Lee and Strazicich (LS) designed a state-of-the-art statistic for testing for a unit root under structural changes. Using Monte Carlo experiments on the Nelson and Plosser data, this present study analyses the effects of scale of variance and data unit on the size-adjusted power of the LS unit root test. It is found that under the null and the alternative hypotheses of unit root shifts from right to left, the goodness of fit of the statistic worsens, and the power increases systematically when the scale of variance increases from 0.01 w to w and from w to 100 w (w being a weighting factor). The power increases when the data unit is reduced to one tenth and per cent (i.e. one hundredth) except for the Industrial Production Index, Total Unemployment Rate and Nominal Wages. To achieve the goal of higher power and better goodness of fit in the LS test, results suggest using the original variance rather than the best goodness-of-fit variance, changing the data unit to per cent, or using a mixed strategy selecting the data unit corresponding to a higher power for each data series.