Statistics software version 25

Statistical analysis will be performed using IBM statistics software version 25 (Armonk, NY, USA). The values of variables will be presented as mean ± standard deviation. Normality tests will be assessed through Shapiro-Wilk tests carried out on each parameter before analysis. Analysis includes all the participants (intent to treat) determining the baseline characteristic. Additional analysis will be performed per protocol on participants with 80% or higher adherence to study protocol. Two-way repeated measures ANOVA will be used to determine differences within groups (pre vs. post) as a repeated factor and intervention (GSM vs. placebo) as a fixed factor, with the model adjusted for the BMI and age, physical activity, and baseline vitamin D status. Post hoc analysis with Bonferroni adjustments will be performed for multiple comparisons. Statistical significance will be set at a level of 0.05.

Statistical analysis was performed using IBM statistics software version 25 (Armonk, NY, USA). Data were analyzed by one-way ANOVA or Student’s t-test. Multiple comparisons were analyzed by the least significant difference test, and knee joint scoring was done by the Mann–Whitney U test.