## 3 Research Methodology
### Data Validity Analysis  
The validity of the results was checked through a statistical analysis of the data gathered for both cohorts. This provides the foundation and the justification for the qualitative analysis that will be presented in the next section. The results of two hypothesis tests comparing the two cohorts and their evolution through the acceleration programmes are: the Levene test [46], which assesses the equality of the variances of the indicators gathered for the in-person and online cohorts, and two versions of the Mann-Whitney test [47], paired and not paired, to assess the equality of the means of those 30 indicators between the cohorts. On the one hand, the null hypothesis verified through the Levene test is that the population variances are equal in both cohorts. That is, the test seeks to confirm the property of homoscedasticity of the samples to be compared. On the other hand, the null hypothesis tested by the Mann-Whitney U nonparametric test is that, for randomly selected values from two populations, the probability of the first value being greater than the second one is equal to the probability of the second value being greater than the first one. That is, it checks if the two samples were drawn from two different populations with equal means. We performed two versions of the Mann-Whitney test: paired and non-paired data. The first one allowed us to check the impact that the acceleration programme has had on the participant indicators, while the second allowed us to compare if the indicators for both cohorts followed a similar distribution. The Mann-Whitney test does not require normality and equal variances, which are hard to demonstrate, but rather that the observations are independent and that the samples are randomly selected. We require a significance value (\(\alpha\)) of 0.05 or less in order to reject the null hypothesis defended by each of the statistical tests performed. Since there are 30 indicators for characterizing the status of each participant, we show the results of the tests through histograms of the significance level, grouped by interval. The red bars on the histograms that are shown in this section correspond to \(p\)-values that are lower than the selected significance value (\(\alpha\leq 0.05\)). We also identify significance levels in the range from 0 to 0.005 and from 0.005 to 0.01. We first present, in Figure 3, the results of the Levene tests comparing the equality of the variances of the two cohorts, both just before entering and after exiting the programme. The first row in Figure 3 corresponds to the comparison between cohorts before entering the acceleration programme, while the second row in Figure 3 corresponds to the cohorts just after exiting it. Only four indicators (PR & Communications', 'Growth metrics', 'Investment strategy' and 'Experience') scored lower than the required significance level at the entry point, while none did so at programme exit. This means that the variance of the companies/start-ups that participated in the programmes was similar in 87%/100% of the indicators measured at the entry/exit points. This allows us to conclude that we had a similar variability, with respect to the indicators, in the participants of both cohorts. Figure 4 shows the histograms of the results of the Mann-Whitney unpaired two-tails tests that compare the 30 indicators at programme entry and exit, for equality of the means of the populations. As can be seen, at programme entry there were 11 indicators for which  
Figure 3: Histograms of Levene test results comparing for equality the variance of the 30 indicators for the COVID and pre-COVID cohorts at programme entry and exit. the Mann-Whitney tests provide a p-value that is higher than the required one (0.05), meaning that we can estimate that the participants of both cohorts had a similar level on only 37% of the selected indicators. After their participation in the programme, 17 indicators passed the test threshold, meaning that the cohorts completed the programmes with similar levels on 57% of the indicators.