The Z-Score is a statistical measure of how far a particular data point is from the mean. It allows you to compare scores from different distributions (e.g. different test subjects, different years, etc.) by considering the distribution’s standard deviation.
To calculate a Z-Score, use this formula:
Z = (x – μ) / σ (Ekwattanakit et al., 2017)
Where: x is the score you want to calculate the Z-Score for μ is the mean or average of the distribution σ is the standard deviation.
From the data provided, the determination of the Z-Score for the BMI involves the calculation of the standard deviation and the average BMI for the sample (Till et al., 2018).
Table 1: Descriptive Statistics
Standard deviation is 4.0371
Mean is 25.83
Z = (25.83) / 4.0371
Z = 6.3984
The Z-Score is a measure of how unusual the data are. A Z-Score of zero means that the data are exactly what you would expect to find if the null hypothesis were true. In the above case, there is a positive Z-score of 6.3984, meaning that the data are more unusual than you would expect if the null hypothesis were true, and a negative Z-score means that the data are less unusual than you would expect if the null hypothesis were true (Fatimah & Sunaryo, 2022). The Z-Score is based on the standard deviation of the data. The standard deviation is a measure of how much variation there is in the data. The larger the standard deviation, the more variation there is in the data.
References
Ekwattanakit, S., Nakavachara, P., & Viprakasit, V. (2017). Microsoft® Office Excel-based worksheet program for rapid calculation of weight-for-age (WA) and height-for-age (HA) z-scores in Thai pediatric population (THAI-Z). Southeast Asian J Trop Med Public Health, 48, 183-191. Web.
Fatimah, F., & Sunaryo, D. (2022). Analysis of The Effect Of The Altman Z-Score Method On Financial Distress. International Journal of Educational Research & Social Sciences, 3(1), 46-61.
Till, K., Morris, R., Emmonds, S., Jones, B., & Cobley, S. (2018). Enhancing the evaluation and interpretation of fitness testing data within youth athletes.Strength & Conditioning Journal, 40(5), 24-33. Web.