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Statistical Analysis

Defensible statistical analysis for research, policy, and legal contexts.

The following analyses address common research questions across academic, organizational, and legal contexts. Each is described in plain language with examples from both academic research and applied settings.

Regression Analysis

Tests whether one or more factors predict an outcome, and how strongly.

Academic ExampleDoes the number of hours studied predict final exam performance after controlling for prior GPA?
Applied ExampleDoes participation in a state reentry program predict recidivism rates across demographic groups?

ANOVA (Analysis of Variance)

Compares averages across three or more groups to determine if the differences are statistically meaningful — not just due to chance.

Academic ExampleDo three different teaching methods produce different learning outcomes?
Applied ExampleDo clients across three regional treatment programs show different recovery rates?

Chi-Square Test

Tests whether two categorical variables (things measured in categories, not numbers) are related.

Academic ExampleIs there a relationship between student major and likelihood of graduating within four years?
Applied ExampleIs there a relationship between service type received and program completion status?

Mediation Analysis

Tests whether Variable A affects Variable C because it first changes Variable B — mapping the pathway of influence.

Academic ExampleDoes cognitive behavioral therapy reduce depression through improvements in negative thought patterns? (Therapy → Fewer negative thoughts → Lower depression)
Applied ExampleDoes a job training program increase employment because it improves interview skills? Understanding the mechanism helps agencies identify which program components are actually working.

Moderation Analysis

Tests whether the relationship between two things changes depending on a third factor.

Academic ExampleDoes study time predict grades differently for students with high anxiety versus low anxiety?
Applied ExampleDoes a substance abuse treatment program work better for younger clients than older clients? Knowing this helps allocate resources and tailor interventions.

Missing Data Analysis and Multiple Imputation

When data records are incomplete — people skipped survey questions, dropped out of a study, or records were lost — this analysis determines why data is missing (random chance vs. systematic pattern) and uses statistical techniques to handle it appropriately. Multiple imputation creates several plausible estimates for missing values based on the data you do have, producing more accurate and defensible results than simply deleting incomplete cases.

Academic ExampleA longitudinal study tracking 500 students over four years has 25% attrition by Year 4. Multiple imputation allows use of all available data and tests whether attrition is related to the outcome — which, if unaddressed, would bias the results.
Applied ExampleA state program database has inconsistent intake records across clinicians. Before evaluating program effectiveness for a federal report, you need to determine whether the missing data is random or correlates with client demographics or outcomes — which would undermine the evaluation's credibility.

Group Comparisons

Tests whether groups are meaningfully different from each other. T-tests compare two groups, ANOVA compares three or more, and nonparametric alternatives are used when the data doesn't meet the assumptions required by the standard tests.

Academic ExampleDo students who received a growth mindset intervention score higher on end-of-term motivation measures than students who didn't?
Applied ExampleDo clients who complete a court-mandated program have different reoffense rates than those who don't? Are program completion rates different across demographic groups — and if so, does that indicate a fairness issue?

Comprehensive Multi-Technique Analysis

When a research question is complex enough that no single statistical method can fully answer it. This involves designing and executing a coordinated sequence of analyses — each building on the last — with a full written report integrating all findings.

Academic ExampleA dissertation examining predictors of teacher burnout using descriptive statistics, correlation analysis, hierarchical regression, and mediation analysis to test a theoretical model — all documented in APA format.
Applied ExampleA state agency wants to understand why program completion rates vary by site, requiring demographic comparisons, regression modeling to identify predictors, and interaction testing to determine whether factors differ by region — with results presented to both technical and executive audiences.

Pricing

Prices reflect Publication-Ready tier with Standard Report.

ServicePrice
Single analysis technique (e.g., regression, ANOVA, chi-square) with results report$1,800–$2,500
Comprehensive multi-technique analysis with full APA results write-up$3,500–$5,000
Mediation / moderation analysis with write-up$2,000–$3,500
Missing data analysis and multiple imputation$1,500–$3,000
Group comparisons (t-tests, ANOVA, chi-square, nonparametric alternatives)$1,200–$2,000

All analyses are conducted in R with full documentation. SAS, SPSS, and Python available on request.

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