The unemployment rate has dropped almost linearly from a peak of 17.4% in 1983, with reversals of trend coming after each recession. Widely held economic theory says that raising the minimum wage results in higher unemployment. But that can be difficult/impossible to tell when unemployment rates are much more heavily influenced by macroeconomic conditions (changes in preferences, globalization, technological innovation, etc.). Shifts in the nature of the labor force away from mining and manufacturing toward health care, retail, law, finance, and other technical jobs requiring computer skills ultimately produced new, different jobs that displaced some workers from the labor force while providing new sectors for other workers. Upticks in the unemployment rate seem to follow the path of recessions (crash of 1987, tech bubble, Great Recession of 2008).
From this information it can be reasoned that workers making under $25,000, around the minimum wage, are not making less in inflation adjusted terms. Not only that, but more and more workers are not in this category. And lastly, that is why the share of total income of the bottom income brackets has dropped; not because they are earning less, but because of the upward mobility of higher earners.
In conclusion, there is an indeterminable relationship between unemployment and minimum wage. It may increase unemployment at the bottom of the income spectrum, but there is not clear data showing this and no way of inferring causality. The minimum wage has stayed constant, in real terms, as unemployment has dropped in WV over the years. It is currently above the 1980-2013 average of $6.55 in 2013 dollars. Increasing it now may slightly increase the share of income going to the bottom tax bracket, but it won't be considerable due to the broader shift of workers up the income brackets and their increasing wages.
This is an issue of importance being hotly debated at the global level. The release of Thomas Piketty's book: Capital in the Twenty-First Century has created a flurry of discussion over inequality and whether it is due to grow indefinitely in the future. Piketty's main thesis is that the growth rate on capital has been higher than the growth rate of labor over the broad course of human history. This makes the people owning capital assets (stocks, buildings, land, machines) wealthier than the people providing goods and services. He uses this point to advocate for a global redistribution of income. While the jury is out on his claim about growth rates, the story for a large amount of people over their lifetimes has been a rising standard of living as they jump up the income scale. The Great Recession may have called this mobility into question, but the numbers have yet to show that it has stopped. There is still wealth to be made for those that can and will work for it.