Measurement error of a phenotypic trait reduces the power to detect genetic associations. We examined the impact of sample size, allele frequency and effect size in presence of measurement error for quantitative traits. The statistical power to detect genetic association with phenotype mean and variability was investigated analytically. The non-centrality parameter for a non-central F distribution was derived and verified using computer simulations. We obtained equivalent formulas for the cost of phenotype measurement error. Effects of differences in measurements were examined in a genome-wide association study (GWAS) of two grading scales for cataract and a replication study of genetic variants influencing blood pressure. The mean absolute difference between the analytic power and simulation power for comparison of phenotypic means and variances was less than 0.005, and the absolute difference did not exceed 0.02. To maintain the same power, a one standard deviation (SD) in measurement error of a standard normal distributed trait required a one-fold increase in sample size for comparison of means, and a three-fold increase in sample size for comparison of variances. GWAS results revealed almost no overlap in the significant SNPs (p<10−5) for the two cataract grading scales while replication results in genetic variants of blood pressure displayed no significant differences between averaged blood pressure measurements and single blood pressure measurements. We have developed a framework for researchers to quantify power in the presence of measurement error, which will be applicable to studies of phenotypes in which the measurement is highly variable.