Quick Answer: Mixed MANOVA Result

The worked Mixed MANOVA example shows that female students have higher mean grade profiles than male students across G1, G2 and G3. The female profile is about 11.64 at G1, 11.83 at G2 and 12.26 at G3. The male profile is about 11.06 at G1, 11.21 at G2 and 11.41 at G3.

The follow-up long-format ANOVA p-value chart shows a significant group effect and a significant repeated-measure time effect. The group p-value is 6.044e-07, the grade_time p-value is 0.007166, and the grade_time × group interaction p-value is 0.6854. This means the two groups differ overall and the grade measures change across time, but the group difference does not change strongly across G1, G2 and G3.

What Is Mixed MANOVA?

Mixed MANOVA is a multivariate repeated-measures design that combines repeated dependent measures with a between-subject grouping factor. It is related to Mixed ANOVA, but it emphasizes the repeated outcomes as a multivariate profile rather than treating each outcome as a completely separate analysis.

In this worked example, G1, G2 and G3 are repeated grade measures from the same students. The group factor is sex, with female and male profiles compared across the repeated grade measures. The mean profile chart shows that the female profile is above the male profile at all three time points.

The repeated-measure correlation matrix strongly supports the multivariate repeated-measures design. G1 and G2 correlate at 0.86, G2 and G3 correlate at 0.92, and G1 and G3 correlate at 0.83. These strong positive correlations show that the repeated grade measures belong together as one grade profile.

Mixed MANOVA is best understood together with Fixed Effects ANOVA, Factorial ANOVA, ANOVA in SPSS, ANOVA in Python, ANOVA in R, ANOVA Assumptions, Eta Squared, and Effect Size.

Mixed MANOVA Formula

A Mixed MANOVA model represents repeated dependent variables as a multivariate outcome profile and compares that profile across a between-subject factor.

For this worked example, the model becomes:

The group term tests whether female and male students have different overall grade profiles. The grade_time term tests whether the repeated measures differ across G1, G2 and G3. The interaction term tests whether the repeated-measure pattern differs by sex group.

Profile Difference

The mean profile chart shows female scores above male scores at each repeated measure. This supports the significant group p-value shown in the follow-up chart.

Repeated-Measure Change

The change-score chart reports F: G2 − G1 = 0.19, F: G3 − G1 = 0.62, M: G2 − G1 = 0.15, and M: G3 − G1 = 0.35. Both groups improve from G1 to later measures, and the female group shows a larger G3 − G1 increase.

Follow-up ANOVA Sources

The follow-up p-value chart reports grade_time p = 0.007166, group p = 6.044e-07 and interaction p = 0.6854. The group and repeated-time effects are statistically significant at .05, while the interaction is not statistically significant.

Mixed MANOVA Hypotheses

Mixed MANOVA has three practical hypothesis areas: the group profile difference, the repeated-measure profile change, and the group-by-time profile interaction.

Dataset and Variables Used

The worked example uses student performance data with three repeated grade measures. The repeated measures are G1, G2 and G3. The between-subject group is sex. The chart labels use sex = F and sex = M.

For supporting concepts, review Descriptive Statistics, Mean Median and Mode, Standard Deviation, Variance, Confidence Interval, F Distribution, P Value, and Null and Alternative Hypothesis.

Python Chart-by-Chart Interpretation

The Python chart sequence explains the Mixed MANOVA result through mean profiles, individual repeated profiles, change scores, follow-up p-values, repeated-measure correlations, residuals versus fitted values and residual Q-Q diagnostics.

Python Chart 1: Mixed MANOVA Mean Profile

This chart shows the repeated grade profile for female and male students. The female profile is above the male profile at G1, G2 and G3. Female mean scores rise from about 11.64 at G1 to about 12.26 at G3, while male mean scores rise from about 11.06 at G1 to about 11.41 at G3.

The two lines move upward across grade time, so both groups show improvement from G1 to G3. The vertical separation between the lines explains the significant group p-value in the follow-up chart.

The lines do not cross, and the group separation remains visible across all three repeated measures. However, the formal interaction p-value is not significant, so the main interpretation should focus on overall group difference and overall repeated-time change.

Python Chart 2: Individual Repeated Profiles

This chart shows individual student profiles across G1, G2 and G3. The thin lines vary widely. Some students improve, some stay almost flat, and some decline. One visible trajectory begins at zero and rises sharply by G2, showing that individual repeated-measure patterns can be very different from the average line.

The bold overall mean profile rises gradually across the repeated grade measures. This matches the significant grade_time p-value and shows that the average repeated-measure movement is upward.

The chart explains why Mixed MANOVA is useful. It respects the repeated nature of the data while summarizing the average profile across many different individual trajectories.

Python Chart 3: Change-Score Profile

This chart summarizes within-student movement from G1 to later grade measures. For female students, G2 − G1 is about 0.19 and G3 − G1 is about 0.62. For male students, G2 − G1 is about 0.15 and G3 − G1 is about 0.35.

Both groups show positive average change scores. The female group has the larger final change from G1 to G3, but the formal interaction result remains non-significant.

This chart should be used as practical interpretation rather than as the only statistical decision. It shows the direction and size of change scores, while the follow-up p-value chart gives the formal source decisions.

Python Chart 4: Follow-up ANOVA P-Values

This chart provides the formal follow-up source decisions. The group source has p = 6.044e-07, the grade_time source has p = 0.007166, and the grade_time × group interaction has p = 0.6854.

The group and grade_time bars are below the alpha line at .05. The interaction bar is far above the alpha line. This means the group profiles differ overall, and repeated measures differ across G1, G2 and G3, but the repeated-time pattern does not differ strongly by group.

This chart is the most important decision chart in the article. It should be reported after the profile and change-score charts because it confirms which visible patterns are statistically supported.

Python Chart 5: Repeated-Measure Correlation Matrix

The correlation matrix shows strong positive relationships among the repeated grade measures. G1 and G2 correlate at 0.86, G2 and G3 correlate at 0.92, and G1 and G3 correlate at 0.83.

These correlations support the multivariate repeated-measures design. The repeated measures are not unrelated outcomes. They form a connected grade profile.

This chart should be used to justify Mixed MANOVA before presenting follow-up results. Strong repeated-measure correlations show why a profile-based method is appropriate.

Python Chart 6: Residuals vs Fitted Values

The residuals-versus-fitted chart shows fitted-value bands around the group and repeated-measure means. Most residuals are spread around the zero reference line, but several negative residuals extend far below zero, reaching roughly the -12 range.

The vertical banding appears because the fitted model is based on group and repeated-measure combinations. The spread shows that individual scores still vary substantially around the model-fitted profile means.

This diagnostic chart supports a cautious reporting statement. The profile effects are meaningful, but the model does not perfectly explain individual grade outcomes.

Python Chart 7: Residual Q-Q Plot

The residual Q-Q plot shows clear tail departure from the normal reference line. The central points follow an increasing pattern, but the lower tail falls well below the reference line.

The most negative residual values create the strongest departure. This matches the residuals-versus-fitted plot, where several cases fall far below zero.

The final report should mention that residual normality is approximate rather than perfect. The group and grade-time effects remain interpretable, but diagnostics should be reported honestly.

R Chart-by-Chart Validation

The R validation charts repeat the same Mixed MANOVA workflow in a second software environment. They confirm the mean profile, individual repeated profiles, change-score pattern, follow-up p-values, repeated-measure correlations and residual diagnostics.

R Chart 1: Mixed MANOVA Mean Profile

The R mean profile confirms the same pattern as the Python chart. Female students have higher mean scores than male students across G1, G2 and G3.

Both lines increase from G1 to G3, with the female line rising more visibly by the final grade measure. The group separation remains stable across the repeated measures.

This validation chart confirms that the group profile pattern is not software-specific.

R Chart 2: Individual Repeated Profiles

The R individual profile chart confirms strong variation among students. The repeated profiles do not all move in the same way, but the bold mean profile still rises from G1 to G3.

The individual trajectories explain why a repeated-measures design is needed. Each student contributes multiple related measurements, not separate independent observations.

The chart supports the practical message that the average repeated-measure pattern is upward while individual change remains heterogeneous.

R Chart 3: Change-Score Profile

The R change-score chart confirms the same numeric pattern. Female students show about 0.19 for G2 − G1 and 0.62 for G3 − G1. Male students show about 0.15 for G2 − G1 and 0.35 for G3 − G1.

The final change from G1 to G3 is larger than the short change from G1 to G2 for both groups. This supports the repeated-measure time effect.

The chart also shows that female change is larger in the displayed averages, but this should not be overreported as a significant interaction because the interaction p-value is high.

R Chart 4: Follow-up ANOVA P-Values

The R p-value chart confirms the same follow-up decisions. The group effect is significant, the grade_time effect is significant, and the interaction is not significant.

The interaction bar is much larger than the .05 alpha line. This confirms that the repeated-measure pattern does not differ strongly by group in the follow-up test.

This validation chart should be used to support the final statistical interpretation.

R Chart 5: Repeated-Measure Correlation Matrix

The R correlation matrix confirms the same strong repeated-measure structure. G1-G2 is 0.86, G2-G3 is 0.92, and G1-G3 is 0.83.

These values show that the repeated grade measures are highly related. This validates the multivariate repeated-measures design.

The chart is useful for explaining why Mixed MANOVA is preferable to disconnected outcome-by-outcome testing.

R Chart 6: Residuals vs Fitted Values

The R residual chart confirms the same diagnostic pattern. Residuals are centered around zero overall, but several negative residuals are far from the center.

The fitted-value bands appear because the model predicts group and repeated-measure profile means. The residual spread shows that individual scores still contain unexplained variation.

This chart supports a balanced conclusion: the profile effects are statistically meaningful, but the diagnostic pattern should still be reported.

R Chart 7: Residual Q-Q Plot

The R Q-Q plot confirms the same tail departure. The lower tail is the strongest source of non-normal behavior, while the central residuals follow the general trend more closely.

This does not erase the group or grade-time effects. It gives diagnostic context for the final report.

The correct interpretation is that the repeated-measure and group profile findings are useful, while residual normality should be described as imperfect.

SPSS Output and R Report PDFs

The supplied report files support the Mixed MANOVA workflow. The R report provides validation charts, and the SPSS output PDF provides menu-based output for reporting.

Download Mixed MANOVA R Report PDF

Download Mixed MANOVA SPSS Output PDF

Output Items to Read

SPSS, R, Python and Excel Workflows for Mixed MANOVA

The same Mixed MANOVA workflow can be reproduced in SPSS, R and Python. Excel can prepare profile charts, change scores and correlation matrices, but the formal model should be run in SPSS, R or Python because the design uses repeated measures and a between-group factor.

SPSS Workflow

R Workflow

Python Workflow

Excel Workflow

Code Blocks for Mixed MANOVA

SPSS Syntax for Mixed MANOVA

* Mixed MANOVA / repeated-measures multivariate GLM in SPSS.
* Repeated measures: G1 G2 G3.
* Within-subject factor: grade_time.
* Between-subject factor: sex.

TITLE "Mixed MANOVA: G1 G2 G3 Repeated Measures by Sex".

GLM G1 G2 G3 BY sex
  /WSFACTOR=grade_time 3 Polynomial
  /METHOD=SSTYPE(3)
  /PLOT=PROFILE(grade_time*sex)
  /PRINT=DESCRIPTIVE ETASQ HOMOGENEITY
  /CRITERIA=ALPHA(.05)
  /WSDESIGN=grade_time
  /DESIGN=sex.

OUTPUT EXPORT
  /CONTENTS EXPORT=VISIBLE
  /PDF DOCUMENTFILE="mixed_manova_output.pdf".

Python Code for Mixed MANOVA

import pandas as pd
import statsmodels.api as sm
from statsmodels.multivariate.manova import MANOVA
from statsmodels.formula.api import ols

df = pd.read_csv("dataset.csv")

for col in ["G1", "G2", "G3"]:
    df[col] = pd.to_numeric(df[col], errors="coerce")

df["sex"] = df["sex"].astype("category")
df_model = df.dropna(subset=["G1", "G2", "G3", "sex"]).copy()
df_model["subject_id"] = range(1, len(df_model) + 1)

# Multivariate repeated-measure profile model by group
manova_model = MANOVA.from_formula("G1 + G2 + G3 ~ C(sex)", data=df_model)
print(manova_model.mv_test())

# Long-format follow-up ANOVA
long_df = df_model.melt(
    id_vars=["subject_id", "sex"],
    value_vars=["G1", "G2", "G3"],
    var_name="grade_time",
    value_name="score"
)

followup_model = ols("score ~ C(grade_time) * C(sex)", data=long_df).fit()
followup_table = sm.stats.anova_lm(followup_model, typ=2)
print(followup_table)

# Mean profile
mean_profile = long_df.groupby(["sex", "grade_time"])["score"].mean().reset_index()
print(mean_profile)

# Change scores
df_model["G2_minus_G1"] = df_model["G2"] - df_model["G1"]
df_model["G3_minus_G1"] = df_model["G3"] - df_model["G1"]

change_scores = df_model.groupby("sex")[["G2_minus_G1", "G3_minus_G1"]].mean()
print(change_scores)

# Repeated-measure correlation matrix
corr = df_model[["G1", "G2", "G3"]].corr()
print(corr)

# Follow-up diagnostics
long_df["fitted"] = followup_model.fittedvalues
long_df["residual"] = followup_model.resid
print(long_df[["score", "fitted", "residual"]].head())

R Code for Mixed MANOVA

library(tidyverse)

df <- read.csv("dataset.csv")

df$G1 <- as.numeric(df$G1)
df$G2 <- as.numeric(df$G2)
df$G3 <- as.numeric(df$G3)
df$sex <- as.factor(df$sex)

df_model <- df %>%
  select(G1, G2, G3, sex) %>%
  drop_na() %>%
  mutate(subject_id = row_number())

# Multivariate profile model
manova_model <- manova(cbind(G1, G2, G3) ~ sex, data = df_model)

summary(manova_model, test = "Pillai")
summary(manova_model, test = "Wilks")
summary(manova_model, test = "Hotelling-Lawley")
summary(manova_model, test = "Roy")

# Long-format follow-up
long_df <- df_model %>%
  pivot_longer(
    cols = c(G1, G2, G3),
    names_to = "grade_time",
    values_to = "score"
  )

followup_model <- aov(score ~ grade_time * sex, data = long_df)
summary(followup_model)

# Mean profile
long_df %>%
  group_by(sex, grade_time) %>%
  summarise(
    n = n(),
    mean = mean(score),
    sd = sd(score),
    .groups = "drop"
  )

# Change scores
df_model %>%
  mutate(
    G2_minus_G1 = G2 - G1,
    G3_minus_G1 = G3 - G1
  ) %>%
  group_by(sex) %>%
  summarise(
    mean_G2_minus_G1 = mean(G2_minus_G1),
    mean_G3_minus_G1 = mean(G3_minus_G1),
    .groups = "drop"
  )

# Correlation matrix
cor(df_model[, c("G1", "G2", "G3")])

Excel Notes for Mixed MANOVA

Excel can support Mixed MANOVA reporting, but it should not be the main statistical engine.

Useful Excel steps:
1. Keep one row per student.
2. Columns: sex, G1, G2, G3.
3. Create PivotTable:
   Rows = sex
   Values = mean G1, mean G2, mean G3
4. Create a line chart for the repeated-measure mean profile.
5. Calculate change scores:
   G2 minus G1 = G2 - G1
   G3 minus G1 = G3 - G1
6. Calculate repeated-measure correlations:
   =CORREL(G1_range,G2_range)
   =CORREL(G2_range,G3_range)
   =CORREL(G1_range,G3_range)
7. Run the formal Mixed MANOVA in SPSS, R or Python.
8. Report group effect, grade_time effect, interaction effect and diagnostics.

APA Reporting Wording

When reporting Mixed MANOVA, state the repeated measures, between-group factor, profile result, follow-up p-values and diagnostic context. The interaction should not be overinterpreted when its p-value is clearly above .05.

Common Mistakes

When to Use Mixed MANOVA

Use Mixed MANOVA when the same participants have several related repeated measures and you want to compare those repeated profiles across groups. In this example, G1, G2 and G3 are repeated measures, and sex is the between-subject grouping factor.

Compare this method with Mixed ANOVA, Factorial ANOVA, Fixed Effects ANOVA, ANOVA in SPSS, ANOVA in R, ANOVA in Python, ANOVA Effect Size, ANOVA Assumptions, and T Test vs ANOVA.

Downloads and Resources for Mixed MANOVA

Use these resources to reproduce the Mixed MANOVA workflow. The R report and SPSS output PDF are included as verification files. Script and workbook placeholders can be replaced after the final downloadable files are uploaded to the WordPress Media Library.

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