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Concepts (plain language)

These ideas help you pick the right statistic without heavy theory.

Mean vs median vs Huber

Think of 6 measurements and one big error:

[10, 12, 11, 15, 10, 1000]
  • Mean: rises a lot because of 1000.
  • Median: stays at the real center.
  • Huber: behaves like the mean when data is clean, but "brakes" outliers.

Simple rule: - Use the mean if data is clean. - Use median or Huber if there are outliers.

MAD and IQR

  • MAD (Median Absolute Deviation) measures dispersion around the median.
  • IQR (Interquartile Range) measures the spread between 25% and 75%.

If MAD or IQR are high, there is lots of noise or long tails.

R quantiles

R defines 9 ways to compute quantiles. StatGuard implements all of them.

  • Type 7: R default. Good balance.
  • Types 1-3: more discrete (less interpolation).
  • Types 8-9: bias adjustments for certain distributions.

If you are unsure, start with type 7.