Statistical Analysis

To analyze the treatment, post-treatment, and overall long-term changes in the study, the data were processed and analyzed using SPSS version 22 (SPSS Inc., Chicago, IL), a widely recognized statistical software tool commonly used in the field of social sciences and medical research. The analysis aimed to assess both the immediate and long-term effects of the treatment under investigation. Given that the nature of the data did not conform to a normal distribution, several preliminary tests were conducted to examine the shape of the data distribution.

The skewness and kurtosis statistics were computed as part of the diagnostic process to determine the normality of the data. Skewness refers to the degree of asymmetry in the distribution of the data, while kurtosis assesses the "tailedness" or the sharpness of the peak of the distribution curve. If both values deviate significantly from the expected range for a normal distribution (skewness between -2 and 2, and kurtosis between -7 and 7), this indicates that the data are not normally distributed (Field, 2013). In this case, the results confirmed that the distributions were not normal, which is common in clinical data, where measurements often exhibit skewed or leptokurtic distributions.

To summarize the central tendencies and variations in the data, medians and interquartile ranges (IQRs) were reported rather than the mean and standard deviation, as these measures are more robust to non-normality (Graham, 2012). The median provides a better measure of central tendency when the data are skewed, as it is less influenced by extreme values, and the interquartile range offers a clearer picture of data spread, focusing on the middle 50% of the data.

For hypothesis testing, the Mann-Whitney U-test was employed to evaluate between-group differences, particularly when comparing two independent groups that might have non-normal distributions. This non-parametric test is useful for assessing whether there are statistically significant differences between the ranks of two independent groups (Mann & Whitney, 1947). Within-group differences, such as changes over time or between various stages of treatment, were assessed using the Wilcoxon signed-rank test. This test is particularly suitable for paired data, such as pre- and post-treatment measurements, where the data are not normally distributed (Wilcoxon, 1945).

Overall, the combination of non-parametric tests and robust descriptive statistics enabled a thorough analysis of treatment effects, accounting for the distributional properties of the data. These methods are commonly applied in clinical trials and epidemiological studies where data often violate assumptions of normality (Conover, 1999).

References:

Conover, W. J. (1999). Practical Nonparametric Statistics (3rd ed.). Wiley.
Field, A. (2013). Discovering Statistics Using SPSS (4th ed.). SAGE.
Graham, J. W. (2012). Missing Data: Analysis and Design. Springer Science & Business Media.
Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. The Annals of Mathematical Statistics, 18(1), 50-60.
Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80-83.

Summary

• The statistical analysis utilized SPSS version 22 to evaluate treatment effects over time.
• Data analysis informed by non-normal distribution indicated that skewness and kurtosis were assessed to establish normality.
• Non-normality was determined through skewness (-2 to 2) and kurtosis (-7 to 7) measures.
• Medians and interquartile ranges (IQRs) were used over means and standard deviations for robustness against non-normality.
• The Mann-Whitney U-test was applied for between-group comparisons of independent groups.
• The Wilcoxon signed-rank test was used for within-group analyses of paired data.
• The integration of non-parametric tests and robust statistics ensured comprehensive evaluation of treatment outcomes.
• These methods are standard in clinical trials and epidemiological research where normality assumptions may not hold.