I can't speak to the statistic about households, because I don't understand enough about how that's measured or where the correlation would be significant.

However:

> According to a separate study cited by the Journal, only 22.7 percent of new entrepreneurs in 2013 were aged 20–34, compared to 26.4 percent the year before.

This statistic doesn't necessarily support what you're claiming, since it doesn't control for an increase across the board, primarily from other groups.

It's possible that this statistic could be true even while the percentage of people those age who join is rising, because another group rose faster, reshaping the cohort statistics even while there was a gain for everyone.

Example with made up numbers:

20% of young adults; 30% of older adults in 2013.

25% of young adults; 50% of older adults in 2014.

Young adults fell as a percentage of the new cohort from 40% to 33%, year over year, even as the likelihood that a young adult would become an entrepreneur rose.

That is, without controlling for other factors, the statistic about the relative population of young adults in the latest cohort doesn't tell us anything about young adults' behaviors.

there are situations where percentage is misleading.

10% of people start a startup today, 5% 5 years ago.

20% of young people start today , 30% 5 years ago.

chance of a young person starting today? 2%, 5 years ago? 1.5% . therefore young people are more likely to start a startup today than 5 years ago

To clarify I think what you meant in your example is that 20% of those who start today are young while there were 30% of the same cohort 5 years ago.