Statistical Assumption
Tests

Analysis
Stage

"Methodological Validity and Parametric Conformity"

The accuracy of statistical inferences depends on the conformity of the data with the theoretical assumptions of the selected tests (assumption conformity). Parametric analyses conducted on a dataset where assumptions are violated artificially increase the risk of "Type I Error" (False Positive), producing spurious results. At Datametri, before proceeding to the analysis phase, we subject the mathematical limits of your data to a rigorous audit across these four main axes:

Normality Assumption Audit

Shapiro-Wilk Q-Q Plot

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Most parametric tests (t-test, Pearson, ANOVA) rely on the assumption that the dependent variable exhibits a normal distribution in the population (Gaussian Distribution). Violation of this assumption distorts the standard error margins of the test statistics (t, F, Z).

Analytical Approach: Depending on the sample size, Shapiro-Wilk (n < 50) or Kolmogorov-Smirnov (n > 50) tests are applied. It is verified whether Kurtosis and Skewness coefficients are within the ± 1.5 range.
Visual Assessment: The conformity of the data to the normal distribution line is examined microscopically via Q-Q Plot curves.

Which Questions Does This Analysis Answer?

Analytical Confidence: Does the data possess the mathematical symmetry capable of supporting parametric tests (like ANOVA)?
Test Decision: Due to the skewness of the distribution, would it be a more scientific approach to report my results using Non-Parametric tests (like Kruskal-Wallis) based on the median?

Added Value to Your Research

Reviewers for high-impact factor (Q1) journals are not convinced by the mere statement "normality was tested." Including the Q-Q plot and its interpretation in the methodology section elevates the "Statistical Rigor" level of your study to the maximum.

The Q-Q (Quantile-Quantile) plot is an auditing tool that compares the quantiles of your sample data with the quantiles of a theoretical normal distribution. The red line represents the ideal normality line; the blue area represents the 95% confidence bands. The observed points remaining within this band prove that the deviation from normality is not statistically significant (p > 0.05).

Homogeneity of Variances (Homoscedasticity)

Levene's Test Residuals Analysis

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In inter-group comparisons or regression models, it is expected that the variances (spread widths) of the groups are approximately equal to each other (homogeneity of variance). Heterogeneous variances (heteroscedasticity) distort the standard errors, thereby corrupting the confidence intervals.

Analytical Approach: Equality of variance among groups is audited with Levene's Test or Bartlett's Test.
Methodological Solution: When the assumption is violated, the analysis is stabilized by applying Welch’s t-test or Brown-Forsythe corrections, which are robust against unequal variances, instead of classical tests.

Added Value to Your Research

The constancy of variance certifies that the model operates with the same accuracy at every prediction level. Utilizing "Robust" methods like the Welch correction proves your Methodological Competence.

The scatter of the error terms (residuals) against the predicted values indicates the constancy of variance (homoscedasticity). If the errors expand to the right in a "funnel" shape (Fan-shape), it indicates that the homogeneity of variance is disrupted (heteroscedasticity) and the OLS estimators are no longer optimal (not BLUE).

Multicollinearity Audit

VIF & Tolerance Regression Assumption

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In Multiple Regression models, if the independent variables have a very high correlation with each other (r > 0.80), it becomes impossible for the model to measure the "unique" contribution of each variable. This situation causes the coefficients (betas) to change signs or become statistically insignificant.

Analytical Approach: Variance Inflation Factor (VIF) and Tolerance values are calculated for each independent variable. In academic literature, a VIF > 10 (or Tolerance < 0.10) value points to a serious multicollinearity problem.
Solution: Overlapping variables are either combined through factor analysis (dimension reduction) or the weaker one is eliminated from the model.

Which Questions Does This Analysis Answer?

Are the variables in my model copies of one another (redundant), or does each add a unique value in explaining the variance?
Are the standard errors of my regression coefficients inflated due to excessive correlation among variables (multicollinearity)?

Auditing VIF values guarantees the stability of the findings by controlling the "leverage effect" and "variance inflation" in the multiple regression model. Even though Pearson correlations (r) between variables exceeding 0.80 might artificially inflate the model's explanatory power (R-squared), it destroys the reliability (p-values) of individual predictors.

Independence of Errors

Durbin-Watson Test Autocorrelation

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Especially in longitudinal or time-series data, it is a fundamental regression assumption that the error (residual) of an observation is not correlated with the error of the preceding or succeeding observation (no autocorrelation).

Analytical Approach: Autocorrelation among errors is audited using the Durbin-Watson statistic (d). The ideal d value is expected to be in the range of 1.5 to 2.5 (ideally 2.00).
Violation Condition: The violation of this assumption (positive or negative autocorrelation) artificially inflates the model's R-squared value and t-statistics, causing variables that are actually insignificant to appear significant (p < 0.05).

Why Do You Need This Statistical Audit?

Assumptions are the pillars upon which empirical findings are built. Presenting Durbin-Watson and VIF tables forms your strongest academic defense against the potential criticism from reviewers: "Assumptions are violated; these regression results might be spurious (spurious regression)."

Datametri Statistical Assumption Perspective

We know that the scientific power of an analysis is only as strong as its weakest assumption. At Datametri, we structure assumption tests not merely as formalities to be reported; but as an analytical armor that defends the internal validity of your study.

Methodological Armor

Prevents potential criticisms from reviewers regarding methodological validity right from the start (a priori) by empirically proving the mathematical limits of your dataset.

Accurate Test Allocation

Based on the results of the applied normality and variance tests, we chart the most suitable Parametric or Non-Parametric (Robust) modeling route for your data, in line with scientific literature.

High Scientific Rigor

By reporting the assumptions transparently and in-depth (Q-Q, Scatter plots) within the methodology section of the article, we elevate your research to Q1-indexed international publication standards.

Statistical AssumptionTests

Datametri Statistical Assumption Perspective

Methodological Armor

Accurate Test Allocation

High Scientific Rigor

Let's Test the Mathematical Validity of Your Data

Statistical Assumption
Tests