Alpha to Critical Values

Calculates the \(z\), \(t\), \(\chi^2\), or \(F\) critical value/s of confidence limits associated with the specified significance level/s \(\left( \alpha \right)\) .

alpha2crit(
  alpha = c(0.001, 0.01, 0.05),
  dist = "z",
  two.tailed = TRUE,
  right.tail = TRUE,
  ...
)

Arguments

alpha	Numeric vector. Significance level \(\left( \alpha \right)\) . By default, alpha is set to conventional significance levels alpha = c(0.001, 0.01, 0.05).
dist	Character string. dist = "z" for the standard normal distribution. dist = "t" for the t distribution. dist = "F" for the F distribution. dist = "chisq" for the chi-square distribution.
two.tailed	Logical. If TRUE, two-tailed alpha. If FALSE, one-tailed alpha. Ignored if dist = "F" or dist = "chisq" as both tests are one-tailed using the right tail.
right.tail	Logical. If TRUE, right tail (positive critical value). If FALSE, left tail (negative critical value). Ignored if two.tailed = TRUE. Ignored if dist = "F" or dist = "chisq" as both tests are one-tailed using the right tail.
...	Degrees of freedom. df for dist = "t" and dist = "chisq". df1 and df2 for dist = "F".

Value

Returns \(z\), \(t\), \(\chi^2\), or \(F\) critical value/s associated with the specified significance level/s \(\left( \alpha \right)\). The results are sorted from smallest to largest.

References

Wikipedia: Statistical significance

Wikipedia: Confidence interval

See also

Other alpha functions: alpha2prob(), ci2crit(), ci2prob(), nhstplot()

Examples

# z two-tailed
## vector
alpha2crit(
  alpha = c(
    0.001,
    0.01,
    0.05
  )
)
#> [1] -3.290527 -2.575829 -1.959964  1.959964  2.575829  3.290527
## single numeric value
alpha2crit(alpha = 0.05)
#> [1] -1.959964  1.959964
# t two-tailed
## vector
alpha2crit(
  alpha = c(
    0.001,
    0.01,
    0.05
  ),
  dist = "t",
  df = 1000
)
#> [1] -3.300283 -2.580755 -1.962339  1.962339  2.580755  3.300283
## single numeric value
alpha2crit(
  alpha = 0.05,
  dist = "t",
  df = 1000
)
#> [1] -1.962339  1.962339
# z one-tailed right
## vector
alpha2crit(
  alpha = c(
    0.001,
    0.01,
    0.05
  ),
  dist = "z",
  two.tailed = FALSE
)
#> [1] 3.090232 2.326348 1.644854
# t one-tailed right
## vector
alpha2crit(
  alpha = c(
    0.001,
    0.01,
    0.05
  ),
  dist = "t",
  two.tailed = FALSE,
  df = 5
)
#> [1] 5.893430 3.364930 2.015048
# F one-tailed
## vector
alpha2crit(
  alpha = c(
    0.001,
    0.01,
    0.05
  ),
  dist = "F",
  two.tailed = FALSE,
  df1 = 2,
  df2 = 2
)
#> [1]  19  99 999
# chisq one-tailed
## vector
alpha2crit(
  alpha = c(
    0.001,
    0.01,
    0.05
  ),
  dist = "chisq",
  two.tailed = FALSE,
  df = 1
)
#> [1]  3.841459  6.634897 10.827566
# z one-tailed left
## vector
alpha2crit(
  alpha = c(
    0.001,
    0.01,
    0.05
  ),
  dist = "z",
  two.tailed = FALSE,
  right.tail = FALSE
)
#> [1] -3.090232 -2.326348 -1.644854
# t one-tailed left
## vector
alpha2crit(
  alpha = c(
    0.001,
    0.01,
    0.05
  ),
  dist = "t",
  two.tailed = FALSE,
  right.tail = FALSE,
  df = 5
)
#> [1] -5.893430 -3.364930 -2.015048