Shiller's test or 'Shiller's volatility puzzle' states that the volatility in stock prices cannot be expained by rational expectations about future dividents. so it contradicts the EMH.
It tests the semi-strong form of the EMH. This is because excessive volatility is where a market is more volatile than can be justified by the "news arriving" (p12 in Course Notes), which means new publicly available information.
couldn't one argue that it also contradicts the strong form of EMH - since insiders (eg Directors) may know future dividends (in the same way that Shiller knew the 100 years of dividend data) but it still wouldn't help them predict the future share price?