
- Meets all properties of nominal, ordinal, and interval scales, while additionally possessing an absolute, non-arbitrary true zero value.
- A value of zero signifies the complete non-existence or lack of the measured attribute ( $\text{Value} = 0$ denotes zero quantity).
- Examples: Mass/weight, linear distance/height, elapsed chronological age, monetary balances.
- Permissible Mathematical Operations: All arithmetic calculations, including meaningful division, multiplication, computation of ratios, and comprehensive advanced parametric modeling.

JASP Interface Navigation and Data Management

Importing Datasets into JASP:
- Obtain the empirical dataset from Canvas under the designated lab module section.
- Method A (Operating System Level): Navigate to the local file directory on the computer, right-click the dataset file, and select the option to open the file with JASP.
- Method B (Application Level):
- Launch the JASP software interface.
- Click the Main Menu icon (represented by horizontal lines in the top-left corner).
- Select Open from the primary menu options.
- Click Computer and use the file browser to locate and load the saved dataset.
JASP Workspace Layout:
- Data Panel: The primary central spreadsheet window displaying the imported observations organized as a matrix of rows (individual participants/experimental units) and columns (recorded variables).
- Analysis Ribbon: The persistent horizontal toolbar across the top header of the interface providing access to statistical test engines (e.g., Descriptives, T-Tests, ANOVA, Regression).
- Output Panel: The dynamic right-hand pane that automatically renders real-time mathematical summary tables and high-resolution graphical visualizations as parameters are checked.
Visual Measurement Indicators in JASP:
- Grouped Circles Icon: Designates a Nominal variable (unranked categorical data).
- Bar Graph / Histogram Icon: Designates an Ordinal variable (ranked or hierarchical categorical data, such as academic class standing).
- Ruler Icon: Designates a Scale variable (continuous metric data spanning interval and ratio levels of measurement suitable for mathematical arithmetic).
Modifying Variable Metadata and Value Labels:
- Double-clicking a specific column header within the Data Panel opens the Value Settings configuration window.
- Modifiable metadata include: Variable Name, Column Type (Nominal, Ordinal, Scale), Labels, and operational descriptions.
- Recoding numerical values to descriptive labels:
- In binary categorical columns (e.g., biological sex), select numeric value $1$ and input the string label male.
- Select numeric value $2$ and input the string label female.
- Confirm changes to immediately update the main data spreadsheet view.
- Reclassifying levels of measurement:
- Single-click or double-click the measurement icon next to the column header (e.g., converting a major variable categorized by default as Scale to Ordinal or Nominal).

Step-by-Step Procedure for Descriptive Statistical Analyses

Executing Standard Descriptive Statistics:
- Navigate to the top Analysis Ribbon and click on Descriptives.
- Click the primary option: Descriptive Statistics.
- Variable Selection:
- Locate the candidate target variables in the left-hand directory list (chat 1, tap 1, and att 1 / here 1).
- Select each variable and click the directional right-arrow button to transfer them into the active Variables input field.
- Default Output Metric Inspection:
- By default, JASP populates the summary output table with: number of valid cases, missing cases, sample mean ( $\mu$ or $\bar{x}$ ), sample standard deviation ( $s$ or $SD$ ), minimum value, and maximum value.
- Configuring Advanced Statistical Moments:
- Expand the Statistics options menu located directly below the variable entry fields.
- Locate the measures of central tendency and check the boxes for Median and Mode.
- The summary output table automatically updates dynamically to reflect these additional parameters.
- Generating Graphical Visualizations:
- Expand the Basic Plots options menu.
- Check the box labeled Distribution plots to generate corresponding frequency histograms/density plots in the output pane.
- Managing Workflow Windows:
- Click the small directional triangle next to an analysis title within the configuration drawer to collapse and minimize the settings window.
Executing Subgroup-Split Descriptive Analyses:
- Click Descriptives -> Descriptive Statistics from the top ribbon to initiate a clean, secondary analysis module.
- Populate the Variables field with the identical target variables (chat 1, tap 1, att 1 / here 1).
- Select the categorical grouping variable (sex) and transfer it into the Split input field.
- Relabeling the Analysis Output:
- Click directly into the title bar of the new analysis (which reads "Descriptive Statistics" by default).
- Rename the title string to: Descriptive statistics by gender and press Enter to commit.
- Configuring Split Statistics and Graphics:
- Within the Statistics menu, check Median and Mode.
- Within the Basic Plots menu, check Distribution plots.
- The output pane will dynamically construct segmented tables and parallel distribution graphs separated by each level of the splitting variable (male versus female cohorts).

Exporting Results and Homework Submission Guidelines

Export Procedure:
- Navigate to the upper-left corner of the JASP interface and open the Main Menu.
- Select Export from the navigation options, then click Computer.
- In the file system browser, designate a storage directory and assign the target file name.
- File Extension Alteration:
- The default output export format is set to Hypertext Markup Language (.html).
- Change the file type selection menu specifically to Portable Document Format (.pdf).
- Click Save to compile and export the complete descriptive tables, split groupings, and distribution plots into a finalized PDF document.
Homework Assignment Workflow Requirements:
- Accurately decode, clean, and assign qualitative labels to raw numerical variables in the data matrix.
- Transfer specified study variables into the descriptive analysis module.
- Ensure every required metric is actively toggled in the configuration panel, explicitly verifying checkboxes for Mean, Standard Deviation, Minimum, Maximum, Median, and Mode.
- Generate and include all requested visualization charts via Distribution plots under the Basic Plots menu.
- Confirm all required settings prior to output generation, as omitted checkboxes will invalidate the resulting summary tables.
- Export the final compiled output strictly as a .pdf file, as Canvas upload gateways reject HTML and unsupported proprietary extensions.

Classroom Dialogue and Student Interactions

Interactive Prompt on Dependent Variable Identification:
- Prompt: In a study investigating how a student's declared academic major influences their academic satisfaction at Biola University, identify the dependent variable.
- Student Response: Satisfaction.
- Outcome: Confirmed correct; satisfaction represents the outcome variable ( $y$ ), while the major represents the independent variable ( $IV$ ).
Peer Collaboration on Operationalizing Variable Levels:
- Discussion Focus: Developing concrete categorical levels for the experimental variables identified in the lecture examples.
- Participant Exchange (Mikey and peer):
- Soil Moisture levels proposed: "Dry", "Damp/Moist", and "Wet".
- Student Satisfaction levels proposed: Multi-point scaling ranging across "Very Low", "Low", "Somewhat Disagree", "Strongly Disagree", up to "Dissatisfied", "Somewhat Satisfied", and "Very Satisfied".
Student Academic Discussion (Course Logistics and Performance):
- Conversation: Mikey and a peer discussed performance on a recent class examination.
- Schedule Clarification: One participant takes the class lecture once per week in a single three-hour session on Wednesdays, whereas the other had lecture earlier that day.
- Exam Outcomes and Grading Policy: Students discussed frustration over second-guessing specific answers right at the deadline. It was noted that the instructor awarded points back to the class for specific questions that the entire cohort answered incorrectly, acknowledging structural issues with those items.
Technical Inquiries and Workarounds:
- Hardware Constraint Raised: A student noted an inability to download JASP because their primary device is an iPad running iPadOS.
- Instructor Clarification and Resolution: JASP is not compatible with tablet operating systems. The student was instructed to sign into a campus computer lab workstation during the session or utilize a desktop/laptop computer at home to access JASP and complete homework assignments.
Formative Check on Software Comfort:
- Informal Polling: The room provided a visual "thumbs" check on initial impressions of the JASP interface.
- Instructor Feedback: Acknowledged that statistical software often feels intimidating initially, but comfort increases with repeated practice; step-by-step presentation slides and reference materials were committed to Canvas to assist with post-lab assignments.