Package 'Mychisq'

Goodness of fit test

Description

This function is for the goodness of fit test of one categorical variable

Usage

gofchisq(x, p, conf.level = 0.95)

Arguments

x	an observed frequency vector
p	probability of each group
conf.level	confidence level for testing hypothesis, default is 0.95, user can change to 0.90 or otherwise

Value

output for the goodness of fit test

References

Chernoff, H. and Lehmann, E.L. (1954) The Use of Maximum Likelihood Estimates in Chi-Square Tests for Goodness of Fit. Annals of Mathematical Statistics, 25, 579-586. <doi.org/10.1214/aoms/1177728726>.

Examples

x=c(12,9,10,7,12)
prob=c(1/5,1/5,1/5,1/5,1/5)  #1:1:1:1:1
gofchisq(x=x,p=prob)

---

Independence test

Description

This function is for the independence test of two categorical variables

Usage

indchisq(O, conf.level = 0.95)

Arguments

O	an observed matrix has a rows and b columns
conf.level	confidence level for testing hypothesis, default is 0.95, user can change to 0.90 or otherwise

Value

output for the independence test

References

Plackett, R. L. (1983). Karl Pearson and the Chi-Squared Test. International Statistical Review / Revue Internationale de Statistique, 51(1), 59–72. <doi.org/10.2307/1402731>.

Examples

v <- c(80,60,150,50,40,20)
X<- matrix(v,ncol=2,byrow = TRUE)  # 3x2
indchisq(X)

---

Plot of Chi-squared distribution

Description

The plot of Chi-squared distribution with k degrees of freedom

Usage

plotchisq(df = 8)

Arguments

df	degrees of freedom

Value

The figure of Chi-squared distribution with k degrees of freedom

Examples

plotchisq(df=15)

---

Confidence interval for the population standard deviation

Description

A function 'sigmaCI()' is used to compute a confidence interval of the population standard deviation when given a numeric vector

Usage

sigmaCI(x, conf.level = 0.95)

Arguments

x	a numeric vector
conf.level	a confidence level, default is 0.95; the user can change to 0.90 or otherwise

Value

a confidence interval of the population standard deviation

References

Rattanalertnusorn, A. (2024). R and its application (3rd ed.). TPN press. <https://www.researchgate.net/publication/371944275_porkaermxarlaeakarprayuktchingan_R_and_its_applications>.

Examples

heigth <- c(155.5, 165.5, 170, 164.5, 180, 162, 173, 158.5, 168.5, 175, 164.5, 167)
sigmaCI(x=heigth,conf.level = 0.90)

---

Hypothesis testing for the population variance

Description

The function 'sigmatest()' is used to test the hypothesis about the population variance

Usage

sigmatest(
  x,
  sigma,
  alternative = c("two.sided"),
  conf.level = 0.95,
  verbose = TRUE
)

Arguments

x	a numeric vector
sigma	a population standard deviation under the null hypothesis
alternative	an alternative hypothesis, default is "two.sided"; the user can change to "greater" or "less"
conf.level	a confidence level for hypothesis testing, default is 0.95; the user can change to 0.90 or otherwise
verbose	a special variable is used for protected unexpected print output; the default is TRUE, do NOT change

Value

output of one sample Chi-squared test for variance

References

Rattanalertnusorn, A. (2024). R and its application (3rd ed.). TPN press. <https://www.researchgate.net/publication/371944275_porkaermxarlaeakarprayuktchingan_R_and_its_applications>.

Examples

heigth <- c(155.5, 165.5, 170, 164.5, 180, 162, 173, 158.5, 168.5, 175, 164.5, 167)
sigmatest(x=heigth, sigma = 3, alternative = "two.sided", conf.level = 0.95)

---

Confidence interval for the population variance

Description

A function 'varCI()' is used to calculate a confidence interval for the population variance when given a numerical vector

Usage

varCI(x, conf.level = 0.95)

Arguments

x	a numeric vector
conf.level	a confidence level, default is 0.95; the user can change to 0.90 or otherwise

Value

a confidence interval of the population variance

References

Rattanalertnusorn, A. (2024). R and its application (3rd ed.). TPN press. <https://www.researchgate.net/publication/371944275_porkaermxarlaeakarprayuktchingan_R_and_its_applications>.

Examples

heigth <- c(155.5, 165.5, 170, 164.5, 180, 162, 173, 158.5, 168.5, 175, 164.5, 167)
varCI(x=heigth,conf.level = 0.90)

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