Final answer:
Statistical limitations for determining a proper sample size include the underlying distribution of observations and experiences from past studies. Adequate sample size typically starts from 30 observations for normal populations, but larger sizes are required for non-normal distributions. There are no fixed 'adequate' sample sizes as it varies based on the research context.
Step-by-step explanation:
When it comes to determining the sample size for comparing two populations, it is essential to balance the need for accuracy with the risk of oversampling. Statistical limitations are guidelines that help to decide an appropriate sample size. These limitations are based on a variety of factors including underlying distribution of observations, experiences from previous studies, and the nature of data, such as distribution and variability.
A sufficient sample size allows for a more accurate estimate of the population parameter and reduces sampling variability. Conventional wisdom suggests that for a sample to adequately represent a population, at a minimum, it should have 30 observations or come from a normally distributed population. In cases where populations are not normally distributed, larger samples are required. Moreover, in inferential statistics, larger samples tend to minimize the importance of the underlying distribution of data.
Essentially, there are no fixed rules for an 'adequate' sample size, as it heavily depends on the research hypothesis, the variability within the data, and other contextual factors. In situations where larger samples are not possible, such as in crash tests or studies on rare medical conditions, smaller samples can still be informative, but they may come with increased uncertainty.