How to decide whether a stock opening price is more or less equal to its closing price as compared to intraday price action

I want to study how many times a certain stock market index (e.g. DJI, DAX) historically had approximately the same opening and closing price, i.e. relative to the action price during the very same day. That is, the likelihood of whether a certain stock market index closed at the same price as the opening price, regardless of the action inbetween.

I have already computed the relative difference between the opening and closing prices. But how to compare this with the intraday volatility?

I have access to opening price, closing price, highest price and lowest price for each stock market index for the last 20 years. Are these data sufficient for an analysis, and any ideas as how to perform this analysis? Links, technical explanations etc. are most welcome.