Deduce the order of convergence of explicit Euler

Question

I'm reading the following lecture slides : https://courses.maths.ox.ac.uk/node/view_material/1191. See Page $86$ for my question. In the slides, they are verifying order of convergence of explicit Euler method. We know from theory that explicit Euler is $O(\Delta t + \Delta x^2)$ accurate. I have written MATLAB code that is telling me that two time refinements per refinement in the space coordinate results in the error going down by a factor of roughly four. How can I deduce from this that explicit Euler is $O(\Delta t + \Delta x^2)$ accurate?