equal to operator

Hi,
I have the below script executed

arg="dir"
if "$arg" = "dir"
then
    echo "true"
else
    echo "false"
fi

Please let me know what happens in the if command.
My output is:

dir: dir: No such file or directory
false
which is not the desired output.
When i used test command it works fine.
Please explain the significance of = (and if command) in the above code.

You can have a read of:

BASH Programming - Introduction HOW-TO: Conditionals

Regards