RESEARCH SUPPORT
ANOVA test support
for choosing the right ANOVA for your design
Which ANOVA to use follows from the experimental unit and the error term behind each effect, not from the number of groups. Follow-up comparisons are planned before any results are seen, with assumptions judged in context.
No Commitment Required
Strictly Confidential
In-House PhD-Level Statisticians
Fixed Project Fee
Same-Day Response
What Does Matching an ANOVA to a Design Involve?
ANOVA test support starts with the experimental unit, the thing that was independently assigned or measured, because it sets the error term behind each effect and decides which ANOVA to use. One outcome measured on the same people can call for a one-way, factorial, repeated measures or mixed model, depending on who was assigned to what and how often each person was measured. Choosing a post hoc test follows from that model, so that the follow-up comparisons answer the research question with error control across them. The in-house PhD-level statisticians who settle these choices with the researcher work at OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research. The reasons are recorded beside the results.
WHEN TO ENGAGE
Experiments Waiting for a Model Choice
Which analysis applies is often unclear until it is known how participants were allocated and how many times each was measured.
Allocation Not Yet Final A study with several groups or conditions is being planned, and the model, the number of replicates per cell and the follow-up comparisons should be settled while the design can still change.
Same Participants, Many Conditions Each participant is measured under every condition or at several times, so the observations are not independent and the model has to reflect that dependence in its error term.
A Baseline Measure Exists Participants were measured before and after, and the researcher must choose between analyzing change, adjusting for the baseline and modeling both time points together.
Output From a Default Model A model was run with its default settings, and the question is whether its error term, its tests and its follow-up comparisons actually suit the way the study was run.
DESIGN AND MODEL FAMILY
Fitting the Model to the Way Data Were Collected
The family is read from the design: how groups were formed, how often each unit was measured and what else was recorded.
Groups Formed by Allocation
Groups formed by random allocation on one factor point to One-Way ANOVA, extended to a factorial layout when several factors are crossed and their interaction is of interest.
Repeated Conditions
When each participant provides a measurement under every condition, Repeated Measures ANOVA fits the structure, and assumptions about the correlations among conditions are examined.
Between and Within Factors
A group factor combined with repeated measurements is a case for Mixed ANOVA, where the group-by-time pattern usually carries the research question and the error terms differ by effect.
Covariate Adjustment
A covariate such as a baseline score enters through ANCOVA, whose assumption about how the covariate relates to the outcome in each group is checked before adjusted means are reported.
Contrasts and Comparisons
Which pairs or contrasts matter, and which method of error control covers them, is decided with the research question, with planned contrasts replacing blanket pairwise tests where the hypotheses allow.
Effects and Reporting
Effect sizes with confidence intervals and the checks on assumptions are reported in line with the conventions of Comparative & Hypothesis Testing, with the cell sizes stated.
MODEL MISMATCHES
Mismatches Between an ANOVA and the Study It Analyzes
Output from the wrong model looks as orderly as output from the right one, so a mismatch shows up only when the model is compared with the design.
Rows Mistaken for Units Each row of the data file is taken as the experimental unit, though conditions were randomized to blocks or clusters of rows, so the analysis treats rows as if each had been assigned on its own.
One Error Term for Every Effect Between-unit and within-unit factors are tested against one pooled residual, when the between-unit effects need the variation among units as their error term, and those tests turn out too liberal.
One Missed Session, One Lost Participant A participant missing one session is dropped from the whole within-subjects analysis, which shrinks the sample and assumes the gaps are unrelated to the outcome, whereas a model fitted to every available observation keeps that participant.
Post Hoc Chosen by Habit One pairwise procedure is applied to every design by default, though some designs call for planned contrasts, and procedures differ in how they control error and in power.
Bounded Outcomes in a Normal Model A count of events or a percentage correct, with many values at zero or at the ceiling, is analyzed with a model built for continuous outcomes, where a model for counts or proportions would describe the data better.
Covariate Changed by Treatment A covariate that the treatment itself influenced, or whose relation to the outcome differs across groups, is adjusted for as if it were a neutral baseline.
DELIVERABLES
A Design Memo and the Models It Specifies
The memo, the model files and the comparison list show a methods reviewer why each analysis was chosen and what its tests refer to.
Design Memo A short account of factors, levels, the experimental unit and the allocation, with the model family that follows from them and the reason each alternative was set aside.
Model Choice Record For each outcome, the fixed and random terms, the error term used for each test and the handling of unequal cell sizes, stated before the results are interpreted.
Assumption Review Residual plots and spread by group, with a judgment of how far each departure matters for the conclusions and what a robust alternative would change if it were used.
Planned Comparison List The contrasts or post hoc comparisons that answer the research question, the family of tests they belong to and the method of error control applied across that family.
Effect Estimates Group means or model-based means with confidence intervals and a standardized effect size suited to the design, together with the sample sizes per cell.
Annotated Model Syntax The commands for every model, annotated with the design feature each setting represents, so that a collaborator can rerun the analysis and see why it was specified that way.
ILLUSTRATIVE EXAMPLE
Choosing the Model for an Incubation Experiment
An illustration of how a crossed design with repeated measurements is matched to a model that counts the right units.
ILLUSTRATIVE EXAMPLE · SOIL MICROBIOLOGY INCUBATION RESEARCH · UNITED STATES
A doctoral researcher in soil microbiology incubated soil samples at three moisture levels and two temperatures and measured microbial respiration in the same jars at four time points.
The design was factorial with repeated measurements on each jar, so the plan treated the jar as the experimental unit, specified a model with the moisture-by-temperature interaction as the primary test and named the follow-up comparisons before any results were examined. The complication was that several subsamples had been taken from each jar and entered as if they were separate replicates, which would have multiplied the apparent sample size. The subsamples were averaged within the jar, the unequal number of jars per cell was recorded together with the sums of squares used, and the departures from the assumptions were judged from the residuals and from a robust alternative.
Outcome: The researcher received the design memo, the model choice record, the planned comparison list, the effect estimates with 95% confidence intervals, the assumption review and the annotated syntax.
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
Fitting Factorial, Repeated and Mixed Layouts
Factorial, repeated-measures and mixed layouts can be fitted in each program, though some display the error term and the sums of squares type more plainly than others.
HOW WE ASSESS YOUR PROJECT
We Review Your Actual Research
Your assessment is based on a review of your actual research materials and analytical requirements, not a generic project category.
You Submit Your Project Details
Share whatever is available at the current stage, such as the research aim, protocol or proposal, dataset, variable list, manuscript or statistical requirements.
We Review Your Research and Define the Scope
Your statistically trained Research Coordinator reviews the materials to understand the study design, research questions, data structure, analytical requirements and expected deliverables. If clarification is needed, additional documents or information can be requested before the assessment is finalized.
Your Analysis Is Completed and Delivered
Once the scope and fixed project fee are agreed, the in-house statistician completes the work and the Research Coordinator remains the communication point through delivery, with the analysis, deliverables and timeline as agreed.
RESEARCH RESPONSIBILITY
Design Facts and Conclusions Rest With the Researcher
Only the researcher knows how participants were recruited and assigned, so the account of the design comes from you and the model follows it.
Agreed Statistical Support OnlineSPSS provides the agreed methodological, analytical and statistical reporting support, defined in a scope that is confirmed before any work begins.
No Intellectual Contribution OnlineSPSS does not claim any intellectual contribution to your research. Authorship of the article, thesis or report remains yours.
Your Research Decisions The hypotheses, the design itself, the substantive interpretation of the group differences and the conclusions remain yours, with overall responsibility.
Confidential Handling Research data and project details are handled confidentially, project information is not published, and an NDA is available where required.
FREQUENTLY ASKED QUESTIONS
ANOVA Planning, Contrasts and Units of Analysis
Planned contrasts, the unit that counts as a replicate and the timing of the model decision lie behind many revised analyses of variance.
How do I know which ANOVA to use for my study?
The experimental unit and its error term decide which ANOVA to use, so two questions come first: what was independently assigned to a condition, and was any unit measured more than once? A cage, class or batch assigned together is one unit however many animals, pupils or samples it holds. Once those answers are fixed, the crossed factors, the repeated measurements and any baseline covariate select the model, and the error term for each effect follows. ANOVA test support covers that reading of the design, the follow-up comparisons and effects reported with confidence intervals.
Can planned contrasts replace post hoc tests?
Yes, when the comparisons of interest are specified before the data are examined and are few. Planned contrasts test the hypotheses directly and usually have more power than a blanket pairwise procedure. A contrast chosen after seeing which means differ is not planned, and it belongs with the post hoc comparisons and their error control. Choosing a post hoc test then depends on the comparisons wanted and the data: Tukey’s procedure suits all pairwise comparisons when variances are reasonably similar, Games-Howell suits unequal variances, Dunnett suits comparisons of each group with a control, and Holm or Bonferroni adjustments suit a prespecified subset of comparisons.
Can one model combine a baseline covariate with repeated measurements?
Usually. A covariate measured once can enter a model that has both group and repeated factors, where it adjusts the group comparison, and it is mean-centered so that the test of the repeated factor keeps its meaning. A covariate that changes from one occasion to the next needs a model that allows time-varying predictors, which an ordinary ANOVA does not.
Should the model be chosen before or after looking at the data?
Before, from the design and the research question. Checking assumptions on the data is appropriate and can change the method, but trying several models and reporting the one with the smallest p-value inflates false positives. Where the data force a change, it is reported as a departure from the plan with its reason.
How do you protect my research data and confidentiality?
Your data and project details are handled confidentially, and project information is not published. Researcher names and institutions are not used publicly without permission. 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, such as the design description, the allocation scheme and the dataset, 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
Your Design Points
to the Model Family
Which participants, animals or samples count as independent, and which factors are crossed with which, decide the analysis more than any software menu does, and both are known before data collection ends.
No Commitment Required
Strictly Confidential
Fixed Project Fee
In-House PhD-Level Statisticians
Same-Day Response
Serving Researchers Since 2014