4. Inferential statistics

Furthermore, the CV enables the laboratorians to put up an effective comparison regarding the SDs with varying units. Computation of a dataset's SD necessitates prior computation of the

of all the dataset's values from the set's mean. Variance, as a dispersion measure, denotes the difference dominant between each data value and the data's average. Afterward, the SD is simply the variance's square root. An additional approach of connoting SD is using the CV, which is computed via division of the SD by the mean of the data, and multiplying the quotient by 100 to represent it as a percentage (Figure 1). The CV proves to simplify the comparison of SDs accruing to test outcomes connoted in varying concentrations and units. The CV encounters extensive application in summarizing the underlying QC data, and it can

The most prevalent shape distributions accruing to datasets include the normal distribution (or the Gaussian distribution). This distribution proves to describe many lab variables that are continuous besides sharing various unique properties—the mode, median, and mean are identical. This distribution is further symmetric—since half of the values dominate the left side of the mean, whereas the other half is on the right side of the mean value. The symmetrical shape normally encounters the perception of being a "bell curve." The aggregate area covered by the Gaussian curve totals to 1.0 or rather 100%. Precisely, selecting a value in a Gaussian distributed dataset reveals that there is a 68% probability of finding the value between 1 SD and the mean value. Likewise, there is 95% likelihood of finding the value between 2 SDs and the mean value. There is further 99% probability of finding the value between 3SDs and the mean value of the dataset (Figure 1). Universally, plotting patient data in histograms makes it a simple approach to visualize the underlying distribution of the dataset. Nonetheless, one can as well perform other mathematical analyses like normality tests to affirm whether data fits into a certain distribution.

COM (comparison of method) is common for laboratorians dealing with data for many patients per unit time. A COM examination entails evaluating the patient's specimens by a reference (existing) technique and a test (new) approach. The resultant data from such comparisons encompass two measurements accruing to each of the patient's specimen. Convention enables plotting of the values acquired via the reference approach on the x-axis, whereas the values yielded by the test approach dominate the y-axis. Nevertheless, linear regression is a statistical approach whose analysis offers objective measures accruing to the dispersion and location of the best fit line. A linear regression yields three aspects—the y-intercept, the correlation coefficient, and the slope. The sign of the correlation coefficient indicates the relationship between the two plotted variables, and a higher coefficient indicates the prevalence of a splendid agreement notably between the comparative methods and the test [3, 4].

The difference plot, also called the Bland–Altman plot, is an additional approach regarding visualization of paired data. This approach graphs the absolute bias or even the percent bias

3. Descriptive statistics for groups of paired observations

). Variance precisely implies the average accruing to the squared distances

dataset's variance (s<sup>2</sup>

12 Quality Control in Laboratory

2.4. Measures of shape

be less than 1% for the highly precise analyzers.

Inferential statistics is the subsequent degree of complexity past paired descriptive statistics. They are deployed in drawing conclusions or rather inferences convening the SDs or mean of two datasets. Nevertheless, inferential statistics acknowledges the relevance of data distribution regarding shape. The respective distribution is key in determining the type of inferential statistics to use in analyzing the underlying data. Data depicting Gaussian distribution is normally analyzed deploying "parametric" tests that encompass ANOVA (a Student's t-test or analysis of variance). "Nonparametric" analysis is used for the data that is not normally distributed. Reference interval studies mostly depict nonparametric tests, wherein population data frequently depict skewness [1]. A precaution entails that an inappropriate analysis regarding sound data can direct the practitioner toward drawing a wrong conclusion.
