Multicollinearity represents a high degree of linear intercorrelation between explanatory variables in a multiple regression model and leads to incorrect results of regression analyses. Diagnostic tools of multicollinearity include the variance inflation factor (VIF), condition index and condition number, and variance decomposition proportion (VDP). The multicollinearity can be expressed by the coefficient of determination (Rh2) of a multiple regression model with one explanatory variable (Xh) as the model’s response variable and the others (Xi [i≠h] as its explanatory variables. The variance (σh2) of the regression coefficients constituting the final regression model are proportional to the VIF (11-Rh2). Hence, an increase in Rh2 (strong multicollinearity) increases σh2. The larger σh2 produces unreliable probability values and confidence intervals of the regression coefficients. The square root of the ratio of the maximum eigenvalue to each eigenvalue from the correlation matrix of standardized explanatory variables is referred to as the condition index. The condition number is the maximum condition index. Multicollinearity is present when the VIF is higher than 5 to 10 or the condition indices are higher than 10 to 30. However, they cannot indicate multicollinear explanatory variables. VDPs obtained from the eigenvectors can identify the multicollinear variables by showing the extent of the inflation of σh2 according to each condition index. When two or more VDPs, which correspond to a common condition index higher than 10 to 30, are higher than 0.8 to 0.9, their associated explanatory variables are multicollinear. Excluding multicollinear explanatory variables leads to statistically stable multiple regression models.

According to the central limit theorem, the means of a random sample of size, n, from a population with mean, µ, and variance, σ2, distribute normally with mean, µ, and variance, . Using the central limit theorem, a variety of parametric tests have been developed under assumptions about the parameters that determine the population probability distribution. Compared to non-parametric tests, which do not require any assumptions about the population probability distribution, parametric tests produce more accurate and precise estimates with higher statistical powers. However, many medical researchers use parametric tests to present their data without knowledge of the contribution of the central limit theorem to the development of such tests. Thus, this review presents the basic concepts of the central limit theorem and its role in binomial distributions and the Student's t-test, and provides an example of the sampling distributions of small populations. A proof of the central limit theorem is also described with the mathematical concepts required for its near-complete understanding.

Missing values and outliers are frequently encountered while collecting data. The presence of missing values reduces the data available to be analyzed, compromising the statistical power of the study, and eventually the reliability of its results. In addition, it causes a significant bias in the results and degrades the efficiency of the data. Outliers significantly affect the process of estimating statistics (e.g., the average and standard deviation of a sample), resulting in overestimated or underestimated values. Therefore, the results of data analysis are considerably dependent on the ways in which the missing values and outliers are processed. In this regard, this review discusses the types of missing values, ways of identifying outliers, and dealing with the two.

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BackgroundTraumatic placement of a needle during a neuraxial blockade has been related to many complications such as postdural puncture headache, trauma to neural structures and even spinal hematoma, causing permanent neurologic deficits. Although efforts to minimize the complications caused by traumatic neuraxial blockade have been made, nothing was found to be clear. The authors investigated the predictors of difficult neuraxial blockade using the first puncture success and number of attempts as measures to assess the difficulty.MethodsIn this prospective observational study, 253 patients scheduled for elective surgery underwent spinal or epidural anesthesia. Patient data (age, sex, height, weight, body mass index, and quality of anatomical landmarks), the provider's level of experience, type of blockade (spinal or epidural), needle type/gauge and the distance from skin to subarachnoid or epidural space were recorded. Significant variables were first determined by Student's t-test and Pearson's chi square test and then logistic and Poisson regression tested the association of the first puncture success and number of attempts with the significant variables.ResultsThe provider's level of experience and the distance from skin to subarachnoid or epidural space were significant in logistic and Poisson regression. Body mass index was significant only in Poisson regression and the quality of anatomical landmarks was significant only in logistic regression.ConclusionsProvider's level of experience and the distance from skin to subarachnoid or epidural space influenced the difficulty in performing a neuraxial blockade.

Although supraclavicular brachial plexus block (SCBPB) was repopularized by the introduction of ultrasound, its usefulness in shoulder surgery has not been widely reported. The objective of this study was to compare motor and sensory blockades, the incidence of side effects, and intraoperative opioid analgesic requirements between SCBPB and interscalene brachial plexus block (ISBPB) in patients undergoing arthroscopic shoulder surgery.Patients were randomly assigned to 1 of 2 groups (ISBPB group: n = 47; SCBPB group: n = 46). The side effects of the brachial plexus block (Horner's syndrome, hoarseness, and subjective dyspnea), the sensory block score (graded from 0 [no cold sensation] to 100 [intact sensation] using an alcohol swab) for each of the 5 dermatomes (C5–C8 and T1), and the motor block score (graded from 0 [complete paralysis] to 6 [normal muscle force]) for muscle forces corresponding to the radial, ulnar, median, and musculocutaneous nerves were evaluated 20 min after the brachial plexus block. Fentanyl was administered in 50 μg increments when the patients complained of pain that was not relieved by the brachial plexus block.There were no conversions to general anesthesia due to a failed brachial plexus block. The sensory block scores for the C5 to C8 dermatomes were significantly lower in the ISBPB group. However, the percentage of patients who received fentanyl was comparable between the 2 groups (27.7% [ISBPB group] and 30.4% [SCBPB group], P = 0.77). SCBPB produced significantly lower motor block scores for the radial, ulnar, and median nerves than did ISBPB. A significantly higher incidence of Horner's syndrome was observed in the ISBPB group (59.6% [ISBPB group] and 19.6% [SCBPB group], P < 0.001). No patient complained of subjective dyspnea.Despite the weaker degree of sensory blockade provided by SCBPB in comparison to ISBPB, opioid analgesic requirements are similar during arthroscopic shoulder surgery under both brachial plexus blocks. However, SCBPB produces a better motor blockade and a lower incidence of Horner's syndrome than ISBPB.