In most cases, the sample elements, in this case clients, will also be the actual sampling units which are selected and will also be the observation units which will be actually interviewed. The client will also be the unit of analysis later when the data are analyzed. So it is good to distinguish the element, the sampling unit, the observation unit, and the unit of analysis, though all are often the same, as in a study of clients. A variable is a measurable item, such as a trait, characteristic, opinion or attitude which varies for the units being studied, such as the age, race, gender, levels of satisfaction, etc. of clients. A statistic is the statistical description of a variable for the sample, such as 33.3 is the average age of the clients in the sample.
Statistics estimate parameters.
Probability samples when done properly enable us to estimate the probability that a statistic is a good estimation of a parameter. Random selection is where each element of the population has an equal chance of being selected in the sample. The principle of random selection must be maintained if we are to have a probability sample that can be used to estimate the probability that our statistics are representative of parameters. As we might suspect, the larger the sample, the higher the probability our sample is representative. For random samples, the sample statistics that estimate population parameters will have a higher probability of being representative the larger the sample.