Hypothesis Testing for Different Groups. Free Essay

Statistics refers to a mathematical discipline that focuses on data collection, analysis, presentation, interpretation, and organization. Two methods can be applied while analyzing statistical data, including inferential and descriptive methods (Frey, 2018). The descriptive method uses the standard deviation and means, whereas the inferential method is used when the data is analyzed as a subclass of a given population (Opie & Fallin, 2019). The inferential method allows the researcher to determine whether the pattern observed is due to chance or intervention. The study is focused on descriptive statistics, where it is assumed that there is no significant difference in the productivity of the two clinics.

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There are several ways in which an individual can use to perform statistical tests of specific datasets (Xia & Sun, 2017). The type one prefers is dependent on the data samples and hypothesis scenarios. Some of the various types of statistical tests include correlational tests that focus on the association of the variables. Examples of such correlation tests are the chi-square, Pearson, and spearman correlation.

The other type of test is the mean comparison tests. The tests give the differences of means in datasets. They include the paired t-test, independent t-test, and the ANOVA test. A paired t-test is applied when there are only two variables to be tested, and they must be from the same population. An Independent t-test is when the variables to be tested are from different populations. ANOVA is used when the variables to be tested are more than two (Xia & Sun, 2017).

From our case study, an investor is interested in deciding whether to get one or two clinics based on their productivity. The main task here is to determine if there is any significant difference in the productivity of the two clinics given their monthly patient visit data. Assuming that both clinics are situated in the same area but in different locations, the best test to get used here is the paired t-test. To get to use the t-test, a hypothesis must be put in place, which is then proven at the end of the analysis. Two hypothesis tests get mostly applied in statistics: the null and alternative hypothesis.

A null hypothesis is denoted H0, and it tries to negate what the investigator expects or predicts. According to the null hypothesis, there is no difference between the variables under study. An alternative hypothesis denoted as H1, predicts, or suggests the presence of a potential difference between the variables under investigation. The two types of alternative hypotheses are directional and non-directional. Directional gives the expected findings and is mostly used to study variables relationships instead of groups’ comparison. Non –directional has no defined direction (Dwivedi et al., 2017).

From the case of study, the investor needs to know if there is a significant difference between the two clinic's productivity so that he/she can decide on where to invest. The best hypothesis to use here is the null hypothesis, where the difference in the two clinic's productivity is assumed to be zero. The analysis of the two datasets collected for the two clinics is subjected under a t-test analysis for paired samples, and the results are as follows.

Results

Table 1: A table representing t-test outcomes for both clinics

t-Test: Two-Sample Assuming Equal Variances

Pooled Variance 1885.528636 Hypothesized Mean Difference 0 Df 198 t Stat -3.372473414 P(T<=t) one-tail 0.000447968 t Critical one-tail 1.652585784 P(T<=t) two-tail 0.000895937 t Critical two-tail 1.972017478

From the table above, the t statistic result is -3.3725, and t critical is 1.972. The probability is observed to be 0.000896. The set level of significance of this study is α=0.05. The clinic I have a variance of 2188.5 and clinic two a variance of 1582.5. The pooled variance is 1885.528636.

Discussion

From the results above, the p-value is less than 0.05. Therefore, it implies that there is a significant difference between the two clinics’ productivity. The null hypothesis that the productivity of both clinics is the same gets rejected. The test statistic value is negative to imply that the hypothesized mean more than the sample mean. It is also evident that our null hypothesis fails to hold. The variances of the two clinics are not equal, as assumed. Low variance is related to lower returns and risk. High variance is associated with high yields and risk.

Conclusion

From the above discussion, it can be concluded that the average patient visits for the two clinics vary. Using the p-value obtained in our analysis, the null hypothesis at a significance level of 5% is rejected since the value obtained was less than 0.05. If the investor is an aggressive investor and less risk-averse, he/she should invest in the two clinics. If the investor is a conservative who does not tolerate taking risks, Clinic One is the best place to make his investments.

References

Dwivedi, A. K., Mallawaarachchi, I., & Alvarado, L. A. (2017). Analysis of small sample size studies using a nonparametric bootstrap test with pooled resampling method. Statistics in medicine, 36(14), 2187-2205. https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.7263

Frey, B. B. (Ed.). (2018). The SAGE encyclopedia of educational research, measurement, and evaluation. Sage Publications. https://www.example.edu/paper.pdf

Opie, C., & Fallin, L. (2019). Analyzing and Presenting your Research Data. Getting Started in Your Educational Research: Design, Data Production, and Analysis, 191. https://books.google.com/books?hl=en&lr=&id=ELuODwAAQBAJ&oi=fnd&pg=PA191&dq=analysing+and+presenting+statistical+data&ots=SMsMr6f-PX&sig=ileI8-RXtWBbunDZIovbSzJI14U

Xia, Y., & Sun, J. (2017). Hypothesis testing and statistical analysis of microbiome. Genes & diseases, 4(3), 138-148. https://www.sciencedirect.com/science/article/pii/S2352304217300351