Researches in the medical field are done to seek solutions to existing medical problems which include problems on prevention, and medication, among others. It is impossible to study an entire population, and thus the reason why statisticians take samples of varied sizes for easier analysis and accurate conclusion. It is important to note that the determination of sample size is very important to the accuracy of the conclusion made on the research. This implies that sample size may be relevant or irrelevant, depending on certain factors on the research or the study population. When calculating the sample size of a given study, researchers ae advised neither to use very large nor too small sample sizes because they are known for various disadvantages.
While too small sample sizes may be cheaper to the researcher, it may possibly undermine the relevance of the sample size, and subsequently result in null results (Nayak, 2010). Researchers may get tempted to pick small sample sizes based on their limited time, convenience, and limited resources. Nevertheless, this may possibly make their samples irrelevant because they will end up lacking sufficient subjects to study, and would subsequently make irrelevant conclusions on the research. On the other hand, too large sample sizes may seem sufficient to the researchers. Nevertheless, they lead to resource wastage, and may as well be unethical. Therefore, the size of the sample population is very important. Researchers should pick moderate sample sizes matching the magnitude of their respective researches to get accurate results and make good recommendations.
Delegate your assignment to our experts and they will do the rest.
For medical researches, large clinical researches require relatively larger sample sizes than smaller and fewer clinical studies. This implies that the nature of the study may determine the relevance of a sample size during a research (Pagano & Gauvreau, 2018). For example, if a researcher decides to pick a small sample size for a clinical prevention trial of an epidemic, the sample size may prove to be irrelevant because of the nature of the study. Such research would be done better using a relatively larger sample size. Similarly, a small clinical trial, such as determining the safety of using a certain device, would require a relatively smaller sample size to draw an accurate conclusion. Therefore, researchers should pick appropriate sample sizes that match the nature of their studies. In addition to that, there are other factors that ought to be considered because they may possibly affect the relevance of a sample size. They include the margin of error, standard deviation, and attrition rate.
Discussion 2- Reflection
Probability is a concept that I have encountered in life before, and I have used the terms of probability quite often. Learning about the mathematical concept of probability was quite interesting because I found the idea quite easy to grasp. The mathematical illustrations for probability were so real because they simply indicate the chance of occurrence of a given issue. The fact that the mathematical illustrations were based on the entire population proves the idea behind the specific percentage of chance of occurrence of a given a specific group. Indeed, probability occurs in the case of random selection from a large population.
I also enjoyed learning about the various properties of probability, and the illustration that subsequently proves them. Probability applies to every possible occurrence in a given population. The fact that each outcome is considered regardless of their level of chances makes probability to indeed sum to one. This can be proved by the fact that whenever there is a certainty of the occurrence of one event, then the probability can be set at one. Having an additional possible occurrence reduces the probability of the other event while increasing that of another. Moreover, this property also adds value to the property of adding probabilities of disjoint events. It was also interesting to see how the various properties of probability can be illustrated, especially on the sum of probabilities. Adding up the various probabilities is good in reviewing whether one is right on probability calculation.
Nevertheless, I found the concept of cumulative probability somewhat challenging. Calculating the cumulative probability and deriving the figures in a bar graph was not an easy task for me. I found it specifically challenging to understand the Pr (X<x) notation. In as much as it was easy to understand the definition, that there can be the probability that value can fall within a given range, plotting the definition in the cumulative probability graph was specifically challenging. All the same, I was able to understand the theory behind the concept. There are occasions in my life when I have come across uncertain calculations that are predicted to fall within given ranges.
Assignment
In statistics, larger sample sizes are regarded as good because they increase the possibility of a good quality research conclusion. This is because sample sizes are used in research to represent whole populations, and thus picking appropriate sizes gives researchers better ways to look at entire populations. Notably, increasing the sample size brings about a decrease in variability in the research. Increasing the sample size typically makes the sampling distribution to incline towards normal. Subsequently, using an infinite amount of successive random samples makes the sampling distribution mean to become equal to the mean of the population. Boddy (2016) suggests that the variability of sampling is inversely proportional to sample sizes such that as the former increases, the latter decreases. The main reason why this happens so is to make the sample size and the sampling distribution to become more leptokurtic. It is common knowledge that the sampling distribution range is smaller than that of the original population, something that can explain the inversely proportional relationship between sample sizes and sampling distribution.
Frequency in the context of statistics refers to the number of times that a data value occurs. For example, if twelve students score the mark of 90 in a test, then it can be said that the mark of 90 has a frequency of twelve. Frequency also appears as probability theory. In this particular context, the probability is deemed as the frequency of a given outcome vis-à-vis the frequency with which it would occur. Frequency distributions can be used to derive probability. This can be done by putting down a frequency distribution of all the possible outcomes of an event.
For example, flipping a coin can possibly bring two outcomes, which are head or tail. Statistically, this set of outcomes can be represented as the ratio of tails to heads to be 1 to 1. Similarly, this relationship can be expressed by defining the frequency of each possible outcome, with the frequency being the fraction or percentage of the number of times the activity achieves a given outcome. For the ratio stated above, there are two possible outcomes, which implies that the relative frequency of tails and heads are each 0.5 or ½. The relative frequency can be expressed in the form of probability. Normally, relative frequency is equivalent to probability. From the above example, this can be ascertained since the relative frequencies of both outcomes can be added to get 1. The above relationship between frequency and probability is important because it helps researchers understand probability with more clarity. Notably, one gets to ascertain the figures of probability using frequency distributions and relative frequency figures.
References
Boddy, C. R. (2016). Sample size for qualitative research. Qualitative Market Research: An International Journal .
Pagano, M., & Gauvreau, K. (2018). Principles of biostatistics . Chapman and Hall/CRC.
