how would you tell deviations from normality by looking at a box plot?

To identify deviations from normality by looking at a box plot, you can consider the following points:

1. Skewness: Look for a skewness in the distribution of the box plot. If the median is not in the center of the box and the whiskers are of different lengths, it suggests a deviation from normality.

2. Outliers: Check for dots (outliers) beyond the whiskers of the box plot. Outliers could indicate extreme values or errors, suggesting a departure from a normal distribution.

3. Symmetry: Observe the shape of the box plot. A normal distribution typically exhibits symmetrical box plots, where the left and right sides of the box are approximately equal in length.

4. Whisker Length: Compare the lengths of the upper and lower whiskers. If one whisker is noticeably longer than the other, it might indicate a departure from normality.

It is important to keep in mind that a box plot alone may not provide definitive evidence of normality. It is recommended to use additional statistical tests, such as the Shapiro-Wilk test or the Anderson-Darling test, to get a more accurate assessment of normality. These tests provide quantitative measures and p-values to evaluate departures from normality.