Exceptional Responders, Outliers, and Radical Remissions

Many covalent molecules have central atoms that do not have eight electrons in their Lewis structures. These molecules fall into three categories:

Outliers are observed data points that are far from the least squares line. They have unusual values and need to be examined carefully. Though an outlier may result from erroneous data, at other times, it may hold valuable information about the population under study and should be included in the data. Hence, it is crucial to examine what causes a data point to be an outlier.
The z score is used to find outliers or unusual values. It should be noted that any values beyond -2 and +2 are...

An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500), while others may indicate that something unusual is happening. Outliers are present far from the least squares line in the vertical direction. They have large "errors," where the "error" or residual is the...

Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This...

Radicals adjacent to electron-donating groups are called nucleophilic radicals. These radicals readily react with electrophilic alkenes. The SOMO–LUMO interactions are the driving force for the reaction, where the high-energy SOMO of the electron-rich, nucleophilic radicals interacts with the low-energy LUMO of the electron-deficient, electrophilic alkenes. Such SOMO–LUMO interactions are the basis of reactive radical traps, affecting the selectivity in radical reactions. For...

Radicals adjacent to electron‐withdrawing groups are called electrophilic radicals. These radicals readily react with nucleophilic alkenes. For example, the malonate radical, in which the radical center is flanked by two electron‐withdrawing groups, reacts readily with butyl vinyl ether, which consists of an electron‐donating oxygen substituent. The reaction between electrophilic malonate radical and nucleophilic vinyl ether is favored because the radical has a...