  Order-disorder phase transition is one of the interesting features in the
opinion dynamics model of sociophysics. This phenomenon is caused by noise
parameters, which can be treated as social responses such as anticonformity and
independence (nonconformity) in a social context. This paper explores the
effect of nonconformity behavior on changes in the macroscopic state of the
system. A probability $p$ represents anticonformity and independence, and the
model is defined on the complete graph and the two-dimensional (2D) square
lattice. We also introduce a skepticism parameter represented by $s$, which
describes a voter's propensity to behave nonconformist. Our results
analytically and numerically show that the model undergoes a continuous and
discontinuous phase for all values of non-zero $s$ and at specific $q$-sized
agent. No phase transition is observed in the model with independent voters on
the 2D square lattice, and the model with anticonformist voters undergoes a
continuous phase transition. We also analyze the effect of the probability $p$
and skepticism level $s$ on the outcome of the system's opinion.
