Education Inferential Statistics

Education Inferential Statistics

Goal

Choose, run, interpret, and report common inferential analyses aligned to education research questions, variable types, and study design.

Use After

Use after:

• education-descriptive-statistics
• education-quantitative-data-cleaning
• education-quantitative-study-design
• education-program-evaluation
• education-mixed-methods-design

Do not expose the skill name to users. Present it as "假设检验与统计推断".

Inputs

• Research questions/hypotheses
• Cleaned dataset
• Variable roles and types
• Group/timepoint structure
• Descriptive statistics
• Planned design: survey, experiment, quasi-experiment, pre-post, evaluation

Workflow

1. Map each hypothesis to variables:
   • outcome/dependent variable
   • predictor/independent variable
   • group/timepoint
   • covariates/controls
2. Select analysis based on question and variable type.
3. Check assumptions:
   • independence
   • normality/large-sample robustness
   • homogeneity of variance
   • linearity
   • multicollinearity
   • expected cell counts for chi-square
4. Run the analysis.
5. Calculate effect size:
   • Cohen's d
   • eta squared / partial eta squared
   • odds ratio
   • r
   • standardized beta where useful
6. Interpret results:
   • statistical significance
   • effect size
   • confidence interval
   • educational/practical meaning
7. Draft result paragraph and table.
8. Warn about overclaiming or method mismatch.

Method Selection Guide

Tool Calls

R

install.packages(c("tidyverse", "rstatix", "effectsize", "car", "broom", "performance", "emmeans"))
library(tidyverse)
library(rstatix)
library(effectsize)
library(car)
library(broom)

Independent t-test:

t.test(score_post ~ group, data = data)
effectsize::cohens_d(score_post ~ group, data = data)

Paired t-test:

t.test(data$score_pre, data$score_post, paired = TRUE)
effectsize::cohens_d(data$score_post, data$score_pre, paired = TRUE)

ANOVA:

fit <- aov(score_post ~ group, data = data)
summary(fit)
effectsize::eta_squared(fit)
TukeyHSD(fit)

ANCOVA/regression:

fit <- lm(score_post ~ group + score_pre + gender + grade, data = data)
summary(fit)
car::Anova(fit, type = 3)
performance::check_model(fit)

Chi-square:

tab <- table(data$group, data$pass)
chisq.test(tab)

Correlation:

cor.test(data$self_efficacy, data$score_post, method = "pearson")

Python

pip install pandas scipy statsmodels pingouin scikit-posthocs

t-test:

from scipy import stats
stats.ttest_ind(group_a, group_b, nan_policy="omit")
stats.ttest_rel(pre, post, nan_policy="omit")

ANOVA/regression:

import statsmodels.formula.api as smf
import statsmodels.api as sm
model = smf.ols("score_post ~ C(group) + score_pre + gender + grade", data=df).fit()
sm.stats.anova_lm(model, typ=2)
model.summary()

Chi-square:

import pandas as pd
from scipy.stats import chi2_contingency
table = pd.crosstab(df["group"], df["pass"])
chi2_contingency(table)

Correlation:

from scipy.stats import pearsonr, spearmanr
pearsonr(df["self_efficacy"], df["score_post"])

SPSS

Analyze -> Compare Means -> Independent-Samples T Test
Analyze -> Compare Means -> Paired-Samples T Test
Analyze -> Compare Means -> One-Way ANOVA
Analyze -> General Linear Model -> Univariate
Analyze -> Descriptive Statistics -> Crosstabs
Analyze -> Correlate -> Bivariate
Analyze -> Regression -> Linear
Analyze -> Regression -> Binary Logistic

Output Format

1. Analysis Plan

2. Assumption Check

3. Result Table

4. Regression Table

5. Result Wording Template

Chinese:

独立样本 t 检验结果显示，实验组在后测写作成绩上的平均得分（M = [ ], SD = [ ]）高于对照组（M = [ ], SD = [ ]），差异达到/未达到统计显著水平，t([df]) = [ ], p = [ ]，Cohen's d = [ ]。这表明 [教育意义解释]。

English:

An independent-samples t-test showed that the intervention group (M = [ ], SD = [ ]) scored higher/lower than the comparison group (M = [ ], SD = [ ]), t([df]) = [ ], p = [ ], Cohen's d = [ ]. This suggests that [educational interpretation].

Education-Specific Guidance

• For class-based interventions, check whether students are nested within classes.
• For pre/post quasi-experiments, prefer ANCOVA/regression controlling for pretest when comparing posttest.
• For small samples, emphasize effect size and confidence intervals; avoid strong claims.
• For nonrandomized designs, avoid saying "caused" unless design supports it.
• For Likert items, analyze scale scores rather than single items where possible.
• For multiple outcomes, consider multiple-comparison risk.

Quality Rules

• Do not choose a statistical test only because it is familiar.
• Match test to variable type and design.
• Report effect sizes, not only p-values.
• Statistical significance is not educational importance.
• Correlation/regression does not prove causation.
• If assumptions are badly violated, recommend alternatives or robust methods.

User-Facing Closure

End by routing to interpretation or next analysis:

统计检验结果可以进入论文“结果”部分了。接下来我可以帮你做三件事：A. 生成结果表，B. 写结果段落，C. 继续做信效度/中介调节/高级模型。你想先看哪一步？