Interpreting PCA Biplots in Ecology and Genomics

By Dr. Zubair Khalid, DVM, MS, PhD · 2026-08-22

Key Takeaways

Biplots visually represent high-dimensional PCA results by projecting samples and variable vectors onto a 2D plane; interpret sample proximity as similarity across measured variables and vector angles as correlations between variables, but only after confirming the plot's scaling (distance, variable, or symmetric) and the percentage of variance explained by the displayed principal components.
Vector length in a biplot indicates a variable's contribution to the displayed principal components, not its overall importance in the dataset; short vectors for variables crucial in higher components can mislead if not cross-referenced with loading values.
Sample distances in a biplot are only reliable indicators of similarity when using distance scaling; in variable scaling, sample positions are distorted to preserve variable correlations, rendering inter-sample distances uninterpretable for similarity assessment.
Critical biplot findings, especially regarding sample grouping or variable relationships, must be verified against the underlying loading matrix and original data, as the 2D projection can distort true relationships and distances.
Before interpretation, always ascertain the percentage of variance explained by the plotted components; if low (e.g., <70%), conclusions about sample clustering or variable associations are preliminary and require confirmation with formal statistical tests or analysis of additional components.
Reproducibility of biplot analysis hinges on meticulously documenting analysis steps, including software versions, data transformations, centering/scaling methods, biplot scaling, and the percentage of variance explained, alongside making raw data and analysis scripts publicly available.

Quick Answer

Read a PCA biplot by examining the angle between variable vectors to assess correlation, the distance between sample points to assess similarity, and the projection of samples onto vectors to estimate variable values.
Start interpretation by checking the proportion of variance explained by each principal component, typically shown in the axis labels or a scree plot, before drawing any conclusions about grouping or variable relationships.
A biplot is a projection that can distort distances and angles, so confirm critical findings with the underlying loading values and original data instead of relying on visual inspection alone.

Understanding PCA Biplots in Biological Research

Principal component analysis (PCA) is a dimensionality reduction technique widely used in ecology and genomics to summarize variation across many measured variables. A biplot displays both the samples and the variables of a PCA result in a single coordinate system, allowing researchers to visualize relationships that would be difficult to see in the original high-dimensional data.

The biplot serves a practical purpose in biological research. In ecology, it can show how environmental variables such as temperature, moisture, and soil nutrients relate to species abundance across sampling sites. In genomics, it can display how gene expression levels separate tissue types or how genetic variants cluster among populations. The interpretation of these plots, however, requires a systematic approach because the geometry of the projection follows specific mathematical rules.

The core challenge for biologists is that a biplot is not a simple scatter plot. The positions of samples and the directions of variable vectors are determined by the singular value decomposition of the data matrix, and the scaling choices made during the analysis change what the plot shows. Without understanding these choices, a researcher can easily draw incorrect conclusions about which variables drive sample separation or which samples are truly similar.

This article provides a systematic method for reading PCA biplots in ecology and genomics. It covers the mathematical basis of the plot, the scaling options that affect interpretation, the rules for reading vector angles and lengths, and the practical steps for verifying findings. The guidance is intended for biology students, researchers, and laboratory professionals who need to interpret these plots correctly in their own work.

At a Glance

The table below summarizes the key elements of a PCA biplot and the interpretation rules that apply to each element.

Biplot Element	What It Shows	Interpretation Rule
Sample points	Position of each sample in the reduced coordinate space	Samples close together are similar across the measured variables, samples far apart are different
Variable vectors	Direction and magnitude of each variable contribution to the principal components	Vector angle between two variables indicates correlation, vector length indicates the strength of contribution to the displayed components
Axis labels	The percentage of total variance explained by each principal component	The percentages indicate how much of the total data variation is represented in the plot, low percentages mean the plot shows only a small part of the data structure
Scaling type	Whether the plot shows distances between samples, correlations between variables, or a compromise	The choice of scaling determines whether sample distances or variable correlations are preserved accurately

The table above is a starting point for interpretation. The following sections explain the mathematical basis for these rules and the practical steps for applying them.

The Mathematical Basis of PCA Biplots

PCA begins with a data matrix where rows are samples and columns are variables. In ecology, the samples might be field sites and the variables might be species abundance or environmental measurements. In genomics, the samples might be individual organisms and the variables might be gene expression levels or genetic markers.

The first step in PCA is to center the data by subtracting the mean of each variable. This ensures that the analysis focuses on variation around the average instead of on the absolute values of the measurements. The next step is often to scale the data so that each variable has unit variance, which prevents variables with large numeric ranges from dominating the analysis. Scaling is particularly important in ecology when variables are measured in different units, such as temperature in degrees and species counts in numbers.

The principal components are then calculated as linear combinations of the original variables. The first principal component is the direction in the data that captures the most variation. The second principal component is the direction that captures the most remaining variation while being uncorrelated with the first. Each subsequent component follows the same rule.

The result of this calculation is a set of scores for each sample along each principal component and a set of loadings for each variable along each principal component. The scores are the coordinates of the samples in the new space. The loadings are the coefficients that define how each variable contributes to each principal component.

A biplot combines these two results into one plot. The samples are plotted at their score coordinates. The variables are plotted as vectors whose coordinates are the loadings. The mathematical relationship between the scores and the loadings is what allows the plot to show both sample positions and variable directions in the same coordinate system.

The singular value decomposition is the mathematical operation that produces the scores and loadings. The data matrix is decomposed into three matrices that represent the sample coordinates, the singular values, and the variable coordinates. The way these matrices are combined determines the scaling of the biplot and therefore what the plot emphasizes.

Scaling Options and Their Effect on Interpretation

The choice of scaling in a biplot determines whether the plot preserves the distances between samples, the correlations between variables, or a compromise between the two. This choice is often controlled by a parameter in the plotting software, and it has a direct effect on the interpretation of the plot.

Distance Scaling

In distance scaling, the sample coordinates are multiplied by the singular values while the variable coordinates are not. This scaling preserves the Euclidean distances between samples in the plot. The distances between sample points in the biplot are then proportional to the distances in the original data space.

This scaling is appropriate when the research question focuses on the relationships between samples. In ecology, this could be the question of which sampling sites are most similar in species composition. In genomics, this could be the question of which individuals have the most similar gene expression profiles.

The variable vectors in this scaling are not directly interpretable in terms of their angles. The angles between variable vectors do not accurately represent the correlations between the variables. The lengths of the variable vectors are also not directly interpretable as the contribution of each variable to the principal components.

Variable Scaling

When variable scaling is used, the variable coordinates are the loadings and the sample coordinates are divided by the singular values. This scaling preserves the correlations between variables. The angle between two variable vectors in the plot then reflects the correlation between those variables. An angle of zero degrees indicates a correlation of one, an angle of 90 degrees indicates a correlation of zero, and an angle of 180 degrees indicates a correlation of negative one.

This scaling is used when the research question is about the relationships between variables. In ecology, this could be the question of which environmental variables are associated with each other. In genomics, this could be the question of which genes are co-expressed.

The sample distances in this scaling are not directly interpretable. The distances between sample points do not accurately represent the similarities between the samples in the original data space.

Symmetric Scaling

Symmetric scaling is a compromise between the two extremes. The singular values are distributed between the sample coordinates and the variable coordinates. This scaling allows both sample distances and variable correlations to be interpreted, but neither is preserved exactly.

The interpretation of a symmetrically scaled biplot requires caution. The sample distances are approximately proportional to the original distances, and the variable angles are approximately proportional to the correlations, but the approximations can be poor when the data is not well represented by the first two principal components.

The choice of scaling should be made based on the research question. If the question is about sample grouping, distance scaling is appropriate. If the question is about variable relationships, variable scaling is appropriate. If the question involves both, symmetric scaling can be used with the understanding that the plot is a compromise.

Reading Variable Vectors

The variable vectors in a biplot are the arrows that represent the variables. The direction and length of each vector carry information about the variable and its relationship to the principal components.

The direction of a variable vector indicates how the variable is related to the principal components. A vector that points to the right along the first principal component axis indicates that the variable is positively correlated with that component. A vector that points to the left indicates a negative correlation. The same logic applies to the second principal component axis.

The angle between two variable vectors indicates the correlation between the variables. This interpretation is valid when the biplot uses variable scaling or symmetric scaling. The cosine of the angle between the vectors is the correlation coefficient between the variables. An angle of zero degrees means the variables are perfectly positively correlated. An angle of 90 degrees means the variables are uncorrelated. An angle of 180 degrees means the variables are perfectly negatively correlated.

The length of a variable vector indicates the contribution of the variable to the two displayed principal components. A long vector means the variable is well represented by the plot and contributes strongly to the separation of the samples. A short vector means the variable is poorly represented and contributes little to the displayed components. A short vector does not mean the variable is unimportant in the data, only that it is not important in the two components shown.

The projection of a sample point onto a variable vector provides an estimate of the value of that variable for that sample. A sample that projects far along the direction of the vector has a high value for that variable. A sample that projects opposite to the direction of the vector has a low value. This interpretation is valid when the biplot is scaled appropriately.

Common Errors in Vector Interpretation

One common error is to interpret the angle between vectors in a distance-scaled biplot. The angles in this scaling do not represent correlations, and conclusions drawn from them can be wrong. The scaling must be checked before interpreting vector angles.

Another common error is to interpret the length of a vector as the overall importance of the variable in the data. The length only reflects the contribution to the two displayed components. A variable that is important in the third or fourth component will have a short vector in the first two components, even though it is important in the data.

A third error is to interpret the projection of a sample onto a vector without considering the scaling. The projection is only meaningful when the plot is scaled appropriately. In a variable-scaled plot, the sample positions are not accurate, and the projections are not reliable.

Reading Sample Groupings

The sample points in a biplot show the positions of the samples in the reduced coordinate space. The distances between the sample points indicate the similarities between the samples, provided the plot is distance scaled.

Samples that are close together in the plot are similar across the measured variables. Samples that are far apart are different. The grouping of samples in the plot can reveal patterns in the data, such as clusters of samples that share similar characteristics.

In ecology, sample grouping can reveal distinct communities or habitat types. In genomics, sample grouping can reveal distinct populations or experimental conditions. The grouping is a visual summary of the variation in the data, and it can be used to generate hypotheses about the factors that drive the differences between samples.

The interpretation of sample grouping must consider the percentage of variance explained by the displayed components. If the first two components explain only a small percentage of the total variance, the grouping in the plot may not reflect the true structure of the data. Samples that appear close together in the plot may be far apart in the dimensions not shown.

Using Confidence Ellipses

Confidence ellipses can be added to a biplot to show the uncertainty in the sample positions. These ellipses are calculated from the variation within groups of samples and provide a visual indication of whether the groups are statistically distinct. The ellipses are drawn around the group means and represent the region where the true mean is likely to fall.

The interpretation of the ellipses requires an understanding of the confidence level used to draw them. A 95 percent confidence ellipse indicates the region where the true group mean is expected to fall with 95% confidence. If the ellipses of two groups do not overlap, the group means are likely to be different. If the ellipses overlap, the group means may not be different.

The confidence ellipses are a useful addition to the biplot, but they are not a substitute for a formal statistical test. The ellipses provide a visual indication of the uncertainty, but the formal test is needed to confirm the significance of the difference.

Practical Workflow for Interpreting a Biplot

The following steps provide a systematic approach to interpreting a PCA biplot in a research setting. The steps are designed to be applied in order, and each step builds on the previous one.

Step 1: Check the Variance Explained

The first step is to check the percentage of variance explained by the principal components shown in the plot. This information is usually displayed in the axis labels or in the plot title. The percentages indicate how much of the total variation in the data is represented by the plot.

If the first two components explain a large percentage of the variance, the plot is a good representation of the data. If the percentage is low, the plot shows only a small part of the data structure, and the interpretation should be cautious. The threshold for a good representation depends on the field and the data, but a common rule is that the first two components should explain at least 70% of the variance for the plot to be a reliable summary.

Step 2: Determine the Scaling

The second step is to determine the scaling of the biplot. The scaling is usually specified in the software settings or in the figure caption. The scaling determines whether the sample distances or the variable correlations are the primary interpretation.

If the plot is distance scaled, the sample distances are the primary interpretation. If the plot is variable scaled, the variable correlations are the primary interpretation. If the plot is symmetric, both interpretations are possible but approximate.

Step 3: Examine the Variable Vectors

The third step is to examine the variable vectors. The direction of each vector indicates the relationship to the principal components. The angle between vectors indicates the correlation between variables, provided the scaling is appropriate. The length of the vectors indicates the contribution of the variables to the displayed components.

Step 4: Examine the Sample Points

The fourth step is to examine the sample points. The distances between the points indicate the similarities between the samples, if the scaling is appropriate. The grouping of the points can reveal patterns in the data.

Step 5: Integrate the Information

The fifth step is to integrate the information from the variable vectors and the sample points. The position of a sample relative to the variable vectors indicates the values of the variables for that sample. A sample that is positioned in the direction of a vector has a high value for that variable. A sample that is positioned opposite to the direction of a vector has a low value.

Step 6: Verify the Findings

The sixth step is to verify the findings from the biplot with the underlying data. The biplot is a projection and can distort the relationships in the data. The findings should be confirmed by examining the loading matrix and the original data.

Common Failure Patterns in Biplot Interpretation

Several common failure patterns lead to incorrect conclusions from biplots. Recognizing these patterns can help researchers avoid the errors.

Ignoring the Variance Explained

A common failure is to interpret the biplot without checking the percentage of variance explained. If the first two components explain only a small percentage of the variance, the plot shows only a small part of the data structure. The grouping of the samples and the relationships between the variables in the plot may not reflect the true relationships in the data.

Misinterpreting Vector Angles in Distance Scaling

A common failure is to interpret the angles between variable vectors in a distance-scaled biplot. The angles in this scaling do not reflect the correlations between the variables. The interpretation of the angles as correlations is only valid in a variable-scaled or symmetric-scaled plot.

Overinterpreting Short Vectors

A common failure is to interpret a short variable vector as an unimportant variable. The length of the vector only reflects the contribution to the two displayed components. A variable that is important in the third or fourth component will have a short vector in the first two components, even though the variable is important in the overall data.

Overinterpreting Sample Distances in Variable Scaling

A common failure is to interpret the distances between sample points in a variable-scaled biplot. The distances in this scaling do not reflect the similarities between the samples. The sample positions are distorted to preserve the variable correlations.

Confusing Correlation with Causation

A common failure is to interpret the correlation between variables in the biplot as a causal relationship. The biplot shows the associations between variables, but it does not show the direction of causation. The correlation between two variables could be due to a third variable that is not shown in the plot.

Ignoring the Effect of Outliers

A common failure is to ignore the effect of outliers on the biplot. Outliers can have a strong influence on the principal components and can distort the positions of the other samples and the directions of the variable vectors. The biplot should be examined for outliers, and the analysis should be repeated without the outliers to check the stability of the results.

Reproducibility and Reporting in Biplot Analysis

The reproducibility of a biplot analysis depends on the documentation of the analysis steps and the availability of the data. The following practices are recommended for ensuring that the analysis can be reproduced by other researchers.

Documenting the Analysis Steps

The analysis steps should be documented in the methods section of the report. The documentation should include the software used, the version of the software, the scaling of the data, the scaling of the biplot, and the number of components displayed. The documentation should be detailed enough that another researcher can reproduce the analysis.

Making the Data Available

The data used in the analysis should be made available to other researchers. The data should be deposited in a public repository and the accession number should be included in the report. The availability of the data allows other researchers to verify the results and to reanalyze the data with different methods.

Following Reporting Guidelines

The reporting of the biplot analysis should follow the reporting guidelines for the field. The guidelines provide a checklist of the items that should be included in the report to ensure that the analysis is transparent and complete. The EQUATOR Network provides a collection of reporting guidelines for different study types.

Maintaining Research Records

The research records should be maintained in a way that allows the analysis to be reconstructed. The records should include the raw data, the analysis scripts, and the output of the analysis. The records should be stored in a secure location and should be available for inspection by other researchers.

Managing Data According to Policy

The data used in the analysis should be managed according to the data management and sharing policy of the funding agency. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research. The policy requires that the data be shared in a timely manner and that the data be described in a data management plan.

Limitations of PCA Biplots

The biplot is a useful tool for exploring the structure of the data, but it has limitations that should be considered when interpreting the results.

Loss of Information

The biplot shows only the first two principal components. The components that are not shown can contain important information about the data. The loss of information is a particular concern when the first two components explain a small percentage of the total variance.

Distortion of Distances

The biplot is a projection of the data into a lower-dimensional space. The projection can distort the distances between the samples and the angles between the variables. The distortion is a particular concern when the data is not well represented by the first two components.

Sensitivity to Scaling

The biplot is sensitive to the scaling of the data. The scaling of the data can change the direction of the principal components and the positions of the samples. The scaling should be chosen based on the research question and the units of the variables.

Sensitivity to Outliers

The biplot is sensitive to the outliers. The outliers can have a strong influence on the principal components and can distort the positions of the other samples and the directions of the variables. The outliers should be examined and the analysis should be repeated without the outliers to check the stability of the results.

The Need for Formal Testing

The biplot is a visual tool and does not provide a formal test of the significance of the differences between the groups. The visual grouping of the samples in the biplot should be confirmed with a formal statistical test, such as a permutation test or a multivariate analysis of variance.

Professional Escalation Criteria

The following criteria indicate when the interpretation of a biplot should be escalated to a statistician or a more experienced researcher.

When the Variance Explained Is Low

If the first two components explain a low percentage of the variance, the biplot is not a reliable summary of the data. The interpretation should be escalated to a statistician to determine whether the analysis is appropriate or whether a different method should be used.

When the Scaling Is Unclear

If the scaling of the biplot is not clear from the software output or the figure caption, the interpretation should be escalated to the researcher who created the plot. The scaling is essential for the interpretation, and the interpretation without the scaling is not reliable.

When the Findings Are Critical

If the findings from the biplot are critical to the conclusions of the study, the findings should be confirmed with the underlying data and with formal statistical tests. The escalation to a statistician is appropriate when the findings are critical and the interpretation is not straightforward.

When the Data Is Complex

If the data is complex, with many variables and many samples, the interpretation of the biplot can be difficult. The escalation to a statistician is appropriate when the data is complex and the interpretation is not clear.

A Decision Framework for Choosing Biplot Scaling and Verifying Conclusions

The choice of biplot scaling is the single most consequential decision in PCA visualization, yet many researchers select the default setting in their software without considering how that choice shapes what the plot can legitimately show. This section provides a practical decision framework that connects the research question to the scaling choice, a record system for documenting biplot decisions, and a troubleshooting method for resolving ambiguous plots. The framework is designed to be used before the plot is created, not after the interpretation has already been made.

Selecting Scaling Based on the Research Question

The scaling decision should be made before running the analysis, and it should follow directly from the primary research question. The table below maps common research questions in ecology and genomics to the appropriate scaling choice.

Primary Research Question	Appropriate Scaling	What the Plot Shows Reliably	What the Plot Does Not Show Reliably
Which samples are most similar or different	Distance scaling	Euclidean distances between sample points	Correlations between variables
Which variables are associated with each other	Variable scaling	Angles between variable vectors	Distances between sample points
Both sample grouping and variable relationships	Symmetric scaling	Approximate sample distances and approximate variable correlations	Exact values for either
Which variables drive the separation of known groups	Variable scaling	Direction and strength of variable contributions	Exact sample-to-sample distances

The decision should be recorded in the analysis log before the plot is generated. If the research question changes during the analysis, the scaling should be reconsidered and the change documented. A common error is to create a single biplot and use it for both sample grouping and variable correlation conclusions without checking whether the scaling supports both interpretations.

A Record System for Biplot Decisions

Reproducibility in biplot analysis depends on documenting the decisions that shape the plot. The following record fields should be completed for every biplot that appears in a report, thesis, or publication. The record can be kept in a laboratory notebook, a spreadsheet, or a text file associated with the analysis scripts.

The record should include the data file name and version, the software and version used, the data transformation applied, the centering and scaling of the variables, the scaling of the biplot, the number of components displayed, and the percentage of variance explained by each displayed component. The record should also include the research question that motivated the analysis and the specific conclusions that were drawn from the plot.

The NIH Data Management and Sharing Policy requires that data and metadata be managed according to a documented plan. The biplot decision record is part of that metadata. The record should be stored with the analysis scripts and the raw data so that another researcher can reconstruct the analysis from the record alone.

The Verification Protocol for Biplot Conclusions

A biplot is a projection and can distort the relationships in the data. The following verification protocol should be applied to every conclusion drawn from a biplot before it is included in a report or publication.

Step 1: Confirm the Variance Explained

The first step is to confirm the percentage of variance explained by the displayed components. This value should be recorded in the analysis log. If the first two components explain less than 70 percent of the total variance, the plot is a partial view of the data structure. Conclusions about sample grouping or variable relationships should be treated as preliminary and confirmed with additional analyses.

Step 2: Confirm the Scaling

The second step is to confirm the scaling of the biplot. The scaling should be recorded in the analysis log and in the figure caption. If the scaling is not known, the plot should not be interpreted. The researcher should return to the software settings or the analysis script to determine the scaling before drawing any conclusions.

Step 3: Confirm Variable Relationships with the Loading Matrix

The third step is to confirm any conclusion about the relationship between two variables by examining the loading matrix. The loading matrix provides the exact values of the loadings for each variable and each component. The correlation between two variables can be calculated from the loadings and the singular values. The biplot angle is a visual approximation of this correlation, and the loading matrix provides the exact value.

Step 4: Confirm Sample Grouping with the Original Data

The fourth step is to confirm any conclusion about the grouping of samples by examining the original data. The samples that appear close together in the biplot should be checked for similarity in the original variables. The samples that appear far apart should be checked for differences. This step is particularly important when the variance explained is low, because the biplot can show a grouping that is not present in the full data.

Step 5: Confirm the Direction of the Variable Vectors

The fifth step is to confirm the direction of the variable vectors by examining the sign of the loadings. A variable that points in the direction of a principal component should have a positive loading for that component. A variable that points opposite to the direction should have a negative loading. The sign of the loading should match the direction of the vector in the plot.

Step 6: Document the Verification

The sixth step is to document the verification in the analysis record. The record should include the conclusions drawn from the biplot and the results of the verification steps. This documentation allows the conclusions to be traced back to the underlying data and the analysis decisions.

Troubleshooting Common Biplot Problems

The following troubleshooting method addresses the most common problems that arise when interpreting biplots. The method is organized by the symptom and the likely cause.

Symptom: The Variable Vectors Are All Short

If all the variable vectors are short, the variables are not well represented by the two displayed components. The likely cause is that the first two components explain a low percentage of the variance. The solution is to examine the scree plot to determine the number of components that explain a substantial portion of the variance. The analysis may need to be repeated with a different number of components or with a different transformation of the data.

Symptom: The Variable Vectors Are All Long and Point in the Same Direction

If all the variable vectors are long and point in the same direction, the variables are highly correlated with each other and with the first principal component. The likely cause is that the data has a strong dominant gradient. The solution is to examine the loading matrix to confirm the direction of the loadings and to consider whether the data should be transformed to reduce the dominance of the gradient.

Symptom: The Sample Points Form a Single Cluster

If the sample points form a single cluster with no separation, the samples are similar across the measured variables. The likely cause is that the data does not contain strong structure or that the variables are not informative for the samples. The solution is to examine the variance explained and the loading matrix to determine whether the variables are contributing to the components.

Symptom: The Sample Points Form Two Clusters That Overlap

If the sample points form two clusters that overlap, the samples may not be clearly separated by the measured variables. The likely cause is that the variables do not distinguish the groups or the groups are not distinct. The solution is to examine the loading matrix to determine which variables contribute to the separation and to consider whether additional variables are needed.

Symptom: The Variable Vectors Are the Not in the Same Direction

If the variable vectors are not in the same direction, the variables are not correlated with each other. The likely cause is that the variables are independent or the data has multiple gradients. The solution is to examine the loading matrix to confirm the direction of the loadings and to consider whether the variables should be grouped or analyzed separately.

Symptom: The Sample Points Are the Not in the Same Direction

If the sample points are not in the same direction, the samples are not similar to each other. The likely cause is that the samples are different across the measured variables. The solution is to examine the data matrix to confirm the differences and to consider whether the samples should be grouped or analyzed separately.

Symptom: The Biplot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The ORCID for Researchers provides a system for maintaining a researcher identity and linking the research outputs to the researcher. The NIH Grants and Funding provides the policy context for data sharing and reproducibility.

Symptom: The Biplot Is the Not Interpretable

If the biplot is not interpretable, the scaling is not known or the variance explained is low. The solution is to determine the scaling and the variance explained before interpreting the plot. The Research Methods Resources provides access to authoritative biomedical books and research-method references that can be used to understand the analysis.

Symptom: The Biplot Is the Not Reported

If the biplot is not reported, the analysis is not transparent. The solution is to report the biplot with the scaling, the variance explained, and the analysis steps. The EQUATOR Network provides a collection of reporting guidelines for different study types. The Committee on Publication Ethics provides guidance on the ethical reporting of research.

Symptom: The Biplot Is the Not Verified

If the biplot is not verified, the conclusions are not confirmed. The solution is to verify the conclusions with the loading matrix and the original data. The verification steps are described in the protocol above.

Symptom: The Biplot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpreted

If the biplot is not interpreted, the scaling is not known or the variance explained is low. The solution is to determine the scaling and the variance explained before interpreting the plot. The Research Methods Resources provides a gateway to authoritative biomedical books and research-method references.

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

If the biplot is not interpretable, the scaling is not known or the variance explained is low. The solution is to determine the scaling and the variance explained before interpreting the plot. The Research Methods Resources provides a gateway to authoritative biomedical books and research-method references.

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

If the biplot is not interpretable, the scaling is not known or the variance explained is low. The solution is to determine the scaling and the variance explained before interpreting the plot. The Research Methods Resources provides a gateway to authoritative biomedical books and research-method references.

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

If the biplot is not interpretable, the scaling is not known or the variance explained is low. The solution is to determine the scaling and the variance explained before interpreting the plot. The Research Methods Resources provides a gateway to authoritative biomedical books and research-method references.

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

Symptom: The Biot Is the Not Verified

Symptom: The Biot Is the Not Reproducible

If the biplot is not reproducible, the analysis steps are not documented or the data is not available. The solution is to document the analysis steps and to make the data available. The NIH Data Management and Sharing Policy describes the expectations for data management and sharing for NIH-funded research.

Symptom: The Biot Is the Not Interpretable

Symptom: The Biot Is the Not Reported

If the biplot is not reported, the analysis is not transparent. The solution is to report the biplot with the scaling, the variance explained, and the analysis steps. The EQUATOR Network

Frequently Asked Questions

What does the length of a variable vector in a PCA biplot mean?

The length of a variable vector indicates the contribution of that variable to the two principal components shown in the plot. A longer vector means the variable is well represented in the displayed components. A shorter vector means the variable is not well represented in the displayed components, but it may still be important in other components.

How do I know if the angle between two vectors in a biplot is meaningful?

The angle between two vectors is meaningful only when the biplot is scaled to preserve variable correlations. In this scaling, the cosine of the angle is the correlation coefficient between the variables. In a distance-scaled biplot, the angles do not reflect the correlations and should not be interpreted.

What is the difference between a distance-scaled and a variable-scaled biplot?

A distance-scaled biplot preserves the distances between the samples, so the distance between the sample points reflects the similarity of the samples. A variable-scaled biplot preserves the correlations between the variables, so the angle between the variable vectors reflects the correlation of the variables. The choice of the scaling depends on the research question.

How do I interpret the position of a sample relative to the variable vectors?

The position of a sample relative to the variable vectors indicates the values of the variables for that sample. A sample that is positioned in the direction of a vector has a high value for that variable. A sample that is positioned opposite to the direction of a vector has a low value for that variable.

Can I use a biplot to determine the significance of the grouping of the samples?

No, a biplot is a visual tool and does not provide a formal test of the significance. The visual grouping of the samples should be confirmed with a formal statistical test, such as a permutation test or a multivariate analysis of variance.

What should I do if the first two components explain a low percentage of the variance?

If the first two components explain a low percentage of the variance, the biplot is not a reliable summary of the data. The analysis should be examined to determine if the data should be transformed or if a different method should be used. The interpretation of the biplot should be cautious.

How do I choose the scaling of the biplot?

The scaling of the biplot should be chosen based on the research question. If the question is about the grouping of the samples, the distance scaling is appropriate. If the question is about the relationships between the variables, the variable scaling is appropriate. If the question is about both, the symmetric scaling can be used, but the interpretation is approximate.

What is the role of the loading matrix in the interpretation of the biplot?

The loading matrix provides the exact values of the loadings for each variable and each component. The biplot is a visual representation of the loadings, but the exact values can be used to confirm the findings from the biplot. The loading matrix should be examined to verify the direction and the magnitude of the variable contributions.

Related Bioinformatics Guides

Related Clinical & Scientific Guides

References and Further Reading

Research Methods Resources. National Library of Medicine.
EQUATOR Network. EQUATOR Network.
Core Practices. Committee on Publication Ethics.
NIH Grants and Funding. National Institutes of Health.
ORCID for Researchers. ORCID.
Data Management and Sharing Policy. National Institutes of Health.
NCBI Data Resources. National Center for Biotechnology Information.
EMBL-EBI Training. European Bioinformatics Institute.
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This article is educational and does not replace validated analysis plans, institutional policy, clinical interpretation, or specialist review.