Frequentist, Bayesian Analysis and Complementary Statistical Tools for Geriatric and Rehabilitation Fields: Are Traditional Null-Hypothesis Significance Testing Methods Sufficient?

Figures & data

Figure 1 Minimal Clinical Important Difference (MCID) For Handgrip Strength Between Pilates Training (PT) And Control Group (CON).

Abbreviations: MCID, minimal clinical important difference; CON, control group; PT, Pilates training.

Figure 2 Magnitude-Based Inference (Mbi) For Handgrip Strength.

Figure 3 Jasp Classification Scheme For The Bayes Factor (BF₁₀).

Abbreviation: JASP: Jeffrey’s Amazing Statistics Program.

Table 1 Model Comparison

Models	P(M)	P(M|data)	BFM	BF10	Error %
Null model	0.20	0.04	0.17	1.00
TIME	0.20	0.56	5.03	13.78	2.99e-7
GROUP + TIME	0.20	0.22	1.15	5.53	1.04
GROUP + TIME + GROUP ✻ TIME	0.20	0.16	0.78	4.03	0.99
GROUP	0.20	0.02	0.07	0.40	9.98e-3

Notes: Models: show the two models tested, null and treatments. The null model is shown first. P(M): for the ANOVA, the analysis sets the prior probabilities of each model to be equal (eg, prior model odds of 0.5). P(M|data): shows the updated probabilities having now seen the data (eg, posterior model probabilities). BF_M: shows how much the data has changed the prior model odds. BF₁₀: shows the Bayes factors for each model, and the first entry is always 1 since the null model is compared against itself. Error %: indicates the sensitivity of numerical fluctuations.

Abbreviation: BF, Bayes factor.

Figure 4 Bayesian Independent Sample T-Test.

Note: BF = Bayes factor. Bayes factors supporting the alternative/null hypothesis (BF10) and null/alternative hypothesis (BF01). The pizza plot distribution shows the proportion of evidence for the H1 (red) and H0 (white) hypothesis. In this data set example, the pizza plot is completely red. The median effect size of 1.351 and 95% credible intervals are also shown.

Figure 5 Bayes Factor Robustness Test.