calc_se {CAISEr} R Documentation

## Calculates the standard error for simple and percent differences

### Description

Calculates the sample standard error for the estimator differences between multiple algorithms on a given instance.

### Usage

```calc_se(
Xk,
dif = "simple",
comparisons = "all.vs.all",
method = "param",
boot.R = 999
)
```

### Arguments

 `Xk` list object where each position contains a vector of observations of algorithm k on a given problem instance. `dif` name of the difference for which the SEs are desired. Accepts "perc" (for percent differences) or "simple" (for simple differences) `comparisons` standard errors to be calculated. Accepts "all.vs.first" (in which cases the first object in `algorithms` is considered to be the reference algorithm) or "all.vs.all" (if there is no reference and all pairwise SEs are desired). `method` method used to calculate the interval. Accepts "param" (using parametric formulas based on normality of the sampling distribution of the means) or "boot" (for bootstrap). `boot.R` (optional) number of bootstrap resamples (if `method == "boot"`)

### Details

• If `dif == "perc"` it returns the standard errors for the sample estimates of pairs (mu2 - mu1) / mu, where mu1, mu2 are the means of the populations that generated sample vectors x1, x2, and

• If `dif == "simple"` it returns the SE for sample estimator of (mu2 - mu1)

### Value

a list object containing the following items:

• `Phi.est` - estimated values of the statistic of interest for each pair of algorithms of interest (all pairs if `comparisons == "all.vs.all"`, or all pairs containing the first algorithm if `comparisons == "all.vs.first"`).

• `se` - standard error estimates

### References

• F. Campelo, F. Takahashi: Sample size estimation for power and accuracy in the experimental comparison of algorithms. Journal of Heuristics 25(2):305-338, 2019.

### Author(s)

Felipe Campelo (fcampelo@ufmg.br, f.campelo@aston.ac.uk)

### Examples

```# three vectors of normally distributed observations
set.seed(1234)
Xk <- list(rnorm(10, 5, 1),  # mean = 5, sd = 1,
rnorm(20, 10, 2), # mean = 10, sd = 2,
rnorm(50, 15, 5)) # mean = 15, sd = 3

calc_se(Xk, dif = "simple", comparisons = "all.vs.all", method = "param")
calc_se(Xk, dif = "simple", comparisons = "all.vs.all", method = "boot")

calc_se(Xk, dif = "perc", comparisons = "all.vs.first", method = "param")
calc_se(Xk, dif = "perc", comparisons = "all.vs.first", method = "boot")

calc_se(Xk, dif = "perc", comparisons = "all.vs.all", method = "param")
calc_se(Xk, dif = "perc", comparisons = "all.vs.all", method = "boot")
```

[Package CAISEr version 1.0.16 Index]