Is there any sources that has mentioned if more than 0.95 is the answer on normality test, the study is still reliable?

The interpretation of normality tests, such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test, depends on various factors, and there isn't a universal threshold that applies to all situations. The choice of significance level (commonly set at 0.05) is somewhat arbitrary, and p-values close to this threshold should be interpreted cautiously. In practice, the decision on whether data can be considered approximately normally distributed often depends on the context of the analysis and the assumptions of the statistical methods being used. A p-value slightly above 0.05 might not necessarily imply a departure from normality that would seriously impact the validity of the analysis. It's essential to consider the specific requirements of the statistical methods you are using and the robustness of those methods to deviations from normality. It's worth noting that normality is an assumption for some parametric statistical tests (e.g., t-tests, ANOVA), and violating this assumption might affect the results of these tests. However, these tests can be somewhat robust to violations of normality, especially with larger sample sizes. In summary, while a p-value slightly above 0.05 in a normality test might not necessarily render the study unreliable, it's important to consider the broader context, the specific requirements of the statistical methods being used, and the implications of any departure from normality on the validity of the results. It's often a good practice to complement normality tests with visual inspections of data (e.g., histograms, Q-Q plots) and to use statistical methods that are robust to deviations from normality when appropriate.

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