Many thanks for your very prompt responses. Sorry for the delay in coming back but I have been rather busy for a couple of days, plus it took quite some time to read all the info in the various links you both supplied.
I ran the ShieldsUp test and was re-assured to find that Sygate's stealth mode does (ALMOST) completely hide me when on the Internet. Inadvertently I ran the test twice; the first time it reported "No unsolicited packets were received", but the second time it said "Received one or more unsolicited packets". Running two more tests have both reported no unsolicited packets. I am a bit puzzled why the second test failed.
However all four tests have reported "A ping reply (ICMP echo) was received". I haven't been able to find any means to stop this. In fact on the Sygate Help Site click here the following appears: -
Enable stealth mode browsing
"Stealth mode" is a term used to describe a computer that is hidden from other computers while on a network. A computer on the Internet, for instance, if in stealth mode, can not be detected by port scans or communication attempts, such as ping. If you enable this feature, your computer will be invisible to other computers on any network you are on.
Surely this implies that Sygate should have prevented the ping reply from being sent, and the ShieldsUp test would then not have detected it. Does anyone have any thoughts on this?