Quick Answer: Split Plot ANOVA Result

The worked Split Plot ANOVA answers three questions at the same time. First, do studytime groups differ in overall grade level? Second, do repeated grade means change across G1, G2 and G3? Third, does the repeated grade-change pattern depend 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 a mixed ANOVA design that contains one repeated-measures part and one independent-groups part. In practical software language, it is often treated as a mixed repeated-measures ANOVA. The word “split plot” comes from experimental design, but the same logic is widely used in education, psychology, medicine, agriculture and repeated testing.

In this example, every student has three repeated outcomes: G1, G2 and G3. These are the within-subject Time levels. Students are also placed into independent studytime groups. This makes the design different from a simple One Way ANOVA, because the same subjects are measured more than once.

The model shows two clear main effects. Studytime groups differ in overall grade level, and repeated grade means change across Time. The interaction is small and not statistically significant, so the correct interpretation is not that every studytime group has a uniquely different growth pattern. The safer conclusion is that studytime matters overall and grades change across G1, G2 and G3.

This guide should be read with Mixed ANOVA, Factorial ANOVA, Fixed Effects ANOVA, One Way ANCOVA, ANOVA Effect Size, Eta Squared, Omega Squared, Cohen’s F Formula and F Distribution.

Split Plot ANOVA Formula

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

In this notation, A is the between-subject factor, studytime. The term B is the within-subject factor, Time. The repeated measures are G1, G2 and G3. The term S(A) means subjects nested within studytime, and AB represents the studytime × Time interaction.

Correct Error Terms

Partial Eta Squared Formula

The effect-size output reports partial eta squared values of about 0.073 for studytime, 0.053 for Time and 0.008 for the interaction. Studytime has the largest practical effect in this split plot model. Time has a smaller but meaningful effect, while 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. These should be reported separately because each answers a different research question.

Dataset and Variables Used

The worked example uses student grade data. Each student has three repeated measurements: G1, G2 and G3. The between-subject grouping factor is studytime, which separates students into four groups. The SPSS output uses 649 valid cases.

Descriptive Means by Studytime

The descriptive pattern explains the statistical result. Studytime group 1 has the lowest repeated profile, group 2 is higher, and groups 3 and 4 are generally highest. The total profile rises from G1 to G3, which supports the significant Time effect.

For background concepts, review Descriptive Statistics, Mean Median and Mode, Standard Deviation, Variance, Confidence Interval, P Value, Null and Alternative Hypothesis and Effect Size.

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, 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 a profile plot, within-subject means, between-subject group means, p-value decisions, partial eta squared, 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 repeated grade profile, studytime group 2 is higher, and studytime 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 visible in the plot and 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 higher studytime groups. 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 grades change over Time and studytime groups differ overall, but the time trend is not strongly different across studytime groups.

Python Chart 5: Split Plot ANOVA Partial Eta Squared

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 support an upward movement across repeated grade measures.

Low outlying values are visible near the lower end of the scale. These cases 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 split plot sources, p-values, effect sizes and decisions 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: Split Plot ANOVA 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 a manual split plot ANOVA table. Excel can prepare summaries and profile 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")

# Descriptive summaries
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)

# Profile plot support data
profile = long.groupby(["studytime", "Time"], as_index=False)["score"].mean()
print(profile)

# For the formal split plot ANOVA table:
# studytime is tested against subjects within studytime
# Time and studytime:Time are tested against Time x subjects within studytime

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, Balanced ANOVA, Brown Forsythe ANOVA, ANOVA Assumptions and ANOVA in SPSS.

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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