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Statistical Power for the Generic T-Test

generic.t.test.Rd

Calculates power for the generic T-Test with (optional) Type 1 and Type 2 error plots.

Usage

power.t.test(ncp, null.ncp = 0, df, alpha = 0.05,
             alternative = c("two.sided", "one.sided", "two.one.sided"),
             plot = TRUE, verbose = TRUE, pretty = FALSE)

Arguments

ncp

non-centrality parameter for the alternative.

null.ncp

non-centrality parameter for the null. When alternative = "two.one.sided", the function expects two values in the form c(lower, upper). If a single value is provided, it is interpreted as the absolute bound and automatically expanded to c(-value, +value).

df

degrees of freedom.

alpha

type 1 error rate, defined as the probability of incorrectly rejecting a true null hypothesis, denoted as \(\alpha\).

alternative

character; direction or type of the hypothesis test: "one.sided", "two.sided", or "two.one.sided". "two.one.sided" is used for equivalence and minimal effect testing.

plot

logical; FALSE switches off Type 1 and Type 2 error plot. TRUE by default.

verbose

logical; whether the output should be printed on the console. TRUE by default.

pretty

logical; whether the output should show Unicode characters (if encoding allows for it). FALSE by default.

Value

df

degrees of freedom.

ncp

non-centrality parameter under alternative.

ncp.null

non-centrality parameter under null.

t.alpha

critical value(s).

power

statistical power \((1-\beta)\).

Examples

# two-sided
# power defined as the probability of observing a test statistic
# greater than the positive critical value OR
# less than the negative critical value
power.t.test(ncp = 1.96, df = 100, alpha = 0.05,
             alternative = "two.sided")

#> +--------------------------------------------------+
#> |                POWER CALCULATION                 |
#> +--------------------------------------------------+
#> 
#> Generic T-Test
#> 
#> ---------------------------------------------------
#> Hypotheses
#> ---------------------------------------------------
#>   H0 (Null Claim) : ncp = null.ncp 
#>   H1 (Alt. Claim) : ncp != null.ncp 
#> 
#> ---------------------------------------------------
#> Results
#> ---------------------------------------------------
#>   Type 1 Error (alpha)   = 0.050
#>   Type 2 Error (beta)    = 0.507
#>   Statistical Power      = 0.493  << 
#> 

# one-sided
# power is defined as the probability of observing a test statistic
# greater than the critical value
power.t.test(ncp = 1.96, df = 100, alpha = 0.05,
             alternative = "one.sided")

#> +--------------------------------------------------+
#> |                POWER CALCULATION                 |
#> +--------------------------------------------------+
#> 
#> Generic T-Test
#> 
#> ---------------------------------------------------
#> Hypotheses
#> ---------------------------------------------------
#>   H0 (Null Claim) : ncp <= null.ncp 
#>   H1 (Alt. Claim) : ncp > null.ncp 
#> 
#> ---------------------------------------------------
#> Results
#> ---------------------------------------------------
#>   Type 1 Error (alpha)   = 0.050
#>   Type 2 Error (beta)    = 0.381
#>   Statistical Power      = 0.619  << 
#> 

# equivalence
# power is defined as the probability of observing a test statistic
# greater than the upper critical value (for the lower bound) AND
# less than the lower critical value (for the upper bound)
power.t.test(ncp = 0, df = 100,
             null.ncp = c(-2, 2), alpha = 0.05,
             alternative = "two.one.sided")

#> +--------------------------------------------------+
#> |                POWER CALCULATION                 |
#> +--------------------------------------------------+
#> 
#> Generic T-Test
#> 
#> ---------------------------------------------------
#> Hypotheses
#> ---------------------------------------------------
#>   H0 (Null Claim) : ncp <= min(null.ncp) or 
#>                     ncp >= max(null.ncp) 
#>   H1 (Alt. Claim) : ncp > min(null.ncp) and 
#>                     ncp < max(null.ncp) 
#> 
#> ---------------------------------------------------
#> Results
#> ---------------------------------------------------
#>   Type 1 Error (alpha)   = 0.050
#>   Type 2 Error (beta)    = 0.723
#>   Statistical Power      = 0.277  << 
#> 

# minimal effect testing
# power is defined as the probability of observing a test statistic
# greater than the upper critical value (for the upper bound) OR
# less than the lower critical value (for the lower bound).
power.t.test(ncp = 2, df = 100,
             null.ncp = c(-1, 1), alpha = 0.05,
             alternative = "two.one.sided")

#> +--------------------------------------------------+
#> |                POWER CALCULATION                 |
#> +--------------------------------------------------+
#> 
#> Generic T-Test
#> 
#> ---------------------------------------------------
#> Hypotheses
#> ---------------------------------------------------
#>   H0 (Null Claim) : ncp >= min(null.ncp) and 
#>                     ncp <= max(null.ncp) 
#>   H1 (Alt. Claim) : ncp < min(null.ncp) or 
#>                     ncp > max(null.ncp) 
#> 
#> ---------------------------------------------------
#> Results
#> ---------------------------------------------------
#>   Type 1 Error (alpha)   = 0.050
#>   Type 2 Error (beta)    = 0.837
#>   Statistical Power      = 0.163  << 
#>