In 2013, one of the most common refrains I heard while selling print ads to small business owners was "We are concentrating on our online advertising". There is no doubt there is, and should be, an upward trend towards owning your online footprint. However, the idea of marketing exclusively online for a brick and mortar business is unwise to say the least. Conversely, an online business should not close their minds to traditional advertising.
In the same way you wouldn't limit where you should sell your products, you should also keep an open mind to where you advertise. Putting all your eggs in one basket in any facet of business is a recipe for mediocrity or worse, failure.
To separate your advertising into "traditional" or "online" is also a little basic. Just like traditional advertising consists of many media, so does the online variety. For the many types I will list here, there are plenty more. Websites, Facebook, Twitter, and Pinterest are just a few. There are also Google ads, YouTube, and more.
There is a perception that many online marketing opportunities are free. While starting a Twitter or Facebook account may be free, quality graphics and time spent writing posts as well as responding to customer posts and questions can take a full time person to handle. A good social media marketer also spends the time tracking trends in your market and the medium in general, and if they are really good, they will post in your voice. As amazing as it may sound, people can tell if the business owner or manager is posting, or if it is a professional online marketer.
If you are a business owner, do a bit of a case study of a large national or multinational company and its advertising and you will clearly see that while less of a percentage of overall marketing dollars are going to traditional media year to year, they are still the largest expenditures in the ad budget.
Like any business, diversity is the key. People will respond to communications by the way they wish to be communicated to. If you wish to reach your maximum number of potential customers, your advertising and marketing plans must include traditional media. Don't buy into "newspapers are dying" mantra. They just aren't as big as they used to be. With traditional media, your message will have much less competition for eyeballs than it did in the nineties.