The purpose of this paper is to improve the quality of published research papers by demystifying the concept of probability sampling designs in research. The paper describes how to decide and present probability sampling designs in research and how to determine the sample size. It was motivated by the observation that, researchers in published journal articles guided by quantitative methods either present misconceptions of probability sampling or are silent about the sampling design. The study is guided by qualitative methodologies. Data was collected by documentary analysis of research and mathematics textbooks as a basis for the ideal concept of probability sampling designs and determination of sample size. This was followed by an analysis of a purposive sample of 57 research papers in 9 different journals, 45 dissertations by masters’ students and 92 research projects submitted by undergraduate students. These were analyzed for their presentation of probability sampling. The study found that, researchers and students are not including how they established the sample size. They confused random sampling for any haphazard activity associated with selecting participants. They are not sure of the conditions under which simple random sampling, systematic sampling, stratified sampling and cluster sampling must be applied. Population analysis in terms of variable distribution is missing. In addition, their descriptions of how the sampling is done (process) needs improvement. These errors are traced to research methods textbooks which are not presenting probability sampling techniques clearly for novice researchers. This study recommends that probability sampling is suitable when the total population is known. Simple random sampling should be applied when the variable is uniformly distributed. Systematic sampling is proper when the variable follows a linear dependency. Stratified sampling is appropriate when the variable is in strata and cluster sampling is fitting when variables emerge in groups. Sample size can be determined from table provided. An illustrative example is included for researchers’ and students’ discussion
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