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

Outliers in a box plot may be evidence of a non-normal distribution, but this might not always be the case. If the box plot has symmetry around the median, the distribution will most likely be normal.

To identify deviations from normality using a box plot, follow these steps:

Step 1: Understand the components of a box plot
A box plot consists of several key components:
- Minimum: The lowest value within the dataset.
- First Quartile (Q1): The 25th percentile, or the value below which 25% of the data falls.
- Median (Q2): The 50th percentile, or the value that falls in the middle of the dataset.
- Third Quartile (Q3): The 75th percentile, or the value below which 75% of the data falls.
- Maximum: The highest value within the dataset.
- Whiskers (min and max): Lines extending from the box, representing the range of the data excluding outliers.
- Outliers: Data points that lie beyond the whiskers, usually represented as individual dots.

Step 2: Assess symmetry and skewness
In a normal distribution, the box plot will show a symmetrical arrangement of the components. The whiskers will be of approximately the same length on both ends, and the median will be aligned with the box's center. If the whiskers are uneven or the median is not centered, there may be a deviation from normality.

Step 3: Check for outliers
Outliers can suggest departures from normality. If there are many outliers on one side of the box plot, it might indicate skewness or a long tail in that direction. The presence of outliers should prompt further investigation of the data.

Step 4: Evaluate box plot shape
A normal distribution will have a box plot with a symmetrical and bell-shaped appearance. If the box plot has an abnormal shape, such as being skewed to one side or exhibiting multiple peaks, it suggests non-normality.

Step 5: Use statistical tests for confirmation
While a box plot can provide initial indications of deviations from normality, it is not a definitive measure. To confirm non-normality, you can use statistical tests like the Shapiro-Wilk test, Anderson-Darling test, or Kolmogorov-Smirnov test.

Remember, the interpretation of a box plot requires considering other statistical tools and the specific context of your data.