# Statistical Tables

Fundamental Statistical Inference Distribution Table
p-value R-Code #R-Code comment mentioning scope of code
Percentile/Quantile R-Code #R-Code comment mentioning scope of code
Wikipedia References

Z-Table
pnorm(z, mean = 0, sd = 1, lower.tail = TRUE) #Defaults to lower tail Standard Normal, but standardization is unnecessary. Multiply by 2 for 2-tailed test
qnorm(p, mean = 0, sd = 1, lower.tail = TRUE) #Defaults to lower tail Standard Normal, but standardization is unnecessary.
Normal Distribution
Z-Test

t-Table
pt(t, df) #Defaults to lower tail central standard t where standardization is required. Multipbly by 2 for 2-tailed test
qt(p, df) #Defaults to lower tail central standard t where standardization is required.
Students' t-Distribution
Student's t-Test

Chi-Squared Table
pchisq(x, df, ncp = 0, lower.tail = FALSE) #Defaults to lower tail central chi-square. For Chi-Squared Test, upper tail is desired. Thus, although a good default for tables as a whole, a bad default for this table. \Chi^2_{df} = \Gamma(\alpha = df, \beta = 1/2) = Z_1^2 + ... + Z_{df}^2
qchisq(p, df, ncp = 0, lower.tail = FALSE) #Defaults to lower tail central chi-square. For Chi-Squared Test, upper tail is desired. Thus, although a good default for tables as a whole, a bad default for this table.
Chi-Squared Distribution
chisq.test(x, p = rep(1/length(x), length(x))) #x: a numeric vector or matrix. For Test of Independence, make x a matrix. For Goodness of Fit Test, make x a vector and modify p as null hypothesis dictates.
Pearson's Chi-Squared Test
Chi-Square Test

F-Table
pf(f, df1, df2, lower.tail = FALSE) #Defaults to lower tail central F. For F-Test, upper tail is desired. F_{df1, df2} = \frac{\Chi^2_{df1}/(df1 - 1)}{\Chi^2_{df2}/(df2 - 1)}
qf(p, df1, df2, lower.tail = FALSE) #Defaults to lower tail central F. For F-Test, upper tail is desired.
F-Distribution
aov(continuousvariable ~ categoricalvariable, data = STAT350df) #Defaults to data = NULL, but it is typically easier to provide the entire data frame of interest into this input. We will explore the R ANalysis Of VAriance (ANOVA) function call after Spring Break.
F-Test
ANOVA