Quantitative research methods are methods that are based on empirical numerical data (quantities). These are used more often in the hard sciences like physics and chemistry but are also used in the social sciences like sociology. If your research methods have to do with measuring numbers and figures, it's probably quantitative.

Qualitative research methods are based on describing behaviors and experiences (qualities). These are primarily used in the humanities and social sciences (for example, anthropology and history use a lot of qualitative methods). Examples of qualitative methods include ethnography and critical analysis - in both cases, you're looking at something and describing what's happening.

Quantitative methods can tell you where Emily goes, but not necessarily why. Quantitative methods can tell you Facebook is popular because you can restrict who sees what, but interviewing someone can show you that perception of why a SNS is popular comes from peers and many other places, like Manu’s case. It lets you develop questions ‘on-the-go’. If you have a quantitative survey, you cannot explore deeper than the set of questions you already have. Whereas, qualitative methods allow for deeper understanding because through qualitative methods you can ‘observe’ past or present situations through a person’s story, you can ask more intimate questions. Qualitative lets the researchers understand the meaning people attach to social media and why they use it.

1. Larger sample sizes

2. Strong attempts at representative sampling

3. Quantitative data on all processes, such as selection of themes, etc.

I think those could be done for a number of qual studies (though not all). They would help a lot.