Discussion of the Types of Statistical Tests Used and Why They Have Been Chosen
Various statistical tests were used in this assignment, which were designed to assess the effects of a clinical intervention on patients. Specifically, it examined whether the intervention had a benefit in reducing patients’ weight. The choice of a particular test is always motivated by the purpose for which the data are processed as well as the nature of the variables used. Among the most frequently used tools in scientific sources are parametric tests: namely, t-tests. It is worth clarifying that the basic assumptions for all t-tests are independence of observations and normality of distributions, as well as homogeneity of sample variance; in addition, the dependent variable must be defined on a continuous scale, and the independent factor must be dichotomous categorical (Zach, 2021). The primary purpose of this test is to evaluate the mean between two samples; and the samples can be collected as different or come from the same group (Bevans, 2022). In this case, the population t-test is subdivided into specific types of instruments, whether it is a one-sample, two-sample, or paired t-test. In the first case, the sample mean is compared to some known parameter, such as the population mean. In the case of two samples collected differentially, a two-sample t-test or, as it is also called, an independent t-test is used. Finally, if the analysis is conducted in the context of Pre/Post effects of treatment, a paired t-test is used. This paper uses two t-tests simultaneously, a paired t-test and an independent t-test, both of which are two-tailed, that is, without hypothesis direction. The paper also uses the Chi-Square Test for Association, which allows us to determine the relationship between two categorical variables. In fact, the Chi-Square Test for Association is used as an analog of regression tests, but regression is not possible for categorical variables, which is solved by using the Chi-Square Test for Association. For paired nominal variables, the McNemar Paired Test is also used to determine the marginal homogeneity of the data – this test determines whether the marginal frequencies of rows and columns are equal (McNemar Test, 2020). The Mann-Whitney U test is also a nonparametric analysis that determines whether samples come from the same population, that is, in other words, whether populations have the same shape with respect to these data (LS, 2021). This tests whether the two populations are equal to each other or different. An alternative T-test is the nonparametric Wilcoxon Z Test, which is used to compare parameters for ordinal data; however, unlike the T-test, Wilcoxon Z can be used when the sample mean is not of interest.
Discussion of the Differences Between Parametric and Nonparametric Tests
The tests described above are classified as parametric or nonparametric. The main difference between the two types of statistics is what assumptions are used for the tests. For example, for parametric analysis, it is assumed that the sample distribution tends to be expected, whereas, for nonparametric tests, this assumption does not have to be met (Frost, 2021). This is why there is no need to check the normality of the distribution for nonparametric tests, unlike for parametric statistics.
Description of the Reported Results of the Statistical Tests Above
The PAIRED SAMPLE T-TEST examined the differences in the mean Baseline Weight and Intervention Groups; the results of the PAIRED SAMPLE T-TEST are shown in Figure 1. It can be seen that the mean Baseline Weight (M = 217.5, SD = 53.4) was higher than the mean for the Intervention Groups (M = 178.3, SD = 44.9). The differences in the means were statistically significant, as t(29) = 7.185, p =.000.
For the INDEPENDENT SAMPLE T-TEST, the weight of the patients depending on the intervention group, was checked. Figure 2 shows the results of the analysis: the mean height for the intervention group is 218.3 (SD = 53.8), whereas, for the baseline group, the mean was slightly lower (M = 216.7, SD = 54.8). Levene’s test shows that the assumption of homogeneity of variance was met (F(28) = 0.019, p =.890), while differences between groups were not statistically significant: t(28) = 0.084, p =.934.
Figure 3 shows the results for the Chi-Square Test: we can see that χ2(1) = 6.982, p = 0.008, which implies that there is a statistically significant relationship between the groups. In other words, it shows that there are differences in Intervention Readmission Rates for baseline readmission levels. Figure 4 also shows the results of the McNemar Paired Test: p =.007, from which it follows that there is a statistically significant difference in mismatch rates between Baseline and Intervention.
Figure 5 provides information on the results of the Mann-Whitney U Test: it shows that patient satisfaction was significantly lower in the intervention group than in the control group (U = 63, p =.035). Finally, Figure 6 shows the results of the Wilcoxon Z Test: significant differences between the weights in the control group and the intervention group were found, as Z = -4.307, p =.000
Summary of the Conclusive Results of the Data Analyses
The results allow us to identify the patterns characteristic of this sample (N = 30). It was shown that the weights of the patients in the intervention group were significantly lower, indicating a clinical benefit from the intervention. Meanwhile, initial pre-intervention weights showed no significant trend toward differences, suggesting that the intervention had a beneficial effect. The inconsistency rate, expressed as the number of errors, was also lower for the intervention group. However, despite the benefits of the intervention group, patient satisfaction was significantly lower for them than for the control group. Thus, the clinical intervention had a benefit for patient weight loss but resulted in less patient satisfaction.
References
Bevans, R. (2022). An introduction to t-tests | definitions, formula, and examples. Scribbr. Web.
Frost, J. (2021). Nonparametric tests vs. parametric tests. SBJ. Web.
LS. (2021). Mann-Whitney U Test using SPSS Statistics. Laerd Statistics. Web.
McNemar Test. (2020). StatTest. Web.
SC. (2021). Types of variables. Statistics Canada. Web.
Zach. (2021). The four assumptions made in a t-test. Statology. Web.
Appendix A
Characteristics and Examples of Variables
Note. Definitions taken from SC (2021).