METHOD GUIDE
GLM Repeated Measures in SPSS
Sphericity, Corrections and Contrasts Explained
The output offers several versions of the same within-subjects test, and the decision about which to report rests on sphericity. This guide covers the checks, how to read each table, and how to report the result in APA 7 with its adjusted degrees of freedom.
IN SHORT
What the Procedure Tests and How to Read Its Tables
GLM Repeated Measures is the SPSS procedure that compares the means of one outcome measured under several conditions or occasions on the same participants, and it can add a between-subjects factor to the model. The test of the within-subjects effect is reported in more than one form, because its standard version assumes sphericity, an equal-variance condition on the differences between levels. To run GLM repeated measures in SPSS, open Analyze, General Linear Model, Repeated Measures, name the within-subjects factor and its number of levels, assign the variables in their true order, and read Mauchly’s test with the epsilon estimates before choosing a row. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, carries out and reviews this analysis through an in-house PhD-level statistician.
ANALYSIS SUPPORT
Analysis Support for This Method
Reading the tables is the last step. For the within-subjects analysis carried out on your own data, or for a design that adds a group factor to the repeated measurements, see the pages below.
Repeated Measures ANOVA
The within-subjects comparison carried out within your study design, with the sphericity handling, the follow-up comparisons, effect sizes and the reporting agreed for your data.
Mixed ANOVA
The design that combines repeated measurements with a between-subjects factor, where the question is whether change over conditions differs between groups.
BEFORE YOU RUN IT
Setting Up a Within-Subjects Model
The procedure asks for a name and a number of levels before it asks for any data, and the decisions below determine whether the tables that follow can be read as intended.
Wide Format, Complete Cases Each participant is one row with one column per level. A participant missing any level is dropped from the analysis, so the number of complete cases is checked against the intended sample.
Name and Order of Levels The levels of the SPSS within-subjects factor must match the order of the variables moved into it. A swapped order silently relabels the conditions, and every contrast then answers a different question.
Conditions or Time Points Counterbalanced conditions need an order check, while time points raise the question of spacing. Trend contrasts assume ordered levels, and unequal intervals need the contrast chosen with care.
Between-Subjects Factors Adding a grouping factor turns the question into one about whether change differs between groups. The interaction then matters more than the main effect of time or condition.
IN SPSS
How to Run GLM Repeated Measures in SPSS
The outline is for IBM SPSS and covers only the steps that shape the output. Dialog labels vary by version, so check them against your own installation.
- Arrange the data with one row per participant and one column per level, and note the order.
- Open Analyze, General Linear Model, Repeated Measures, and name the within-subjects factor and its number of levels.
- Define the factor by moving the variables into the levels in the right order, and add any between-subjects factor.
- Choose the contrast type in Contrasts, and request estimated marginal means for pairwise comparisons with an adjustment.
- Under Options, request descriptives, effect size estimates and the homogeneity checks that apply.
- Read Mauchly’s test first, then the within-subjects tests, then the contrasts or pairwise comparisons.
READING THE OUTPUT
What Each Part of the SPSS Repeated Measures Output Tells You
The same within-subjects effect appears in several tables, and Mauchly's test with its epsilon estimates guides which of them carries the reported result.
| Output element | What it tells you | What to check |
|---|---|---|
| Within-Subjects Factors | The levels and the variable assigned to each | That the order of levels matches your intended design |
| Mauchly’s Test of Sphericity | Whether the variances of the differences between levels are equal, and epsilon estimates | That it is read with epsilon, since it has low power in small samples and flags trivial departures in large ones |
| Tests of Within-Subjects Effects | One F test in several rows: sphericity assumed and the epsilon-adjusted versions such as Greenhouse-Geisser | That the row chosen is justified by epsilon and reported with its adjusted degrees of freedom |
| Multivariate Tests | A test of the same effect that does not require sphericity | That it is considered when sphericity is doubtful and the sample is large relative to the levels |
| Tests of Within-Subjects Contrasts | Specific comparisons across levels, such as linear and quadratic trends by default | That the contrast type matches the question, since trends make no sense for unordered conditions |
| Pairwise Comparisons | Differences between estimated marginal means with an adjustment you select | That the adjustment and the family of comparisons are named in the text |
| Partial Eta Squared | An effect size for each effect, if requested in Options | That it is labeled partial, and that the same effect size is used throughout |
REPORTING
The APA 7 Template for a Within-Subjects Result
Read the wording below as a frame: your own output fills each blank, and no result is stated.
Start with the sphericity result and the corrected test used: F(df1, df2) = ___, p = ___, partial eta squared = ___, using the adjusted degrees of freedom exactly as printed (the GLM output gives no interval for partial eta squared, so any interval comes from another program). State the epsilon value and which adjustment it relates to. Then report the contrasts or pairwise comparisons that answer the research question, as mean differences with adjusted intervals, and name the adjustment. Give the mean and standard deviation at every level and the number of complete cases. In a design with a between-subjects factor, report the interaction before the main effects.
COMMON MISTAKES
Mistakes Reviewers Find in Reported Within-Subjects Models
Six errors prompt most reviewer queries on a within-subjects analysis, and most arise between the sphericity table and the follow-up comparisons.
Correction Picked by p-Value Selecting the sphericity-assumed row when it gives the smaller p-value, and a corrected row otherwise, is an undeclared choice. The rule is fixed first and is stated in the report.
Mauchly's Test Alone A single non-significant p-value does not establish sphericity, because the test has little power with few participants. Epsilon and the adjusted rows give the more useful picture.
Trend Contrasts for Conditions Polynomial contrasts are the default and describe trends across ordered levels. For three treatment conditions with no natural order, a linear trend is meaningless as a finding.
Participants Dropped Silently A participant with one missing level leaves the analysis without any message in the main table. Complete cases are counted, and the pattern of missing data is discussed.
Unadjusted Pairwise Comparisons Several follow-up comparisons without an adjustment inflate the chance of a false positive, and the default in the dialog is no adjustment. The adjustment is chosen and named.
Effect Size Not Labeled Partial eta squared depends on the design and is not comparable with an eta-squared from a between-subjects model. The text says which one is used, and the same one throughout.
Run the model already? Independent Statistical Review checks the sphericity handling, the row you reported and the follow-up before you submit.
FREQUENTLY ASKED QUESTIONS
Questions About Repeated Measures Output
Short answers to what researchers ask about the sphericity table and the rows that follow it, from corrections and contrasts to confidentiality and the assessment.
Which row of Tests of Within-Subjects Effects do I report?
Report the row justified by your sphericity evidence and decided before you look at p, and state which one it is. When sphericity is plausible the sphericity-assumed row is acceptable, and when epsilon is clearly below 1 an epsilon-adjusted row is the safer choice. Many analysts report an adjusted row by default, and the multivariate tests are another option when the sample allows.
Why does Mauchly's test in SPSS show no p-value?
With only two levels there is a single difference score, so sphericity cannot be violated, and SPSS prints Mauchly’s W as 1 with zero degrees of freedom and no significance value. No correction is needed, and the rows of the within-subjects table agree. With three or more levels, read the test together with the epsilon estimates, because it has little power in small samples and flags trivial departures in large ones.
How do I follow up a significant within-subjects effect?
Choose the follow-up from the question. Contrasts suit a planned comparison, such as each time point against the baseline or a trend over ordered occasions. Pairwise comparisons of the estimated marginal means suit an unplanned set, and they need an adjustment. If data are missing or timing is irregular, Linear Mixed Models (Multilevel Modeling) may fit better.
Can OnlineSPSS check the sphericity handling in my repeated measures model?
Yes. An in-house PhD-level statistician can check the order of the levels, the row you reported and the follow-up comparisons in your output, or carry out the analysis on your data from the start. When the analysis is settled and the tables need attention, Results Reporting & Interpretation covers that stage. The research question, the interpretation and the conclusions remain with you.
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 dataset or the output you have, 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.
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