I am trying to plot a graph to show the effect of my significant variable on my dependent variable but the data is binary (presence/absence) for both. Could anyone suggest how best to display the data in a graph that is easy for the reader to understand? With a guide of how to do it?
The visualisation of categorical data can be challenging and is not as well developed as the visualisation of continuous or mixed categorical/continuous data. So unfortunately, the names of the relevant displays aren't as well known, and this makes searching for help difficult.
In this case, it is likely that you need a mosaic plot (also known as a Marimekko chart), which enables you to plot categorical variables on both the x and y axes (and to have hierarchical levels of each).
Below is a classic example showing survival (light grey) vs non-survival (dark grey) as a function of both sex (male vs female) and class (1st, 2nd, 3rd, or crew) for people on the Titanic. (Taken from the Wikipedia page for mosaic plots.) The left-hand panel shows the actual data, while the right-hand one shows the frequencies that would be expected if the survival outcome was independent of the other variables: