## Types of Statistical Test Used

The data analysis utilized various types of statistical tests to reach a conclusive decision on the implications of the data. These tests include paired sample t-test, independent sample t-test, chi-square (independent) test, Mcnemar (paired) test, Mann Whitney U test, and Wilcoxon Z test. Firstly, the paired sample t-test is a parametric test used to compare the difference in means between the two groups from the same subject, unit, individual or related unit (Laerd Statistics, 2021). The main reason for utilizing the paired t-test is to identify statistical evidence that shows that the difference in means between the two groups is significantly not equal to zero. In this analysis, a paired test was chosen to determine whether there is a significant difference between the two related groups: baseline weight and Intervention Weight.

Secondly, an independent sample t-test is a parametric test that compares the mean of two independent groups. It is used to determine whether statistical evidence shows that the mean of two independent groups of the population differs significantly (Laerd Statistics, 2021). This test is dependent on Lavene’s test, which assumes that the two groups have the same variance. In this case, an independent sample t-test was selected to find if statistical evidence proves that the mean of patient weight in the intervention groups differs significantly.

Thirdly, the chi-square (independent) test is a non-parametric test used to determine if there is an association between the categorical variables that are either related or independent in a test. It uses the contingency table to categorize the two variables in rows and columns, each occupying row or column (Laerd Statistics, 2021). This test only assesses the association between the categorical variable and does not provide inferences about causation. In this case, a chi-square (independent) test is employed to find whether there is an association between the baseline readmission and the interview readmission.

Fourthly, the McNemar (paired) test is a non-parametric test used to determine whether there is a proportion change in the pared nominal data. The test differs from the paired t-test because it utilizes the dichotomous variable (Laerd Statistics, 2021). In this study, the McNemar test is selected to identify whether there is a change in proportion between baseline non-compliance and intervention non-compliance. Fifthly, the Mann-Whitney U test is a non-parametric test used to compare the differences in two independent groups whenever the dependent variable is continuous or ordinal but not normally distributed (Leard Statistics, 2021). Compared to the independent t-test, the Mann Whitney U test allows different conclusions to be drawn from the data depending on the assumptions made on the data. In this analysis, the Mann-Whitney U test is employed to determine whether there is a difference in the patients’ satisfaction between the intervention groups.

Lastly, the Wilcoxon Z test is a non-parametric test used to identify the difference between two pairs of groups and determine whether the identified difference is statistically significant (Leard Statistics, 2021). In this analysis, the Wilcoxon Z test identifies the difference between the baseline weight and the intervention weight.

## Differences Between Parametric and Non-Parametric Tests

Parametric tests rely on the assumption of the statistical distribution, and therefore, there are several conditions that need to be satisfied before a test is considered valid. Different parametric tests have different statistical conditions (Leard Statistics, 2021). However, the common condition on parametric tests is the normal distribution of variables to be tested. Examples of parametric tests are sample t-test, one-way ANOVA, etc. The parametric test can lead to reliable results when the distribution is skewed, non-normal, and have different variability. Furthermore, the parametric tests have great statistical power.

Non-parametric tests are tests that do not rely on any particular distribution condition. They can be performed even if the validity test parametric tests are not met (Leard Statistics, 2021). Examples of non-parametric tests include 1- sample Wilcoxon, Mann-Whitney test, 1-sample sign test, etc. Non-parametric tests assess the median of the data, which is helpful in a certain area of studies. The validity of the non-parametric test is dependent on the size of the sample and the non-normality of the data (Leard Statistics, 2021). The tests are valid with small sample sizes and valid with large sample sizes. Additionally, a non-parametric test analyzes outliers, ranked data, and ordinal data.

## Results Description

From the paired-sample t-test results, the descriptive are; Baseline weight (M =217.500, SD = 53.3975), Intervention weight (M = 178.333, SD = 8.1942). The two variables have a notable difference in mean and standard deviation. Baseline weight has a higher mean than intervention weight. The large standard deviation shows that the variation in the mean weight of the baseline weight is higher than the variation of the mean weight of intervention. This portrays that baseline weight data is highly dispersed. The paired t-test result show that t (29) = 7.185, P < 0.05. Since the p-value is less than 0.05, we conclude that it is statistically significant to say that the mean difference between Baseline weight and Intervention weight is different from zero.

From the independent sample t-test result, the descriptive are; Intervention group patient’s weight (M = 218.3333, SD = 53.8406) and Baseline group patient’s weight (M = 216.6667, SD = 54.82657). The descriptive results show that the mean and standard deviation of the two groups is close to each other. From the standard deviations, we can conclude that the variation between the groups is low. The t-test result show that t (28) = 0.084, P =0.984. This portrays that it cannot be assumed that the two groups have the same mean because the p-value is greater than 0.05. Considering Lavene’s test result from the independent t-test, the p-value = 0.890 hence the conclusion the two variables have the same variance.

From the chi-square (independent) test results, ꭓ^{2} (1) =0.482, P = 0.008. This shows an association between Baseline readmission and Intervention readmission because the p-value is less than 0.05. Therefore, the two variables are correlated. From the McNemars test result, ꭓ2 (1) =0.201, McNemars, p =0.007. This shows no difference between baseline compliance and intervention compliance because the p-value is less than 0.05. From Mann Whitney U test results, M = 3.07, U = 63.00, and P = 0.035. The result portrays that the intervention group is statistically significant than the baseline group because the p-value is less than 0.05.

From the Wilcoxon test results, Baseline weight (M = 217.5000, SD = 53.3975) and Baseline weight (M = 217.5000, SD = 53.3975), Intervention weight (M =178.3333, SD = 44.8817)

(Z= -4.307, P < 0.05) Intervention weight (M =178.3333, SD = 44.8817). The Wilcoxon result (Z= -4.307, P < 0.05) shows that observed differences between the two groups is significant. This is because the p value is less than 0.05.

## Analysis Summary

It is statistically significant to say that the mean difference between Baseline weight and Intervention weight is different from zero. Intervention group patient’s weight and Baseline group patient’s weight have the same variability with different means. There is an association between Baseline readmission and Intervention readmission, and there is no difference between baseline compliance and intervention compliance. The result portrays that the intervention group is statistically significant than the baseline group.

## References

Laerd Statistics. (2021). *Features – A list of our statistical guides | Laerd Statistics*. Web.

Leard Statistics. (2021). *Mann-Whitney U Test in SPSS Statistics – Interpreting the Output | Laerd Statistics*. Statistics.laerd.com. Web.