Considering the design effect in cluster sampling

In this manuscript authors have said "cluster random sampling methods were used to select participants. Throughout the five sectors of Isfahan, we randomly chose two centers (clinics) from each area. Based on previously calculated mean and standard deviations for BMI in this population, our target number of participants was 143". We have some points about sampling method and sample size determination in mentioned manuscript. When cluster sampling is used the effect of intra-cluster correlation (ICC, or the strength of correlation within clusters) must be regarded for sample size calculation. 2 This effect called the design effect (Deff). It is a correction factor that is used to adjust the required sample size for cluster sampling. The required sample size, assuming a simple random sample (SRS), should be calculated, and then multiplied by the Deff. ff represents the degree of variance inflation that attributes to cluster sampling. The value of Deff for