This article deals with the variance analysis of democracy index data, obtained from the yearly report prepared by Economist Intelligence Unit (EIU). The EIU calculated democracy index since 2006 for 167 countries covering almost the entire population of the world. Democracy index data vary over time and hence variance and time series analysis has been applied to available democracy index data for the period 2006-2018 to investigate the progress of democracy and to find the reason of democratic change. It is observed that some of the highly democratic countries including the USA gradually converted to moderate democratic countries. It is also observed that there exists a strong negative relation between democracy index and nonreligious population fractions for most of these countries. That is an increase of non-religious population fraction of a country may decrease the democracy index of that country.