statistical-analysis

Statistical Analysis - Intelligent Statistical Analysis Assistant

Skill Overview

Statistical Analysis is a professional statistical analysis assistant skill that helps you choose the appropriate statistical tests, automatically checks statistical assumptions, computes effect sizes and conducts power analyses, and generates academic reports compliant with APA formatting. It is suitable for academic research, experimental data analysis, and manuscript writing.

Applicable Scenarios

1. Academic Paper Data Analysis

When you need to perform statistical analyses for an academic paper, this skill can guide you in selecting the correct tests (e.g., t-tests, analysis of variance, chi-square tests), automatically check whether data meet statistical assumptions, compute and report effect sizes and confidence intervals, and finally generate APA-formatted descriptions of statistical results.

2. Hypothesis Testing for Experimental Research

For controlled experiments or intervention studies, this skill helps you design analysis plans, perform a priori power analyses to determine required sample size, execute between-group comparisons (independent-samples t-test, one-way ANOVA) or within-group comparisons (paired t-test, repeated-measures ANOVA), and provide complete diagnostic checks and post hoc analyses.

3. Exploratory and Bayesian Analysis

When you need to go beyond traditional frequentist methods, this skill offers Bayesian t-tests, Bayesian ANOVA, and Bayesian regression, computes Bayes factors to quantify evidence strength, and provides assessment of support for the null hypothesis—suitable for small-sample research and sequential data analysis scenarios.

Core Features

1. Intelligent Test Selection

Automatically recommends the most appropriate statistical test based on the research question type, data characteristics (continuous/categorical), number of groups, and design type (independent/paired), including parametric tests (t-tests, ANOVA) and nonparametric alternatives (Mann-Whitney U, Kruskal-Wallis), and supports selection of Bayesian methods.

2. Automated Hypothesis Testing and Diagnostics

Performs a complete statistical assumption checking workflow automatically, including tests for normality (Shapiro-Wilk + Q–Q plot), homogeneity of variances (Levene's test + boxplot), linearity checks (scatterplot + residual analysis), and outlier detection (IQR and z-score methods). When assumptions are violated, it provides remedial suggestions and alternative approaches.

3. Professional Statistical Report Generation

Automatically generates statistical result reports formatted according to APA 7th edition, including full descriptive statistics (means, standard deviations, sample sizes), test statistics (t values, F values, degrees of freedom), exact p-values, effect sizes (Cohen's d, partial eta-squared, R²) and their confidence intervals, as well as hypothesis test results and details of post hoc analyses.

Frequently Asked Questions

How do I choose the appropriate statistical test?

Choosing a statistical test requires considering multiple factors: the type of research question (comparing group differences vs. testing relationships), data type (continuous vs. categorical), number of groups (two groups vs. multiple groups), experimental design (independent samples vs. paired samples), and data distribution (normal vs. non-normal). This skill provides a complete decision-tree guide and recommends the most appropriate test based on your specific characteristics.

What is power analysis and why is it needed?

Power analysis is used to determine the sample size required to detect a true effect given an effect size and significance level. A priori power analysis should be conducted before data collection to avoid false negatives (Type II errors) due to insufficient sample size. This skill supports power analyses for various tests such as t-tests and ANOVA, helping you plan a reasonable study design.

What if statistical assumptions are not met?

When data do not meet the assumptions for parametric tests, there are several options: for minor violations of normality with sufficiently large sample sizes (n > 30 per group), parametric tests are often robust; for moderate violations, consider data transformations; for severe violations, use nonparametric alternatives (e.g., Mann-Whitney U test instead of an independent t-test). When homogeneity of variance is violated, use Welch's t-test or the Brown-Forsythe correction. This skill will automatically detect assumption violations and provide concrete recommendations.