The authors introduce two kinds of summability methods, \(\sigma\)-statistical summability and statistical \(\sigma\)-summability, by using the concepts of invariant means, and statistical convergence. A sequence \((x_{k})\) is said to be \(\sigma\)-statistically convergent to \(L\) if for every \( \varepsilon> 0\) \[ \lim_{p\rightarrow\infty}\frac{1}{p}\big|\{\sigma (m)\leq k \leq \sigma^{p}(m): |x_{k}-L| \geq\varepsilon\}\big|=0,\quad \text{uniformly in }m, \] and a sequence \((x_{k})\) is said to be statistically \(\sigma\)-convergent to \(L\) if for every \( \varepsilon> 0\) \[ \lim_{n\rightarrow\infty}\frac{1}{n} \big|\{ p \leq n : |t_{pm}-L| \geq\varepsilon\}\big|=0, \quad\text{uniformly in }m, \] where \(t_{pm}=\frac{x_{m}+x_{\sigma(m)}+x_{\sigma^{2}}(m)+...+x_{\sigma^{p}(m)}}{p+1}\), and \(\sigma\) is a mapping of the set of positive integers into itself satisfying certain conditions. Some inclusion results are obtained and some decomposition theorems are proved for the methods.