Quick Answer: Split Plot ANOVA Result

The worked Split Plot ANOVA tests whether repeated grade scores change across G1, G2 and G3, whether students differ by studytime group, and whether the grade-change pattern depends on studytime group.

The Python summary table reports a significant studytime effect, F = 16.98, p = 1.264e-10, partial η² = 0.07319. It also reports a significant Time effect, F = 36.41, p = 4.441e-16, partial η² = 0.05343. The studytime × Time interaction is not significant, F = 1.731, p = 0.1103, partial η² = 0.007986.

What Is Split Plot ANOVA?

Split Plot ANOVA is an ANOVA design that combines a between-subject factor and a within-subject repeated factor. In many software menus, it appears as mixed repeated-measures ANOVA because one part of the design compares different subjects and another part compares repeated measurements within the same subjects.

In this example, the same students are measured three times through G1, G2 and G3. That is the within-subject Time factor. Students are also separated into studytime groups. That is the between-subject factor. The split plot design answers three questions at once: whether studytime groups differ overall, whether repeated grade means change over time, and whether the time trend is different across studytime groups.

The results show significant main effects for studytime and Time. The profile plot shows that studytime group 1 has the lowest grade profile, studytime group 2 is higher, and studytime groups 3 and 4 are highest. The repeated Time profile rises overall from G1 to G3. The interaction is not significant, so the main conclusion is about separate studytime and Time effects rather than a strong combined effect.

Split Plot ANOVA connects naturally with Mixed ANOVA, Factorial ANOVA, Fixed Effects ANOVA, One Way ANOVA, One Way ANCOVA, ANOVA Effect Size, Partial Eta Squared, Eta Squared, Omega Squared, and F Distribution.

Split Plot ANOVA Formula

A split plot model separates each score into a grand mean, a between-subject group effect, a subject-within-group error term, a within-subject Time effect, a group × Time interaction and a repeated-measure error term.

Here, A is the between-subject factor studytime, B is the within-subject factor Time, S(A) is subjects nested within studytime, and AB is the studytime × Time interaction.

Correct Error Terms

Partial Eta Squared Formula

The effect-size chart reports partial eta squared values of 0.073 for studytime, 0.053 for Time, and 0.008 for the interaction. This means studytime has the largest practical effect in the split plot model, Time has a smaller but meaningful effect, and the interaction is very small.

Split Plot ANOVA Hypotheses

Split Plot ANOVA has separate hypotheses for the between-subject effect, the within-subject effect and the interaction effect.

Dataset and Variables Used

The worked example uses student grade variables as repeated measurements. Each student has G1, G2 and G3. The between-subject factor is studytime, with four groups. The SPSS output used 649 valid cases.

SPSS Descriptive Means by Studytime

The descriptive pattern explains the inferential result. Studytime groups differ in overall level, and G3 is higher than G1 and G2 overall. The interaction is small because the profiles are mostly similar in direction and do not cross strongly enough to produce a significant interaction.

SPSS Output Interpretation for Split Plot ANOVA

The SPSS output uses GLM Repeated Measures. Time is the within-subject factor with three levels assigned to G1, G2 and G3. Studytime is the between-subject factor. The output includes descriptive statistics, Box’s M, multivariate tests, Mauchly’s test, within-subject effects, within-subject contrasts, Levene tests and between-subject effects.

SPSS Reading Order

SPSS Sphericity and Corrections

SPSS Within-Subject Effects

SPSS Between-Subject Effect

SPSS Levene Test Summary

Python Chart-by-Chart Interpretation

The Python chart sequence explains Split Plot ANOVA through profile lines, within-subject means, between-subject group means, p-value decisions, effect sizes, repeated-measure boxplots, residual diagnostics and a compact summary table.

Python Chart 1: Split Plot ANOVA Profile Plot

The profile plot shows that studytime group 1 has the lowest grade profile, studytime group 2 is higher, and groups 3 and 4 are in the highest range. Most profiles move upward toward G3.

The lines are not perfectly identical, but they do not show a strong crossing pattern. This supports the statistical result: the studytime × Time interaction is not significant, while the separate studytime and Time effects are meaningful.

Python Chart 2: Within-Subject Mean Scores

This chart shows the overall repeated-measure pattern. The mean score is lowest at G1, slightly higher at G2, and highest at G3.

The confidence intervals are narrow because the sample size is large. The repeated Time effect is therefore not only visible in the plot but also statistically significant in the p-value summary.

Python Chart 3: Between-Subject Group Means

The between-subject chart shows a clear increase in overall grade level from studytime group 1 toward groups 3 and 4. Studytime group 1 is lowest, group 2 is intermediate, and groups 3 and 4 are highest.

This explains why the studytime effect has the largest partial eta squared value. The main group separation is stronger than the small non-significant interaction pattern.

Python Chart 4: Split Plot ANOVA p-value Summary

The p-value summary shows that studytime and Time are both below the alpha = .05 decision line. The studytime × Time interaction is above alpha with p = 0.1103.

The decision is clear. The model supports the two main effects but does not support a statistically significant interaction. This means the grade profile changes over Time, and studytime groups differ overall, but the time trend is not strongly different across studytime groups.

Python Chart 5: Split Plot ANOVA Effect Sizes

The effect-size chart shows studytime at about 0.073, Time at about 0.053 and the interaction at about 0.008. Studytime is the largest practical effect in this split plot model.

The interaction effect is very small. This supports a conservative interpretation: discuss the studytime group difference and the repeated Time change, but do not overstate the interaction.

Python Chart 6: Repeated-Measure Score Distributions

The repeated-measure boxplots show that G3 is centered higher than G1 and G2. The median and mean markers both support an upward movement across repeated grade measures.

Low outlying values are visible, especially near zero. These low cases help explain why residual diagnostics should be reviewed even when the main ANOVA effects are statistically significant.

Python Chart 7: Residuals vs Fitted Values

The residual plot shows vertical bands because fitted values are based on studytime × Time cell means. Most residuals are distributed around zero, but there are several negative residuals below -10.

The diagnostic conclusion is balanced. The model captures the average split plot pattern, but some individual scores are much lower than their fitted cell mean. These cases should be mentioned as residual diagnostic context.

Python Chart 8: Split Plot ANOVA Summary Table

The summary table gives the compact final result. Studytime is significant, Time is significant, and studytime × Time is not significant.

This table is the best source for final reporting because it includes the correct split plot error terms and shows the decision for each model effect.

R Chart-by-Chart Validation

The R validation charts repeat the same workflow in a second software environment. They confirm the profile plot, within-subject means, between-subject means, p-value decisions, effect sizes, repeated-measure boxplots, residual diagnostics and summary table.

R Chart 1: Split Plot ANOVA Profile Plot

The R profile plot confirms that studytime groups differ in grade level. The same general ordering appears, with group 1 lowest and groups 3 and 4 highest.

The R plot also supports the same interaction conclusion. The profiles do not show a strong enough divergence to support a significant studytime × Time effect.

R Chart 2: Within-Subject Mean Scores

The R within-subject mean chart confirms the upward repeated Time trend. G3 is the highest repeated mean.

This software validation strengthens the Time effect interpretation because the same mean pattern appears in both Python and R.

R Chart 3: Between-Subject Group Means

The R group mean chart confirms the studytime main effect. Overall grade level increases from studytime group 1 toward higher studytime groups.

This confirms that the group difference is stable across software workflows and should be reported as a meaningful between-subject result.

R Chart 4: p-value Summary

The R p-value chart confirms that studytime and Time are statistically significant while the studytime × Time interaction is not.

This validates the final decision structure: two significant main effects and no significant interaction.

R Chart 5: Partial Eta Squared Effect Sizes

The R effect-size chart confirms the same ordering. Studytime has the largest partial eta squared, Time is second, and the interaction is very small.

This supports a practical conclusion focused on main effects. The interaction is too small to carry the interpretation.

R Chart 6: Repeated-Measure Score Distributions

The R boxplots confirm that G3 is centered higher than the earlier grade measures. The low-score outliers are also visible.

This validates both the Time effect and the diagnostic caution. The average pattern is clear, but individual variation remains substantial.

R Chart 7: Residuals vs Fitted Values

The R residual chart confirms the same vertical fitted-value bands and the same presence of lower residual values.

This supports a transparent diagnostic statement. The model explains the cell means, but some individual scores deviate strongly from their fitted means.

R Chart 8: Split Plot ANOVA Summary Table

The R summary table confirms the same formal decision as Python. Studytime and Time are significant, while the interaction is not.

This software agreement makes the final report stable: the studytime group difference and repeated Time change should be emphasized, while the interaction should be described as non-significant.

SPSS, R, Python and Excel Workflows for Split Plot ANOVA

The same Split Plot ANOVA workflow can be reproduced in SPSS, R, Python and Excel. SPSS uses GLM Repeated Measures. R can use long-format repeated-measures models. Python can use mixed models or manual split plot ANOVA tables. Excel can prepare summaries and charts, but SPSS, R or Python should be used for the formal test.

SPSS Workflow

R Workflow

Python Workflow

Excel Workflow

Code Blocks for Split Plot ANOVA

SPSS Syntax for Split Plot ANOVA

* Split Plot ANOVA / Mixed Repeated-Measures ANOVA in SPSS.
* Repeated measures: G1, G2, G3.
* Within-subject factor: Time.
* Between-subject factor: studytime.

TITLE "Split Plot ANOVA: G1 G2 G3 by Studytime".

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

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

Python Code for Split Plot ANOVA Support

import pandas as pd
import numpy as np
from scipy import stats

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

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

wide = df[["studytime", "G1", "G2", "G3"]].dropna().copy()
wide["subject_id"] = np.arange(1, len(wide) + 1)
wide["studytime"] = wide["studytime"].astype("category")

long = wide.melt(
    id_vars=["subject_id", "studytime"],
    value_vars=["G1", "G2", "G3"],
    var_name="Time",
    value_name="score"
)

long["Time"] = long["Time"].astype("category")

# Cell means
cell_means = long.groupby(["studytime", "Time"])["score"].mean()
time_means = long.groupby("Time")["score"].mean()
group_means = long.groupby("studytime")["score"].mean()

print("Cell means:")
print(cell_means)

print("Time means:")
print(time_means)

print("Studytime means:")
print(group_means)

# For formal split plot ANOVA, use a stats package or compute the
# correct split plot error terms:
# studytime tested against subjects within studytime
# Time and studytime:Time tested against Time x subjects within studytime

# Example profile data for plotting:
profile = long.groupby(["studytime", "Time"], as_index=False)["score"].mean()
print(profile)

R Code for Split Plot ANOVA

# Split Plot ANOVA / Mixed Repeated-Measures ANOVA in R

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$studytime <- as.factor(df$studytime)

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

long <- wide %>%
  pivot_longer(
    cols = c(G1, G2, G3),
    names_to = "Time",
    values_to = "score"
  ) %>%
  mutate(Time = factor(Time, levels = c("G1", "G2", "G3")))

# Split plot ANOVA
model <- aov(score ~ studytime * Time + Error(subject_id / Time), data = long)
summary(model)

# Descriptive means
long %>%
  group_by(studytime, Time) %>%
  summarise(
    n = n(),
    mean = mean(score),
    sd = sd(score),
    .groups = "drop"
  )

# Profile plot support table
profile <- long %>%
  group_by(studytime, Time) %>%
  summarise(mean_score = mean(score), .groups = "drop")

print(profile)

Excel Notes for Split Plot ANOVA

Excel support workflow:

1. Keep repeated measures on the same row:
   Subject_ID | studytime | G1 | G2 | G3

2. Calculate repeated-measure means:
   G1 mean = AVERAGE(G1_range)
   G2 mean = AVERAGE(G2_range)
   G3 mean = AVERAGE(G3_range)

3. Create studytime group means:
   PivotTable:
   Rows = studytime
   Values = average of G1, average of G2, average of G3

4. Create profile plot:
   X-axis = Time levels G1, G2, G3
   Lines = studytime groups
   Y-axis = mean score

5. Create repeated-measure boxplots:
   Use G1, G2 and G3 columns.

6. Formal Split Plot ANOVA:
   Use SPSS, R or Python because Excel does not automatically handle
   the subject-within-group and repeated-measure error terms correctly.

APA Reporting Wording

When reporting Split Plot ANOVA, include the within-subject factor, between-subject factor, main effects, interaction, effect sizes and assumption notes. Because Mauchly’s test is significant in the SPSS output, mention the Greenhouse-Geisser or Huynh-Feldt correction for the univariate repeated-measures layer.

Common Mistakes

When to Use Split Plot ANOVA

Use Split Plot ANOVA when the design contains both repeated measurements and independent groups. It is common in education, psychology, medicine, agriculture, repeated testing, pre-mid-post studies and experiments where the same subjects are followed across time while also belonging to different groups.

Split Plot ANOVA should be compared with Mixed ANOVA, Mixed MANOVA, One Way MANOVA, Factorial ANOVA, Fixed Effects ANOVA, Nested ANOVA, ANOVA Assumptions, and ANOVA Effect Size.

Downloads and Resources for Split Plot ANOVA

Use these resources to reproduce the Split Plot ANOVA workflow. The Python report, 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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