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Analysis of Variance (ANOVA) tests compare the mean values of several groups under an assumption of normal distribution, similar data variation, and no overlapping data (Emerson, 2017). While ANOVA tests do not specify areas of variation, they do indicate when the mean variation of statistical significance exists.

Healthcare example: An ANOVA test could be applied to understand whether the day of the week impacts ED wait times. The null hypothesis would be that the wait time on Monday equals the wait time on Tuesday, Wednesday, Thursday, etc. The alternate hypothesis would be that the wait time on each day is different. Through an ANOVA Test on this data set, one can be guided on whether to accept or reject the null hypothesis by referring to the probability value (p-value). If the p-value is low, the null hypothesis can be rejected. Additional testing would be necessary to pinpoint the root cause of variation, but, in the meantime, the ANOVA test would guide an individual in understanding whether variation between groups exists.

Regression analysis is another statistical tool that can be used to explore the relationship between a dependent and an independent variable (Tantawi, 2019). The primary risk with this method is individuals drawing the wrong conclusion from the data. While a regression analysis can indicate a relationship exists, a related variable may be causing the relationship instead of the initial variable being reported on.

Healthcare Example: One example could be the relationship between hand hygiene observations and infectious diseases on a floor. From a regression analysis, one could plot infectious diseases as the dependent variable and hand hygiene observations as the independent variable. One would hypothesize that increased hand hygiene observations may instill a more proactive hand hygiene culture, thereby reducing the spread of infectious diseases in any given unit. When plotting this data, one would most likely see that data would be distributed along the "best fit" line, which would identify the correlation between these variables.