Table 1: Mean 17505, Median 5800; The Mean Is Significantly

Table 1 Mean 17505 Median 5800the Mean Is Significantly Larger T

Table 1 presents descriptive statistics for the variable "Average Length of Stay," revealing a considerable difference between the mean and median values. The mean length of stay is 17.505, while the median is 5.800, indicating a right-skewed distribution. This skewness suggests that a majority of patients have shorter stays, but a small proportion experiences significantly longer stays that pull the mean upward. The skewness coefficient of 8.411 and its standard error of 0.141 further substantiate the asymmetry of the data, confirming a substantial right tail extending toward higher values.

The kurtosis value of 80.036 indicates the distribution is heavily peaked with heavy tails, implying the presence of extreme outliers. Such a high kurtosis value deviates markedly from a normal distribution, which typically has a kurtosis of 3. Outliers are more prevalent, influencing the overall shape and central tendency of the data. These outliers can be attributed to exceptional cases where patients have significantly longer stays due to complex health issues or administrative delays, impacting hospital resource allocation and planning.

The Shapiro-Wilk test for normality yielded a p-value less than 0.001, specifically 0.211, which leads us to reject the null hypothesis of normality. This confirms that the data does not follow a bell-shaped normal distribution; instead, it exhibits skewness and kurtosis characteristic of a non-normal, heavily tailed distribution. The visual representation in Figure 1, which illustrates the distribution of average length of stay, corroborates this finding. The distribution exhibits a pronounced right tail, with most data concentrated at the lower end and a few extreme values stretching the right side of the distribution.

Implications of Distribution Characteristics for Statistical Analysis

The evident skewness and kurtosis have important implications for statistical analysis. Traditional parametric tests such as t-tests or ANOVA assume normally distributed data and homogeneity of variance. Applying these tests directly to such skewed data could lead to misleading results, including inflated Type I error rates or reduced statistical power. Therefore, analysts should consider data transformation techniques, such as logarithmic or square root transformations, to approximate normality. Alternatively, non-parametric methods like the Mann-Whitney U test or the Kruskal-Wallis test may be more appropriate, as they do not assume normality.

Furthermore, the presence of outliers necessitates robust statistical approaches or sensitivity analyses to assess their influence on overall findings. Outliers could reflect genuine variability or data entry errors; hence, careful data validation is essential. Understanding the distribution's skewness also aids in developing appropriate clinical or operational interpretations, emphasizing that most patients have shorter stays, but a minority with extended stays significantly affect average calculations.

Significance of Findings and Practical Recommendations

The divergence between the mean and median highlights the importance of choosing appropriate central tendency measures in health data analysis. In skewed distributions, the median often provides a more representative measure of typical patient length of stay, whereas the mean can be distorted by outliers. Hospital administrators and policymakers should consider this when evaluating performance metrics or planning resource allocation.

Considering the heavy tails and outliers, hospitals could implement targeted interventions to reduce lengthy stays, such as improving discharge planning or enhancing post-discharge support for complex cases. From a research perspective, future studies should explore factors contributing to extended lengths of stay and their impact on hospital efficiency. Statistical methods should be carefully selected, favoring non-parametric techniques or data transformations, to ensure valid conclusions from skewed datasets.

Conclusion

In summary, the analysis demonstrates that the distribution of average length of stay is markedly right-skewed with high kurtosis, indicating significant outliers and non-normality. The statistical tests confirm this non-normality, which must be considered in subsequent analyses. Recognizing these distributional characteristics informs appropriate methodological choices and enhances the interpretability of healthcare data, ultimately aiding in improving patient care efficiency and resource management.

References

• Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test for normality. Biometrika, 52(3-4), 591-611.
• Kurtosis. (n.d.). In Encyclopedia of Statistics in Behavioral Science. John Wiley & Sons.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics (6th ed.). Pearson Education.
• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). Sage Publications.
• Osborne, J. W. (2010). Improving your data transformations: Applying the Box-Cox transformation. Practical Assessment, Research & Evaluation, 15(12), 1-9.
• Ghasemi, A., & Zahediasl, S. (2012). Normality tests for statistical analysis: A guide for non-statisticians. International Journal of Endocrinology and Metabolism, 10(2), 486-489.
• Hampel, F. R. (1974). The influence curve and its applications in robust estimation. Journal of the American Statistical Association, 69(346), 383-393.
• Wilcox, R. R. (2012). Introduction to Robust Estimation and Hypothesis Testing. Academic Press.
• Lehmann, E. L., & Casella, G. (1998). Theory of Point Estimation. Springer.
• Conover, W. J. (1999). Practical Nonparametric Statistics. Wiley-Interscience.