Final answer:
If a sample size is not big enough, it can result in unreliable and unrepresentative outcomes, potentially leading to chance error or bias. Larger sample sizes reduce sampling variability and offer more trustworthy statistics. However, in certain fields like medical testing of rare conditions, small samples might be the only option, and their results should be interpreted with caution.
Step-by-step explanation:
Impact of Sample Size on Research Outcomes
When the sample size in a study is not large enough, the reliability and validity of the results can be negatively affected. Larger samples are preferred because they are more likely to be representative of the population, reducing the chance error and bias that could occur with small samples. In some cases, especially when dealing with normal distributions or when the population itself is small, a smaller sample might still be usable. However, for most statistical studies, particularly those not involving normally distributed data or with larger populations, a sample size of at least 30 is advised.
Sampling variability is another factor influenced by sample size; larger sample sizes reduce the variability between sample results, thus strengthening the reliability of the statistics. Additionally, samples drawn randomly are essential to avoid bias, regardless of the sample size. If a sample is too small, it is more susceptible to deviations that do not accurately reflect the population's characteristics.
In fields such as medical testing for rare conditions or in scenarios like crash testing where large samples are not feasible, smaller samples may be necessitated. Despite this, care must be taken in interpreting results from small samples, which often means understanding the higher margin of error and the potential need for further studies.