Sampling Errors are of two types (as already mentioned in the question) - Biased and Unbiased.
Biased Sampling Error - is one which results in a bias in the sample. The effect of this bias is that the result of the sample will not reflect the true nature of the population. There are three sources of such bias
1. Survey Bias: where the survey questionnaire or the process of collecting data is biased
2. Researcher Bias: bias introduced by the researcher of the study
3. Respondent Bias: bias in the responses if the respondent chooses not to give the correct answer
Unbiased Sampling Error - is one which is the resultant of chance. The sample will never reflect the population simply because the observations will vary from each other.
Selecting a large sample size is one way in which both these biases could be avoided. However, since our analyst has decided to choose a smaller sample size, he should take care of the following things
1. Sampling method: choose the one which gives a random representative sample
2. If there is a questionnaire involved, then ensure that there are no leading questions or questions for which the respondents might have a tendency to not give the right response. Make the survey anonymous so that respondents could give correct responses
3. Determine which is more important - alpha or beta error? Since sample size is fixed, he could then determine either the significance level or Power of the Test that he is going to get and whether it is ok or not