An experiment has to be designed to to test if eating carrots improves eyesight.
This is not an easy experiment that can be completed in a single day. The whole process would require a long period of time. First, two groups of individuals willing to take part in the experiment has to be selected; the members of each of the groups should be representative of the general population. This is done to eliminate variations that may be attributed to the affect of carrots on eyesight in the participants due to factors like gender, race, country of origin, etc.
A period of time has to be fixed for which carrots should be eaten for their affect on eyesight to become apparent. It is also essential to eliminate the affect of other things in a person's diet that may influence the results of the experiment. For this, the participants of each of the groups should basically eat the same things. The only difference should be that the members of one group do not eat carrots and the members of the other group eat a fixed quantity of carrots each day.
After the required time period has elapsed, the eyesight of all the members would have to be tested to determine if there is a change in the eyesight of those in the group that ate carrots compared to those in the the other group that did not eat carrots.