Dentist’ use of anesthetics. Refer to the Current Allergy & Clinical Immunology

Question

Dentist’ use of anesthetics. Refer to the Current Allergy & Clinical Immunology study of the use of local anesthetics in dentistry, presented in Exercise 2.99 (p.72). Recall that the mean number of units (ampoules) of local anesthetics used per week by dentist was 79, with standard deviation of 23. Consider a dentist who used 175 units of local anesthetics in a week. (a) Find the z-score for this measurement. (b) Would you consider the measurement to be an outlier? Explain (c) Give several reasons the outlier may have occurred.

Explanation / Answer

a) Z-Score = (175-mean)/SD = (175 - 79) / 23 =4.1739

b) Yes, the point 175 is outlier

since (Mean - 2SD, Mean +2SD) = (79-2*23, 79+2*23) = (33,125)

The point 175 is not in the above interval

c) If the point is lies between  (Mean - 2SD, Mean +2SD) then it is usal otherwise it is unusal

Outliers can occur by chance in any distribution, but they often indicate either measurement error or that the population has a heavy-tailed distribution. In the former case one wishes to discard them or use statistics that are robust to outliers, while in the latter case they indicate that the distribution has high skewness and that one should be very cautious in using tools or intuitions that assume a normal distribution.

There are a number of reasons for outliers:
1. Some individuals in the sample are extreme;
2. The data are inappropriately scaled;
3. Errors were made on data entry;
4. Unanticipated complexities exist in the relationships among variables;
are just a few examples,

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