STATISTICAL METHOD
Discriminant Analysis
Statistical Consulting for Group Classification
We apply linear or quadratic discriminant analysis to groups defined in advance, check covariance and collinearity assumptions, set prior probabilities, and report cross-validated accuracy, not resubstitution results.
No Commitment Required
Strictly Confidential
In-House PhD-Level Statisticians
Fixed Project Fee
Same-Day Response
METHOD OVERVIEW
What Is Discriminant Analysis?
Discriminant analysis is a supervised method that uses continuous predictors to separate groups defined in advance, such as diagnostic categories or product origins, and to classify new cases into them. Linear discriminant analysis forms combinations of the predictors that best separate the groups, assuming roughly multivariate normal predictors within groups and equal covariance matrices. The quadratic form relaxes equal covariances at the cost of more parameters. Performance is judged on cases not used to fit the rule. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, provides discriminant analysis within your study design, with the relevant checks, estimates, uncertainty measures, interpretation and publication-ready reporting.
WHEN TO ENGAGE
When Is Classifying Known Groups Appropriate?
This method fits a question about assigning cases to groups that already exist, and these are the research situations in which researchers most often ask us to apply or confirm it.
Classifying Into Known Groups Cases belong to known groups, such as diagnostic categories or origins, and a rule built on several continuous measures is needed to assign new cases.
Describing What Separates Groups The question is which combination of measures separates predefined groups, and the discriminant functions and structure coefficients are read to describe the separation.
Imbalanced Groups or Many Predictors One group is much smaller than the others, or predictors are many for the cases available, so priors, validation and stability need explicit handling.
Reviewing a Completed Analysis A classification rate was taken from the training data, and a reviewer has questioned it. Independent Statistical Review verifies the validation and the accuracy figures.
ANALYTICAL APPROACH
How We Apply Discriminant Analysis
Within the family of Multivariate, Scale & Reliability, a classification rule is judged by how it performs on new cases, not by how it fits the sample.
Covariance and Collinearity We examine normality within groups, equal covariance matrices, using Box's M cautiously because it is sensitive to non-normality, and collinearity, then choose linear, quadratic or a regularized form.
Priors and Group Sizes Prior probabilities are set from population prevalence or deliberately equal, and stated, because they move the classification boundary, especially when the groups differ greatly in size.
Honest Validation Accuracy is estimated by cross-validation or an independent test set, never by resubstitution on the training data, and reported for each group beside the overall rate.
Predictors and Sample Size The number of predictors is kept small relative to the smallest group, since many predictors overfit. Any variable selection is repeated inside each validation fold to avoid optimistic estimates.
DELIVERABLES
What You Receive
As part of our Quantitative Data Analysis service, the classification is delivered with the estimates, checks and files needed to report and defend it.
Data & Variable Review Group definitions, group sizes, predictor scales, outliers, missing values and strongly correlated predictors are reviewed, and the priors are agreed with you before any rule is fitted.
Method-Specific Checks Within-group distributions, covariance equality, collinearity and the influence of single cases are examined, with quadratic or regularized forms compared where the linear assumptions look doubtful.
Statistical Results Discriminant functions with standardized coefficients and structure coefficients, group centroids, the confusion matrix, and cross-validated accuracy overall and for each group with intervals.
Publication-Ready Tables & Figures Classification tables, discriminant score plots and coefficient tables, formatted to APA 7 or the journal's requirements, ready to insert into the manuscript.
Interpretation Separation is described through the structure coefficients and the validated performance, with the effect of priors and group sizes stated, and without reading coefficients as causal effects.
Reproducible Analysis Files R scripts, SPSS syntax, Stata do-files or SAS code are provided where applicable, so the rule, the folds and the accuracy estimates can be rerun if the data change.
ALTERNATIVE METHODS
When Another Method May Be More Appropriate
We choose the method by the outcome and the assumptions the data can support. These methods fit binary or multiple groups with fewer assumptions, unknown groups or a test of group means.
01
Logistic Regression
With two groups, mixed predictor types or clearly non-normal predictors, logistic regression models the group probabilities directly and reports odds ratios with intervals.
02
Multinomial Logistic Regression
With three or more unordered groups and predictors that are not multivariate normal, a multinomial model estimates class probabilities without assuming equal covariances.
03
Cluster Analysis
When no group labels exist and the question is whether cases fall into groups at all, clustering searches for that structure without an outcome to train on.
04
MANOVA
When the question is whether group means differ on several outcomes together, not how to classify new cases, MANOVA tests that difference directly and reports effect sizes.
CASE EXAMPLE
How We Work in Practice
An illustration of how a classification question moves from a planned model to a reportable, defensible result.
ILLUSTRATIVE EXAMPLE · FOOD AUTHENTICITY TESTING · UNITED STATES
A food testing laboratory measured fatty acid and phenolic compounds in olive oils from three known regions and needed a rule to classify the origin of new samples.
The plan, fixed before any classification was run, chose linear discriminant analysis with equal priors and repeated stratified cross-validation as the primary performance estimate. The compounds were strongly collinear, and one region had far fewer samples than the others. We therefore reduced the compounds inside each training fold, so the validation stayed honest, and compared quadratic and regularized forms as sensitivity analyses. Accuracy for each region was reported beside the overall rate, each with a bootstrap interval, because the small region could be misclassified with little effect on the overall figure.
Outcome: The laboratory received cross-validated accuracy overall and by region with bootstrap intervals, the confusion matrix, the discriminant functions, the comparison of forms, the scripts and a methods paragraph.
This example does not describe a real client or project. We never share details of actual client work, in line with the confidentiality we promise every researcher. This illustrative example is included to show the type, scope, and standard of work involved in this kind of analysis.
SOFTWARE
Statistical Software for Group Classification
Classification rules are run in the statistical software researchers already use, with syntax or scripts provided where applicable.
RESEARCH DISCIPLINES
Classification Across Research Fields
Assigning cases to known groups from several measurements is common in applied research, and each field brings its own groups, predictors and standards for validating a rule.
A Defined Process for Your Analysis
We review your dataset, research question and design before any work begins, so the scope, deliverables, timeline and fixed project fee are clear from the outset.
01
Share Your Research Materials
Send your dataset, research question, study design and any existing analysis plan or output. We will let you know if anything else is needed to assess the project.
02
Receive Your Assessment
Your statistically trained Research Coordinator reviews the project and confirms the required analysis, deliverables, timeline and fixed project price before work begins.
03
Analysis & Delivery
Once you confirm the scope, an in-house statistician completes the agreed analysis and delivers the outputs, interpretation and reporting files.
RESEARCHER VOICE
What Researchers Say
Feedback from a researcher who wanted a second review of overlapping predictors and unstable coefficient estimates.
“I wanted a second set of statistical eyes on our Discriminant Analysis, mainly because of overlapping predictors and unstable coefficient estimates. The review was practical and specific, and the final results were much easier to explain to the rest of the research team. The final reporting was much easier to use in the manuscript and in responding to reviewer comments.”
RESEARCH RESPONSIBILITY
Statistical Support Without Taking Over Your Research
We provide the statistical work for your classification, and the study, its meaning and its authorship stay entirely with you.
Agreed Statistical Support We provide the agreed methodological, analytical and statistical reporting support for your classification, within the scope confirmed before work begins.
No Intellectual Contribution OnlineSPSS claims no intellectual contribution to your research. Our work is statistical support, and authorship remains yours.
Your Research Decisions The research question, the definition of the groups, interpretation and conclusions remain with you, and our statistical interpretation stays within what the data and the design support.
Confidential Handling Research data and project details are handled confidentially and are not published. An NDA is available where required, and can be arranged before sensitive materials are shared.
FREQUENTLY ASKED QUESTIONS
Questions About Classifying Known Groups
Short answers to what researchers ask before a classification analysis, from logistic regression and validation to confidentiality and the assessment process.
Should I use discriminant analysis or logistic regression?
Logistic regression is often the safer choice, because it needs fewer distributional assumptions and handles mixed predictors. Discriminant analysis can classify more efficiently when its own assumptions hold, meaning roughly normal predictors with equal covariances in each group, and it extends naturally to several groups and to describing separation. We compare both on cross-validated performance and state the reasoning.
Why is cross-validated accuracy lower than training accuracy?
Training accuracy is optimistic, because the rule was fitted to the same cases it is scored on, especially with many predictors and few cases. Cross-validation scores each case with a rule that never saw it, so it estimates how the rule would perform on new cases. A large gap signals overfitting, and the lower figure is the one to report.
Does high overall accuracy mean the groups are well classified?
Not when group sizes are very unequal. If one group is small, a rule can classify nearly all cases into the large groups, score a high overall rate and still misclassify most of the small group. We report accuracy for each group with the confusion matrix, consider balanced accuracy, and set the priors with care.
Can you review an analysis that has already been completed?
Yes, we can review a completed classification analysis before submission or a response to reviewers. We check the assumptions, the priors, how accuracy was estimated, whether variable selection leaked into the validation, the group-level performance and the reporting, and confirm what stands or needs to change.
How do you protect my dataset and research confidentiality?
Your dataset, output files and any protocol or analysis plan are handled confidentially, and project information is not published. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
Still have a question? Find more answers in our full FAQ.
NEXT STEP
Need Support With
Classifying Known Groups?
Share your research question, groups and data. We assess whether a discriminant rule fits your aim and confirm the method before any work begins.
No Commitment Required
Strictly Confidential
Fixed Project Fee
In-House PhD-Level Statisticians
Same-Day Response
Serving Researchers Since 2014