Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
The sample was used as a part of the research community, while some procedures were applied to calculate the sample size. In this case, Lemeshow equation was employed to detect the sample size between the experimental and control groups. Notably, this equation is the most widely used approach to compare two groups of equal size and identify the intervention effect on the outcome in pre-post studies (Ary et al., 2018). Furthermore, the Lemeshow test assesses the significance of the difference between two population means, which may be found in the case when the two means are based on the same sample of subjects or matched-pair samples. In this study, this equation was used to assess the two correlated means of EG and CG. As indicated by (Lwanga et al., 1991) the sufficient sample measure for randomised controlled trial was based on α (error sort I, α = 0.05), β (error sort II, β = 0.20), p (level of knowledge in ASD among pre-school teachers) (Lwanga et al., 1991), and d2 (contrast to be recognized amongst experimental and control collection) (Perels et al., 2009).See Table 3.4
n=〖〖2σ^2 (Z〗_(1-α)+Z_(1-β))〗^2/〖(M_1-M_2)〗^2
To determine a suitable sample size adjustment for clustering, standard sample size estimates for individually randomised designs were calculated first and inflated by the design effect (Campbell & Stanley, 2015; Lwanga et al., 1991).
n=(2x0.053 〖〖(5.38)〗^2+ (2.65)〗^2)/(21.57-18.93)=20.23
As mentioned above, the calculated sample size n = 100 would be considered the sample size in this study. To calculate adequate sample size adjusting for clustering, the standard sample size was inflated by the effect size, as shown below:
Effect size = 1 + (M - 1) x ICC = 1 + (16 – 1) x 0.05 = 1.75
20.23 x 1.75 (effect size of cluster random sampling) = 35.40
Where; ICC = 0.05 (Intra-cluster correlation) (Ary et al., 2018).
M = 16 (Average Cluster Size; the average number of pre-school teacher for each cluster)
Assuming the drop from 10 % = 17 + 35.40 = 52.40, eight participants were added into the final sample size, n = 120. They were equally distributed between the experimental (60) and control (60) groups, as it was previously determined according to the equation of the sample size.