Final answer:
The most convincing outcome to demonstrate a causal relationship between two variables would be two experimental groups that, at the start of the experiment, were not different from each other on measures of IQ, but were different from the control group.
Step-by-step explanation:
The most convincing outcome to demonstrate a causal relationship between two variables would be option 4) two experimental groups that, at the start of the experiment, were not different from each other on measures of IQ, but were different from the control group.
This is because in an experiment, you can manipulate and control the independent variable to observe its effect on the dependent variable, which allows for causal conclusions. In this case, the fact that the two experimental groups were not different from each other at the beginning but showed different outcomes from the control group suggests that the independent variable (the experimental manipulation) had a causal effect on the dependent variable.
On the other hand, options 1) and 3) only show correlations between variables, which do not provide evidence of a causal relationship. Option 2) in a quasi-experimental design can suggest a relationship between variables, but it is not as strong as having two experimental groups and a control group.