Can a sample be random but not representative?
Or can a sample be representative but not random.
Could you give examples of both please?
The answer to both of your questions is: yes.
Consider this simplified situation. Say you work in a firm with 4 departments: IT, Marketing, HR, and Sales. There are 1000 people in each department, so a total of 4000 people. You want to evaluate the general attitude towards a decision to move to a new office, which is much better on the inside, but is located on the other side of the city.
You decide you don’t really want to ask 4000 people, but 100 is a nice sample. Now we know that the 4 groups are exactly equal. So we expect that in those 100 people, we would have 25 from each department.
1) We pick 100 people (out of the 4000) at random at realize that we have 30 IT, 30 Marketing, 30 HR, and 10 from Sales. Obviously the opinion of the Sales department is underrepresented. We have a sample, which is random but not representative.
2) I’ve been working in this firm for quite a while now, so I have many friends all over it. I decide to ask the opinion of my friends from each department, because I want them to feel comfortable in the workplace. I pick 25 people from each department. The sample is representative but is not random.
In the first case, we have underrepresented some group of people.
In the second case, we’ve made a decision based on a specific circle of people and not the general ‘public’.
If I want it to be random and representative, I will pick 25 people from IT at random, then 25 people from Marketing at random, same for HR and Sales. In this way, all groups will be represented and the sample will be random.
Hope this helps!
The 365 Team