Introduction
The effective (or adequate) sample size has the same level of precision as a simple random sample, and its calculation helps ensure that research has sufficient power to reject the null hypothesis. In other words, the adequate sample size is the one that is required for an analysis to be valid. To calculate the effective size of a sample, one needs to conduct a statistical procedure that is called power analysis. It is commonly used to determine the appropriate sample size that is necessary to detect the effect of given research at the desired level of significance. Identification of the effective size of a sample will help the researcher avoid the error of the second kind and make a reasonable conclusion.
Main text
Power analysis can be performed using statistical software, such as ANOVA. To determine if the sample size was adequately calculated, one needs to analyze the feasibility of the confidence level, standard deviation, and the width of the confidence interval chosen by the researcher. These factors are crucial as they have a direct impact on the identification of the effect of an intervention (Ali & Bhaskar, 2016). Then, based on the characteristics of the variable (dichotomous or mean), one needs to recalculate the sample size and compare it with the one estimated by the researcher.
However, the non-normal distribution of the sample may be a subject of concern as it restricts further manipulations with the sample. Bearing that in mind, one could consider conducting the transformation of data to obtain a normal distribution and enable the use of a two-sample t-test or a z-test. If the appropriate approximation cannot be achieved, one needs to use non-parametric tests, such as a Mann-Whitney U test.
A chi-square test is a commonly used type of analysis for testing relationships between categorical variables. In such a case, the calculated chi-square coefficient and the critical value coefficient are compared. To analyze the research data using this method, two criteria should be met. The first one assumes that variables should be measured at the nominal level only. The second one requires that each variable should have two or more independent groups. It is possible to say that the scenario provided does not meet the first criteria as the researcher analyzed not only nominal but also ordinal data. The compliance with the second criteria cannot be discussed as no information is given about the number of independent groups of which each variable consists.
It is worth mentioning that there are several limitations associated with this statistical method. In particular, there is a possibility of overestimating the importance of a finding, which is especially the case for large samples. Since chi-square analysis tests whether two variables are independent in a binary, it cannot be used to prove a hypothesis, yet it can refute one. That is why it is an appropriate level of statistical analysis to answer a research question that intends only to examine the relationship between two variables. However, it does not give insights into the degree of difference between the independent categories. Based on all the above-said, as well as assuming that the research question of a descriptive quantitative study is aimed at measuring a variable, a chi-square analysis is not a reliable tool to use.
If the p-level is less than the significance level, the null hypothesis should be rejected. If the researcher accepted the null hypothesis, he or she should have used chi-square analysis to determine this. However, it has been stated that this method is not recommended for usage in descriptive quantitative studies (Moore, Notz, & Fligner, 2015). It is thus possible that when examining the study, the null hypothesis may be accepted. This can happen if one discovers that a p-value is larger than the significance level. In such a case, it can be assumed that a type I error takes place as the true null hypothesis was rejected by the researcher. This means that there is no relationship between the two variables that have been studied. Studies with the error of the first kind are not recommended for consideration in evidence translation for a particular reason which will be discussed below.
Conclusion
Considering all the findings regarding the effective sample size, appropriateness of chi-square analysis that was performed to answer the research question, and the conclusion regarding the null hypothesis, one could state that this evidence cannot be used to inform practice change. Firstly, the effective size of the sample could be higher to ensure that the data is normally distributed. Secondly, a chi-square analysis cannot be used to analyze ordinal and nominal data, and it is not the best option to answer the research question. Thirdly, the error of the first kind implies that when relying on the findings of the research, the desired outcome will not occur as no connection between variables exists. Therefore, the evidence from this research is highly unreliable, and its conclusion cannot be further used for the implementation of a practice change.
References
- Ali, Z., & Bhaskar, S. (2016). Basic statistical tools in research and data analysis. Indian Journal of Anaesthesia, 60(9), 662-669.
- Moore, D. S., Notz, W. I., & Fligner, M. A. (2015). The basic practice of statistics (7th ed.). New York, NY: W. H. Freeman & Company.