Which research method allows respondents to answer questionnaires via e-mail or a website?

The correct choice is an online survey, as this research method specifically facilitates the collection of data via digital platforms. Respondents can provide their answers through e-mail or designated websites, making it a convenient option for both participants and researchers. This method often allows for quick distribution and collection of responses, a wider geographic reach, and typically lower costs associated with data collection compared to traditional methods.

In contrast, a face-to-face survey involves direct interaction between the researcher and the respondent, which is not facilitated by e-mail or online platforms. A phone interview requires real-time verbal communication over the phone, thus does not allow written responses via e-mail or a website. Lastly, a mail survey involves sending physical questionnaires through postal services, which also does not utilize electronic means for collecting responses. This distinction highlights why online surveys are uniquely suited for digital data collection methods.