Statistic Inference

Environment Setup

Download R (National Taiwan University Mirror)

Usage

Either using R Console or type R in your command line.

And then using source("Inference.R") to start the program.

Ps. Don't use RScript to open it. Because it will cause the non-interactively error.

Brief Description

Inferences

• Hypothesis Testing
  • p-value
  • Critical Region
• Interval Estimating
• Goodness of Fit Testing
• Testing for Homogenity
• Testing for Independence

File Description

Main Parser

• Inference.R

Inference Parser

• HypothesisTesting.R
• IntervalEstimating.R
• GoodnessOfFit.R
• TestingForHomogeneity.R
• RestingForIndependence.R

Function Supporter

• HypothesisTestingFunctions.R

  • X tagged in N random survey
    • p-value : HT_BINOM_XTAG_PV(alpha)
    • Critical Region : HT_BINOM_XTAG_CR(alpha)

• GoodnessOfFitFunctions.R

  • Test if the die is fair with K faces
    • GOF_MULTINOM_DIE(alpha, K)

• HomogeneityFunctions.R

  • M die with K cells have commmon cell probabilities
    • TFH_MULTINOM_KCELL(alpha, M, K)

• IndependenceFunctions.R

  • Compare attribute A and B (one multinomial distribution with a*b cells)
    • TFI_MULTINOM_abCELL(alpha, a, b)

• PValueCriticalRegion.R

  • PValue(pvalue, alpha) ⎯⎯ p-value inference function
  • PH1(ph0, DRorNot) ⎯⎯ hypothesis 1 parser

• PlotDiagram.R

Todo and Progress

Hypothesis Testing

Binomial Distribution

• Population Proportion (p-value & Critical Region)

Negative-binomial Distribution

Normal Distribution

Chi-square Distribution

T Distribution

Interval Estimating

Goodness of Fit Testing

• Test if the die is fair with K faces (p-value & Critical Region)

Testing for Homogenity

• M die with K cells have commmon cell probabilities (Critical Region & p-value)

Testing for Independence

• Compare attribute A and B (p-value & Critical Region)

Plot Functions

• Chi-square Distribution (p-value & Critical Region)

  • Used by
    • Goodness of Fit: Test if the die is fair with K faces
    • Testing for Homogenity: M die with K cells have commmon cell probabilities
    • Testing for Independence: Compare attribute A and B

• Binomial Distribution (p-value & Critical Region)

  • Used by
    • Hypothesis Testing: Population Proportion

Notes

R Language

• Input variable as number as.numberic(readline("prompt"))
• Print variable value in a string e.g. cat("Hello", variable, "\n") cat(sprintf("Result = %f", res)) print(paste("Hello", "World", sep=""))