Quick Answer: Sidak Correction Result

The worked example compares G3 final grade across four studytime groups after a significant one-way ANOVA. With four groups, there are six pairwise comparisons. If each pair were tested at α = .05 without correction, the chance of at least one false-positive result across the family of tests would increase. The Sidak Correction adjusts the p-values so the full family of comparisons is controlled more carefully.

The group means follow the same pattern across the Python and validation charts. Group 1 has the lowest mean G3 score, about 10.84. Group 2 has a higher mean, about 12.09. Group 4 has a mean near 13.06, and group 3 has the highest mean, about 13.23. After Sidak adjustment, the strongest differences remain those involving group 1 compared with higher studytime groups. The closest pair is group 3 versus group 4, which should not be described as clearly different.

What Is Sidak Correction?

Sidak Correction is a multiple-comparison correction used when a researcher performs more than one statistical test and wants to keep the overall family-wise error rate under control. A family-wise error occurs when at least one false-positive result appears inside a group of tests. The more tests you run, the greater the chance of at least one false alarm if you do not adjust.

In ANOVA post hoc analysis, Sidak Correction is often used for pairwise comparisons. The ANOVA tells whether at least one group mean differs. Pairwise comparisons then test which exact groups differ. Sidak Correction adjusts those pairwise p-values so the final decisions are not based on unprotected raw p-values.

Sidak Correction is closely related to Bonferroni correction. Bonferroni uses α divided by the number of comparisons as the per-test threshold. Sidak uses a probability-based formula that is usually slightly less conservative than Bonferroni. When the number of tests is small, the difference is often modest, but it is still useful to name the exact correction method used.

Before using Sidak Correction, review p-values, Type I and Type II error, one-way ANOVA, ANOVA assumptions, confidence intervals and effect size.

When to Use Sidak Correction

Use Sidak Correction when you are running multiple hypothesis tests and want to control the family-wise error rate. In this guide, the correction is used after one-way ANOVA to adjust pairwise comparisons among four studytime groups.

Sidak Correction Formula

The Sidak per-test alpha level is calculated from the family alpha and the number of comparisons:

Where α is the desired family-wise alpha level and m is the number of comparisons. In this example, α = .05 and m = 6, so:

The Sidak adjusted p-value can also be calculated from the raw p-value:

Null and Alternative Hypotheses for Sidak Correction

Sidak Correction does not change the basic pairwise hypothesis. It changes how the p-value is judged when several tests are performed together.

Dataset and Variables Used

The worked example uses a student performance dataset. The dependent variable is G3 final grade. The grouping variable is studytime, coded into four weekly study-time groups. The analysis first checks whether average G3 differs across studytime groups and then uses Sidak Correction to adjust the pairwise comparison p-values.

Before interpreting Sidak adjusted p-values, review the group means, boxplots, confidence intervals and spread. Helpful related guides include descriptive statistics, box plot interpretation, standard deviation, one-way ANOVA and ANOVA in SPSS.

ANOVA and Sidak Pairwise Decision Table

The ANOVA result gives the reason for doing pairwise comparisons. In this example, the between-group sum of squares is about 465.078, the within-group sum of squares is about 6298.189, and the total sum of squares is about 6763.267. The overall result is F(3, 645) = 15.876, p < .001, which means average G3 differs across studytime groups.

Sidak Pairwise Interpretation Summary

Python Chart-by-Chart Interpretation

The Python charts show the complete Sidak Correction workflow. They include group means, distribution boxplots, Sidak adjusted p-values, raw vs adjusted p-values, mean difference confidence intervals, an adjusted p-value heatmap, and group size with spread.

Python Chart 1: Group Means with Confidence Intervals

The group means chart shows why Sidak-adjusted pairwise comparisons are needed. Group 1 has the lowest average G3 score, group 2 is higher, and groups 3 and 4 are the highest. The chart gives the practical direction of the result before adjustment is applied.

The confidence intervals show uncertainty around each mean. Group 4 has fewer observations than the other groups, so its mean is less precise. This matters when interpreting group 2 vs group 4 and group 3 vs group 4 comparisons.

Python Chart 2: Group Distribution Boxplots

The boxplots show the distribution of G3 scores inside each studytime group. Group 1 is centered lower, while groups 3 and 4 are shifted upward. This supports the ANOVA result and explains why pairwise comparisons involving group 1 are strong.

The boxplots also show that distributions overlap. Overlap is common in real data and does not automatically remove mean differences. The Sidak correction evaluates whether each mean difference remains statistically strong after multiple-comparison control.

Python Chart 3: Sidak Adjusted p-values

The adjusted p-value chart is the main decision chart. Comparisons with Sidak adjusted p-values below .05 are interpreted as significant. The strongest adjusted results involve group 1 versus groups 2, 3 and 4, and group 2 versus group 3.

The chart also identifies the weaker comparisons. Group 2 vs group 4 and group 3 vs group 4 have smaller mean gaps, so their adjusted p-values do not support a strong final claim.

Python Chart 4: Raw vs Sidak Adjusted p-values

This chart shows the effect of correction. Raw p-values are the results before multiple-comparison protection. Sidak adjusted p-values are larger because they account for the fact that several pairwise tests are being performed together.

The most important point is that strong differences remain significant even after adjustment, while weaker comparisons become easier to identify as non-significant. This prevents overreporting and helps the final article stay accurate.

Python Chart 5: Sidak Mean Difference Confidence Intervals

The mean difference confidence interval chart gives direction and uncertainty. Comparisons whose intervals do not include zero are interpreted as significant after adjustment. The largest intervals away from zero involve group 1 compared with higher studytime groups.

This chart is important because p-values alone do not show direction or size. Mean difference intervals show whether one group is higher or lower and how large the difference may be.

Python Chart 6: Sidak Adjusted p-value Heatmap

The heatmap gives a compact view of all pairwise comparisons. Strong cells represent smaller adjusted p-values and clearer evidence of group separation. Weak cells represent comparisons that should not be described as significant.

The heatmap supports the same interpretation as the p-value chart: group 1 is the main lower group, group 3 is the highest mean group, and the highest two groups are not clearly different from each other.

Python Chart 7: Group Size and Spread

The group size and spread chart explains the precision behind the comparisons. Group 2 is the largest group, group 1 is also large, group 3 is smaller and group 4 is the smallest. Smaller groups have less precise mean estimates.

This context matters for final reporting. A high mean in group 4 should be interpreted with caution because the group has fewer observations. Sidak-adjusted decisions combine the mean gap, sample size and within-group spread.

R Chart-by-Chart Validation

The validation charts repeat the same Sidak Correction workflow using a second set of uploaded outputs. They confirm the same group mean pattern, adjusted p-value logic, confidence interval interpretation, heatmap summary and group-size context.

R Chart 1: Group Means with Confidence Intervals

The validation group means chart confirms the Python pattern. Group 1 is lowest, group 2 is higher, and groups 3 and 4 are the highest. This agreement supports the reliability of the final interpretation.

The chart also confirms that groups 3 and 4 are close. That closeness should appear in the final wording as “not clearly separated” rather than “strongly different.”

R Chart 2: Group Distribution Boxplots

The validation boxplots confirm that group 1 is centered lower than the higher studytime groups. This supports the same ANOVA and pairwise comparison conclusion.

The distributions still overlap, which is why adjusted statistical testing is necessary. Sidak Correction evaluates whether the differences remain strong after accounting for six pairwise tests.

R Chart 3: Sidak Adjusted p-values

The validation adjusted p-value chart confirms which comparisons remain significant after Sidak correction. The strongest differences are still the comparisons involving group 1 against higher studytime groups.

The weaker comparisons remain weak after adjustment. This confirms that the final article should not claim that every studytime group differs from every other group.

R Chart 4: Raw vs Sidak Adjusted p-values

The validation raw-versus-adjusted chart confirms the correction effect. Sidak adjusted p-values are more cautious than raw p-values, which reduces the risk of false-positive claims across the family of comparisons.

The chart is useful for students because it visually explains why adjusted p-values should be reported. A raw p-value can look significant before correction but may no longer support a final claim after adjustment.

R Chart 5: Sidak Mean Difference Confidence Intervals

The validation confidence interval chart confirms the direction of the important differences. Intervals away from zero identify clearer adjusted differences. Intervals crossing or touching zero support a non-significant interpretation.

This chart should be used in the article because it makes the result more understandable than p-values alone. Readers can see which group is higher, how large the difference is and how uncertain the estimate is.

R Chart 6: Sidak Adjusted p-value Heatmap

The validation heatmap confirms the final decision pattern in matrix form. It quickly separates the stronger pairs from the weaker pairs.

The heatmap supports a concise final message: group 1 is the main lower group, group 3 is the highest mean group, and groups 3 and 4 are close enough that a significant difference should not be claimed unless the adjusted p-value table supports it.

R Chart 7: Group Size and Spread

The validation group size chart confirms that the design is not perfectly balanced. Group 4 is the smallest group, while group 2 is the largest. This affects confidence interval width and interpretation precision.

The chart reinforces the need for cautious wording. Sidak Correction controls the family-wise error rate, but the analyst still needs to explain sample size and spread so readers understand why some visible differences are not significant.

SPSS, R, Python and Excel Workflows for Sidak Correction

Sidak Correction can be completed in SPSS, R, Python and Excel. SPSS includes Sidak options in several pairwise comparison workflows. R and Python are useful for reproducible p-value adjustment and charting. Excel can calculate the Sidak threshold and adjusted p-values with formulas.

SPSS Workflow

R Workflow

Python Workflow

Excel Workflow

Excel can calculate Sidak Correction directly. It is useful for teaching because the formula is short and transparent. You can calculate raw pairwise p-values, then adjust each p-value using the Sidak formula.

Code Blocks for Sidak Correction

SPSS Syntax

ONEWAY G3 BY studytime
  /STATISTICS DESCRIPTIVES HOMOGENEITY
  /POSTHOC = SIDAK ALPHA(0.05).

R Code

data <- read.csv("dataset.csv")
data$studytime <- factor(data$studytime)

# One-way ANOVA

model <- aov(G3 ~ studytime, data = data)
summary(model)

# Pairwise t tests with Sidak adjustment by formula

groups <- levels(data$studytime)
pairs <- combn(groups, 2, simplify = FALSE)

raw_p <- c()
pair_name <- c()

for (pair in pairs) {
g1 <- pair[1]
g2 <- pair[2]
x1 <- data$G3[data$studytime == g1]
x2 <- data$G3[data$studytime == g2]

test <- t.test(x1, x2, var.equal = TRUE)
raw_p <- c(raw_p, test$p.value)
pair_name <- c(pair_name, paste(g1, "vs", g2))
}

m <- length(raw_p)
sidak_p <- 1 - (1 - raw_p)^m

result <- data.frame(
comparison = pair_name,
raw_p = raw_p,
sidak_adjusted_p = sidak_p,
significant_sidak = sidak_p < 0.05
)

print(result)

Python Code

import pandas as pd
import itertools
from scipy import stats
import statsmodels.api as sm
import statsmodels.formula.api as smf
from statsmodels.stats.multitest import multipletests

df = pd.read_csv("dataset.csv")
df["studytime"] = df["studytime"].astype("category")

# One-way ANOVA

model = smf.ols("G3 ~ C(studytime)", data=df).fit()
anova = sm.stats.anova_lm(model, typ=2)
print(anova)

groups = list(df["studytime"].cat.categories)
rows = []

for g1, g2 in itertools.combinations(groups, 2):
x1 = df.loc[df["studytime"] == g1, "G3"]
x2 = df.loc[df["studytime"] == g2, "G3"]

```
t_stat, raw_p = stats.ttest_ind(x1, x2, equal_var=True)
mean_difference = x1.mean() - x2.mean()

rows.append([g1, g2, len(x1), len(x2), x1.mean(), x2.mean(),
             mean_difference, t_stat, raw_p])
```

pairwise = pd.DataFrame(rows, columns=[
"group_1", "group_2", "n_1", "n_2",
"mean_1", "mean_2", "mean_difference",
"t_statistic", "raw_p"
])

reject, sidak_p, alpha_sidak, _ = multipletests(
pairwise["raw_p"],
alpha=0.05,
method="sidak"
)

pairwise["sidak_adjusted_p"] = sidak_p
pairwise["significant_sidak"] = reject

print("Sidak per-test alpha:", alpha_sidak)
print(pairwise.sort_values("sidak_adjusted_p"))

Excel Formula Pattern

Number of pairwise comparisons:
=k*(k-1)/2

Sidak per-test alpha:
=1-(1-0.05)^(1/m)

Sidak adjusted p-value:
=1-(1-raw_p)^m

Decision using adjusted p:
=IF(sidak_adjusted_p<0.05,"Significant","Not significant")

Decision using adjusted alpha:
=IF(raw_p

APA Reporting Wording for Sidak Correction

A one-way ANOVA was conducted to compare G3 final grade across four studytime groups. The overall ANOVA was statistically significant, indicating that mean final grade differed across studytime levels. Sidak-adjusted pairwise comparisons were then examined to control the family-wise error rate across the six group comparisons.

Sidak-adjusted pairwise comparisons showed that group 1 had lower G3 scores than groups 2, 3 and 4. Group 2 also had lower scores than group 3. The comparisons between group 2 and group 4 and between group 3 and group 4 were not clearly significant after Sidak adjustment. Therefore, the main adjusted conclusion is that the lowest studytime group is separated from the higher studytime groups, while the highest two groups are statistically similar.

Common Mistakes in Sidak Correction

Downloads and Resources

Use the downloadable reports to verify the Sidak Correction charts, adjusted p-values, mean difference confidence intervals, heatmap and group-size context.

Related Guides

Continue with these related Salar Cafe guides to understand ANOVA, pairwise comparisons, p-value corrections and reporting.