For comparing several populations, the fuzzy analysis of variance has been summarized and reviewed where the collected data considered fuzzy rather than crisp numbers. As a practical work based on the real-word data, a case study was carried out to investigate effects of three concentrations (0, 50 and 100 ppm) nanoSiO2 on seedling growth and dry matter weight of fenugreek (Trigonella foenum-graceum L.). All presented data in this study are fuzzy and therefore we need an extended version of analysis of variance to investigate on these fuzzy observations. Although, the presented analysis of variance approach based on vague data can causes to a fuzzy decision, but as an advantage of the proposed approach the vagueness of this fuzzy decision measured.