which type of campaigns have greater need for a control group.
a. an email campaign with links to the e-commerce site.
b.a direct mail campaign with coupon code
c.a banner on the website advertising a in-store sale
answers with explainations expected.
basically control group should be used in almost every campaign. They enable us to show you whether or not a message drove an increase (or decrease) in user engagement, revenue, or conversion. Only two cases when you should avoid control group is:
Agree with @Milan_Vucetic
In addition, I imagine you would like to use a control group in all campaigns that have measurable KPIs like revenue, signups etc. So that you are able to compare and find out how effective has the campaign been. Also, it would be a good idea to keep the control group consistent across all communication belonging to a particular campaign ( For example - Summer Collection sales promotion email1 and reminder email2.). This can give you a better idea of how the control group is behaving.
For testing the validity of content variations ( like banners/ subject lines), it would rather be more helpful to use AB tests instead of control group.
C. A banner on the website advertising a in-store sale