# Born to Win? The Hidden Bias of Birthdates in Spanish Orienteering Talent Selection
## 2 Materials and Methods
### Statistical Analysis  
Statistical analysis was performed using IBM SPSS software (version 28; IBM Corp., Armonk, NY, USA) and Microsoft Excel for Mac (version 16.83; Microsoft Corp., Redmond, WA, USA). To assess differences in the distribution of birth quartiles and semesters in the international events analysed, the chi-square (\(\chi^{2}\)) goodness-of-fit test was applied with a significance level of 5%. Observed distributions were compared to the actual distributions of licensed athletes in Spain by sex and age group, following the recommendations of [PERSON] et al. (2011).  
To quantify the magnitude of the association in the chi-square test, Cramer's V was calculated, in line with the guidelines provided by [PERSON] et al. (2021) and in agreement with previous research ([PERSON] and [PERSON], 2021). Cramer's V is one of the most widely used effect size indicators when the chi-square statistic is significant ([PERSON] and [PERSON], 2021 ([PERSON] and [PERSON], 2021)). It is calculated using the following formula (Equation (1)):  
Equation (1). Cramer's V  
\[Cramer^{\prime}s\ V=\sqrt{\frac{\chi^{2}}{N\ (k-1)}} \tag{1}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Reference Age Group** & **Q1 (\%)** & **Q2 (\%)** & **Q3 (\%)** & **Q4 (\%)** & **S1 (\%)** & **S2 (\%)** \\ \hline F-16 y F-18 (EYOC) & 27.42 & 26.73 & 21.48 & 24.38 & 54.14 & 45.86 \\ F-20 (JWOC) & 29.72 & 26.10 & 22.74 & 21.45 & 55.81 & 44.19 \\ F-E (WOC y EOC) & 22.69 & 28.65 & 23.65 & 25.00 & 51.35 & 48.65 \\ M-16 y M-18 (EYOC) & 26.47 & 27.09 & 23.63 & 22.81 & 53.56 & 46.44 \\ M-20 (JWOC) & 26.56 & 28.04 & 24.04 & 21.36 & 54.60 & 45.40 \\ M-E (WOC y EOC) & 30.92 & 25.59 & 17.89 & 25.59 & 56.51 & 43.49 \\ \hline \end{tabular} Note. M/F-16 = ages 15–16; M/F-18 = ages 17–18; M/F-20 = ages 19–20; M/F-E = senior elite categories (M = male; F = female). Q1 = January–March; Q2 = April-June; Q3 = July–September; Q4 = October–December; S1 = January–June; S2 = July–December.  
\end{table}
Table 2: Percentage distribution by birth quartile (Q1–Q4) and semester (S1–S2) among Spanish licensed orientees (2009–2023), by reference age group and corresponding international competition.  
where \(\chi^{2}\) is the chi-square value, \(N\) is the total sample size, and \(k\) is the lesser of the number of rows or columns in the contingency table.  
Additionally, a Z-test was conducted to compare proportions between birth quartiles and semesters, using a significance threshold of \(p<0.05\).  
Finally, odds ratios (\(OR\)) and their corresponding 95% confidence intervals (95% CI) were calculated to evaluate the likelihood of selection based on relative age quartiles and semesters, disaggregated by sample and sex. This was carried out according to the method proposed by [PERSON] et al. [7]. The \(OR\) interpretation followed these criteria: if the 95% CI includes the value 1, the association is considered non-significant; if the CI is greater than 1, a positive association is suggested; and if below 1, a negative association is inferred [24]. The strength of association was interpreted following [PERSON] and [PERSON] [25], where an \(OR\approx 1.22\) indicates a small effect, \(\approx\)1.86 a medium effect, and \(\approx\)3.0 a large effect.