In regression analysis we make several assumptions about the error term. The following assumptions are often made: 1) the error terms are random variables with mean 0; 2) nonautocorrelation; 3) homoscedasticity, and 4) normality. The assumption of identically and independently distributed (iid) observations that underlies regression procedures is called into question when analyzing complex survey data. Particularly the existence of clusters in two stage samples usually exhibit positive intracluster correlation. If we use Ordinary Least Squares (OLS) procedures to make inferences in regression analysis for two stage cluster samples, we will be faced with a problem. This study aims to know the effect of two stage least squares on the F-Statistic. In general, although OLS procedures are unbiased but not fully efficient for estimation of the regression coefficients. Variance of the OLS estimators for the regression coefficients can be larger than the usual OLS variance expression would indicate. Failure to consider this possibility leads to underestimation of variances, with consequences for confidence intervals and the F-Statistic. The effect of intracluster correlation on the F-Statistic is the distortion of its distribution. The F-Statistic will not follow the Central F distribution anymore. Consequently, the hypothesis testing procedure is invalid.