Question

Consider the single random factor model for a balanced design. Show that MSE is an unbiased estimator of σ2. Under H0 : σ2=0, derive the distribution of SSE/ σ2. (MSE and SSE, represent mean and sum of squared errors)

Answer 1

MSE is an unbiased estimator of σ2 in a balanced design. SSE/ σ2 follows a chi-square distribution under H0 : σ2=0.

Step-by-step explanation:

In the context of a balanced design, the Mean Squared Error (MSE) is an unbiased estimator of the population variance (σ2). This is because the MSE is calculated by dividing the Sum of Squared Errors (SSE) by the degrees of freedom, which yields an unbiased estimate of σ2.

Under the null hypothesis (H0: σ2 = 0), the distribution of SSE/σ2 follows the chi-square distribution with degrees of freedom equal to the number of observations minus the number of model parameters. This allows us to perform hypothesis tests and make inferences about the population variance.