confidence interval

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Contents

• Note
• Misconceptions
• Resources

Note

• confidence level
  • alpha risk = 1 - confidence level, the risk that population parameter (e.g. mean) is not within the CI
  • confidence LEVEL up ⇒ WIDER confidence interval ⇒ less practicall value
  • confidence level 68% ⇒ t-stats ~= 1 (from the T-table)
  • confidence level 95% ⇒ t-stats ~= 2
  • confidence level 99% ⇒ t-stats ~= 3
• CI(mu) = sample mean +- MOE = sample mean +- Tstats * SEmean
  • CI = 2*MOE
• Sample size n
  o   sample size n up ⇒ narrower confidence interval (by sqrt(n))
  o   at n = 25, reduction of 80% of CI is achieved
  o   if n<30, sample mean is a student-distribution and t-stats needs to be defined from the Z-table
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Misconceptions

• “I am 95% confident that the population mean is the sample mean”
• “95% of the data are between lower and upper bound”
  • Correct: The CI is not based on raw data, It is based on descriptive statistics of the sample data.
• “I am 95% confident that the population mean is within the CI in my dataset”
  • Correct: 95% of confidence intervals in repeated experiments will contain the true population mean. CI is not about the population parameter, but the confidence of the sample mean estimation.
• “Confidence intervals for two parameters overlap, therefore they cannot be significantly different.”
  • Correct: The CI doesnt tell anything about the relationship between parameters only refers to the estimate of a parameter.

Resources

• karpov courses
• Design for Six Sigma
• thesaurus
  • Master statistics & machine learning: intuition, math, code

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