PCA Biplot

A 2D visual map showing how elements and constructs relate to each other using Principal Component Analysis (PCA).

• Elements are plotted as points - elements close together were rated similarly across constructs.
• Constructs are shown as arrows (vectors) from the origin - arrows pointing in similar directions measure similar things.
• PC1 and PC2 are the two main dimensions that explain the most variance in your ratings.

How to interpret

• Elements near each other = similar rating patterns
• Constructs pointing same direction = correlated (measure similar things)
• Constructs pointing opposite directions = negatively correlated
• Elements in the direction of a construct arrow = rated high on that construct

Understanding construct arrow labels

Crossplot Analysis

A scatter plot showing where each element falls on two constructs of your choice.

• X-axis = ratings on the first construct (1 = left pole, 5 = right pole)
• Y-axis = ratings on the second construct
• Each point = one element from your grid

How to interpret

• Elements in the same quadrant share similar ratings on both constructs
• The midpoint (3) is marked with dashed lines - this divides the plot into four quadrants
• Use this to explore relationships between specific construct pairs
• Try different construct combinations to find meaningful patterns

Example use

If your constructs are 'friendly-unfriendly' (X) and 'competent-incompetent' (Y), elements in the top-right are seen as both unfriendly AND incompetent.

Synopsis Analysis

Summarises your rating patterns through histograms and variance analysis.

Display options

• Overall Distribution - Histogram of ALL ratings in your grid. Shows if you tend to use certain parts of the scale more than others. Red line = mean, blue line = median.
• Element Distributions - Separate histogram for each element. Shows how each element was rated across all constructs.
• Construct Distributions - Separate histogram for each construct. Shows how ratings vary across elements for each construct.
• Scree Plot - Shows how much variance each principal component explains. Helps determine how many dimensions are meaningful in your data.

How to interpret

• Skewed distributions may indicate response bias or genuine patterns
• Flat distributions suggest differentiated ratings
• In the scree plot, look for an 'elbow' where variance drops off - components before the elbow are most meaningful

Worked example

A student rates 6 school subjects on constructs like 'practical - theoretical'. The Overall Distribution shows most ratings cluster around 3-5, suggesting a slight positive bias. The Element Distribution for 'Mathematics' is spread across the full range (high SD), meaning the student sees Maths as extreme on several dimensions. The Scree Plot shows PC1 explains 60% and PC2 adds 20% - so two dimensions capture most of the picture.

Heatmap

A color-coded grid showing all your ratings at a glance.

• Rows = Elements
• Columns = Constructs
• Colors = Rating values (darker = higher ratings by default, or use color toggle for blue-white-red)

How to interpret

• Look for patterns - rows or columns with similar shading
• Dark/red regions indicate high ratings (toward right pole)
• Light/blue regions indicate low ratings (toward left pole)
• Uniform rows = element rated similarly across all constructs
• Uniform columns = construct doesn't differentiate between elements

Worked example

In a grid of school subjects rated on 'easy - hard', 'practical - theoretical', and 'enjoy - dislike', the heatmap might show a dark band across the 'Mathematics' row on 'hard' and 'theoretical' but light on 'enjoy'. Meanwhile 'Geography' shows the opposite pattern. A uniform column on 'enjoy - dislike' (all mid-tones) would suggest this construct doesn't differentiate your subjects well.

Focus Cluster Analysis

Focus automatically sorts your grid to reveal patterns. Similar elements appear together, and similar constructs appear together.

The display shows 4 parts

• Top dendrogram - shows how constructs (columns) cluster together
• Left dendrogram - shows how elements (rows) cluster together
• Center grid - your ratings, reordered so similar items are adjacent
• Match statistics - similarity percentages for elements and constructs

Reading the dendrograms

• Short connections = very similar items
• Long connections = less similar items
• Items that join low on the tree are more similar than those joining higher up

Parameters

• Minkowski Power - 1.0 (city block, default) treats all differences equally; 2.0 (Euclidean) emphasizes larger differences
• Match Cutoff - only shows matches above this similarity threshold

Common uses

• Finding element groups that cluster together
• Identifying redundant constructs (matches > 90%)
• Discovering main conceptual dimensions

Worked example

After running Focus on a school subjects grid, you might see Mathematics and Physics cluster together at 85% match, and Biology and Geography cluster at 78%. Meanwhile the constructs 'uses equations - no equations' and 'abstract - concrete' join at 92%, suggesting these are essentially the same dimension in the student's thinking. The reordered grid places these similar items adjacent, making the pattern visible at a glance.

Descriptive Statistics

Summary statistics for your grid data, showing patterns in how elements and constructs were rated.

Element Statistics

• Mean - average rating for this element across all constructs. High means = element rated toward right poles; low means = toward left poles.
• SD (Standard Deviation) - how much ratings varied. Low SD = element rated consistently; high SD = element rated very differently on different constructs.

Construct Statistics

• Mean - average rating on this construct across all elements. Near 3 = construct differentiates well; extreme values may indicate bias.
• SD - how much this construct differentiates between elements. Low SD = construct doesn't distinguish elements well; high SD = good differentiation.

What to look for

• Constructs with very low SD may not be useful - they rate all elements the same
• Elements with extreme means may be outliers worth examining
• Compare means to identify patterns in how you perceive different elements

Worked example

In a school subjects grid, Mathematics has a mean of 5.8 (rated toward the right poles on most constructs) while Geography has a mean of 2.3 (rated toward left poles) - these are the most differently perceived subjects. The construct 'enjoy - dislike' has SD = 0.4 (rates all subjects similarly - not very discriminating) while 'practical - theoretical' has SD = 2.1 (strongly differentiates subjects - a useful construct).

What is a Grid Collection?

A grid collection allows you to compare multiple repertory grids from different participants who rated the same elements. This enables group-level analysis using Shaw's (1980) SOCIOGRIDS methodology.

How to use

1. Add grids - Use 'Add Grid(s) to Collection' in the sidebar to upload multiple .rgrid files, or add your current grid
2. Select grids - Click rows in the table to select which grids to include in analysis
3. Check common elements - The system detects elements shared across grids (needed for comparison)
4. Run analysis - Use the Socionets, Mode Grid, or Composite Grid tabs

Opening a grid for detailed view

Select a grid from the dropdown and click 'Load to Editor' to open it in the Build Grid tab for full viewing and analysis.

Requirements

• At least 2 grids selected
• At least 2 common elements across selected grids
• Grids should ideally share the same elements (e.g., same interview protocol)

Worked example

A teacher asks 8 students to each rate the same 6 school subjects (Mathematics, Physics, Chemistry, Biology, Geology, Geography) using their own constructs. Each student's grid is saved as a .rgrid file. The teacher uploads all 8 files, selects them in the table, and sees '6 common elements found'. Now the Socionets tab will show which students think most alike, and the Mode tab will reveal the group's consensus view of these subjects.

Socionets Analysis

Socionets (Shaw, 1980) maps how well participants could understand each other's construct systems.

Reading the Arrows

• A → B (85%) means: if person A used person B's constructs, A would predict 85% of B's ratings correctly. A is very likely to understand how B sees the world.
• B → A (60%) means: B would only predict 60% of A's ratings — B is less likely to understand A's perspective.
• Asymmetry is key: understanding is not always mutual. A may understand B well, but B may struggle to understand A.

What the Numbers Mean

• 90%+ = near-identical construct systems; these people see the world very similarly
• 70–89% = substantial overlap; they would largely understand each other
• 50–69% = moderate overlap; significant differences in perspective
• Below 50% = quite different construing; likely to misunderstand each other

Parameters

• Match Cutoff — only show connections above this threshold (hide weak links)
• Symmetric Matching — average both directions (A→B and B→A) into a single undirected edge

Interpretation

• Thick arrows = strong match; thin arrows = weaker match
• Clusters of connected grids = groups with shared understanding
• Isolated nodes = people with a unique perspective that others don't share

Mode Grid (Consensus Grid)

The Mode Grid (Shaw, 1980) represents the 'typical' or consensus grid from a group of participants. It answers: what would a representative member of this group's grid look like?

Reading the Heatmap

• Each cell shows the consensus rating for that element-construct combination
• Blue = low rating (towards left pole), White = midpoint, Orange = high rating (towards right pole)
• Constructs with high agreement across participants will show clear, saturated colours
• Constructs where participants disagreed will tend towards the midpoint (white)

Consensus Method

• Average — mean of ratings across all grids. Best when ratings are normally distributed.
• Median — middle value. More robust when some participants rate very differently from others.

Construct Handling

• Fold Identical — combine constructs with the same labels and average their ratings. Use when all participants share the same construct set.
• Collect All — include every construct from every grid (labelled by source). Use when participants have different constructs.

Interpretation

• Elements rated similarly across the group appear as clear colour bands — the group agrees on how to view them
• Elements with mixed colours indicate disagreement — people construe them differently
• Use 'Use as Current Grid' to load the mode grid and explore it with all single-grid analyses (biplot, focus, etc.)

Worked example

Eight students each rate 6 school subjects. The Mode Grid extracts the most consensual constructs - perhaps 'practical - theoretical' (mode score 87%) and 'difficult - easy' (mode score 82%) appear in the mode because many students used similar distinctions. The heatmap shows Mathematics as strongly 'theoretical' and 'difficult' (deep orange), while Geography shows as 'practical' and 'easy' (deep blue). Chemistry appears white (near midpoint) - the group is split on where it falls.

PrinGrid Trajectories

Trajectories extend the PCA biplot to show how the same elements are positioned differently across multiple grids.

Reading the plot

• Each grid's elements are shown in a different colour
• Arrows connect the same element across grids, showing movement in construct space
• Long arrows = large changes in how that element is construed
• Short/no arrows = stable, consistent construing

Use cases

• Tracking change over time (pre/post interventions)
• Comparing different perspectives on the same elements
• Identifying which elements changed most in a learning context

Worked example

A student rates 6 school subjects at the start and end of the year. In the trajectory plot, most subjects barely move (short arrows) - their perception is stable. But Chemistry has a long arrow moving from the 'dislike/theoretical' quadrant toward 'enjoy/practical', showing a significant shift in how the student construes Chemistry. This could reflect the impact of a new hands-on teaching approach introduced during the year.

Class Metagrids

A metagrid treats your grid collection as a set of elements and lets you classify them using new constructs.

How to use

1. Your loaded grids automatically become the elements
2. Define bipolar constructs for classifying grids (e.g., 'Expert - Novice')
3. Rate each grid on each construct using the 1-5 scale
4. Click 'Build Metagrid' to create the higher-order grid
5. Click 'Analyse as Current Grid' to run FOCUS, PCA, etc. on the metagrid

Example constructs

• 'Expert perspective - Novice perspective'
• 'Detailed grid - Sparse grid'
• 'Positive overall - Negative overall'

Composite Grid

A Composite Grid merges data from multiple grids into one for unified analysis.

Merge Strategies

• Common Elements + All Constructs - Use shared elements as rows, include all constructs from all grids as columns. Good for comparing how different people construe the same elements.
• Common Constructs + All Elements - Use shared constructs as columns, include all elements from all grids as rows. Good for comparing how the same dimensions apply to different elements.

Source Labeling

When enabled, constructs/elements are labeled with their source grid name (e.g., 'friendly [Grid1]') to track origin.

Use cases

• PrinGrid trajectories showing change over time
• Comparing perspectives on shared elements
• Focus analysis across multiple participants

Worked example

Two students, Alice and Bob, each rated the same 6 school subjects but elicited their own constructs. Using 'Common Elements + All Constructs', the composite grid has 6 rows (the shared subjects) and columns from both students - e.g., 'practical - theoretical [Alice]' alongside 'hands-on - bookish [Bob]'. Running Focus on this composite might reveal that Alice's 'practical - theoretical' clusters tightly with Bob's 'hands-on - bookish' - they are using different words for the same idea.

MINUS Analysis

MINUS subtracts ratings in Grid B from Grid A, cell by cell, to show where two people (or the same person at different times) differ in their construing.

Reading the plot

• Blue cells - Grid A rated lower than Grid B on this element/construct
• White cells - No difference (identical ratings)
• Orange cells - Grid A rated higher than Grid B

Requirements

• Exactly 2 grids selected
• Grids must share both elements AND constructs

Worked example

A student rates 6 school subjects before and after a term. MINUS reveals that Chemistry shifted by +3 on 'enjoy - dislike' (the student grew to like it) while Mathematics shifted by -2 on 'easy - hard' (it got harder). Most other cells are white (0 difference) - the student's views were largely stable. The biggest orange cell (Chemistry/enjoy) and the biggest blue cell (Maths/hard) are the key changes to discuss.

CORE Analysis

CORE (Shaw, 1980) finds the core of shared construing between two grids by iteratively removing elements or constructs that contribute most to disagreement.

How it works

1. Start with all common elements and constructs
2. Calculate overall match percentage
3. Try removing each element/construct and see which removal improves the match most
4. Remove that item and record the improvement
5. Repeat until minimum size is reached or no improvement possible

Interpretation

• Elements/constructs removed early = greatest sources of disagreement
• The final remaining grid = the core of shared construing
• Use 'Analyse Core with FOCUS' to examine the shared structure in detail

Worked example

Comparing Alice's and Bob's grids (6 subjects, 5 shared constructs), CORE starts at 68% overall match. Removing 'Geology' (their biggest disagreement) raises it to 76%. Then removing 'enjoy - dislike' (they have opposite tastes) raises it to 84%. The remaining core of 5 subjects and 4 constructs at 84% match represents what Alice and Bob genuinely share in their construing of school subjects.

Exchange Grid Protocol

The Exchange Grid protocol (Shaw, 1980) measures both agreement and understanding between two people.

The 6 grids

1. A's own grid - A rates elements on A's constructs
2. B's own grid - B rates elements on B's constructs
3. B fills A's grid as B would - shows B's perspective on A's constructs
4. A fills B's grid as A would - shows A's perspective on B's constructs
5. B predicts A's ratings - shows B's understanding of how A construes
6. A predicts B's ratings - shows A's understanding of how B construes

Measurements

• Agreement (grids 1&3, 2&4): Do they construe elements similarly?
• Understanding (grids 1&5, 2&6): Can they predict how the other person rates elements?

Worked example

Alice and Bob both rate 6 school subjects. Alice also fills in Bob's grid as she would (grid 4) and predicts Bob's ratings (grid 6). Comparing grids 2 & 4 (agreement) shows 72% match - Alice and Bob construe subjects fairly similarly. But comparing grids 2 & 6 (understanding) shows 88% - Alice can accurately predict how Bob will rate subjects, even where she disagrees. This means Alice understands Bob's perspective well, even when her own view differs.