Let 2 (T) = i (T i i0 ) 2 / i0 . Then 2 (p) = X 2 /n,

Let ϕ²(T) = ∑_i(T_i – π_i0)²/π_i0. Then ϕ²(p) = X²/n, where X² is the Pearson statistic (1.15) for testing H₀: π_i = π_i0, i = 1, ..., N, and nϕ²(π) is the noncentrality for that test when π is the true value. Under H₀, why does the delta method not yield an asymptotic normal distribution for ϕ²(p)?