The major drawback of this web based Azure speed test tool is that this tool does not measure latency with ICMP ping or TCP ping, due to browser limitation.
If you want to measure ICMP ping latency to Azure datacenters, you might want to check a great tool called PsPing from PsTools suite. PsPing is a command-line utility for measuring network performance, it implements Ping functionality, TCP ping, latency and bandwidth measurement.
Here is how to run your network latency test using PsPing tool:
psping target:portThe target can be ip or dns name of Virtual Machine, Storage, SQL Database and other endpoints that is public accessable