In our workshops, I often use a case study of an organisation who weren't gaining many new members through social media (according to Google Analytics).
Participants tend to reach two completely contradictory conclusions (often within the same groups). Some feel they should spend a lot more time on social media, others feel they should spend a lot less time on social media.
It's a tough question.
Is it a sign that social media doesn't work?
Is it a sign that you're not doing well?
The answer tends to reflect the participant's pre-existing bias (if they spend a lot of time on social media, they feel it's the latter)
The real answer is you don't know. It's not a question of whether the channel does/doesn't work. It's a question of whether it is the most cost-effective means to attract more members. You can't learn that from a single metric.
It doesn't cost much time/effort to post a few social media updates per week. Even a trickle of new members makes it worthwhile.
Unless the accounts look bad due to irregular updates or superior competitors. Then the cost might be too high. Better to let the competition own the least-effective channels to attract new members.
Likewise you might find you attract most of your members by creating regularly eBooks, best practice guides, building inbound links from popular sites. Yet the cost/resource to create these makes it a poor channel for attracting members.
A single data point doesn't tell you what is or isn't working. You need to know how much of your time and resources you're spending on each channel to identify where best to spend your time.
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