I am trying to identify if there is seasonality in the data set. The condition is that I don't want to use graphs or any kind of visual interpretation to understand seasonality, but to use statistics to tell me if seasonality is present and how significant is it? can anybody help me on this?
Things come to mind .... the auto-correlation function can be "blurred/obfuscated" by the presence of anomalous observations (pulses) and level shifts , trend changes among other things. Trend detection and seasonality detection can be done if one recognizes that there are two distinct forms of seasonality .. one is seasonal memory (sarima) the second is seasonal dummies . Discerning between them for each time series under consideration is important in the analysis.
If three months of the year are the only ones effected by seasonality while 9 are not the seasonal arima (memory) may not stand out while three seasonal dummies would be appropriate. I would make sure that this distinction is available in any software that you try to employ. Many researchers using freely available solutions often find that a pure seasonal memory model is not significant while upon closer inspection there is significant seasonality for some months. An important task worth doing is worth doing correctly .
I am unaware of any free software that comprehensively deals with this subject.