Basic statistics

Maximiliano Garnier-Villarreal

2026-05-22

library(GMisc)

This document highlights some functions of the GMisc package related to classical statistics, focusing on summarized data rather than vectors.

Confidence intervals

There are a few functions that can compute confidence intervals based on vectors or tables (a full sample), but sometimes all you get are the point estimates and corresponding sample information. Even though the formulas are straight forward to implement, these have been programmed here for easiness.

The cases shown here are:

• For the mean:
  • One-sample Z-test
  • Two-sample Z-test
  • One-sample t-test
  • Two-sample t-test
• For the variance (standard deviation):
  • One-sample (\chi^2-test)
  • Two-sample (F-test, ratio of variances)

For the variance cases the functions also report the confidence interval for the standard deviation.

One-sample Z-test

This has the form:

\bar{x} \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}

The function for computing it is ci_z, with arguments x for the sample mean, sig for the population standard deviation, n for the sample size, and conf.level for the desired confidence level:

ci_z(x = 80, sig = 15, n = 20, conf.level = 0.95)
#> # A tibble: 1 × 3
#>    mean lower upper
#>   <dbl> <dbl> <dbl>
#> 1    80  73.4  86.6

Two-sample Z-test

This has the form:

\left(\bar{x}_1-\bar{x}_2\right) \pm z_{\alpha/2} {\sqrt{\frac{\sigma^2_1}{n_1} + \frac{\sigma^2_2}{n_2}}}

The function for computing it is ci_z2, with arguments x1 for the mean of sample 1, sig1 for the population 1 standard deviation, n1 for the sample size of 1, x2 for the mean of sample 2, sig2 for the population 2 standard deviation, n2 for the sample size of 2, and conf.level for the desired confidence level:

ci_z2(x1 = 42, sig1 = 8, n1 = 75, x2 = 36, sig2 = 6, n2 = 50, conf.level = 0.95)
#> # A tibble: 1 × 3
#>   mean_diff lower upper
#>       <dbl> <dbl> <dbl>
#> 1         6  3.54  8.46

One-sample t-test

This has the form:

\bar{x} \pm t_{\alpha/2,v} \frac{s}{\sqrt{n}}

The function for computing it is ci_t, with arguments x for the sample mean, s for the sample standard deviation, n for the sample size, and conf.level for the desired confidence level:

ci_t(x = 80, s = 15, n = 20, conf.level = 0.95)
#> # A tibble: 1 × 4
#>    mean    df lower upper
#>   <dbl> <dbl> <dbl> <dbl>
#> 1    80    19  73.0  87.0

Two-sample t-test

This has the general form:

\left(\bar{x}_1-\bar{x}_2\right) \pm t_{\alpha/2,v} {\sqrt{\frac{s^2_1}{n_1} + \frac{s^2_2}{n_2}}}

The function for computing it is ci_t2, with arguments x1 for the mean of sample 1, s1 for the sample 1 standard deviation, n1 for the sample size of 1, x2 for the mean of sample 2, s2 for the sample 2 standard deviation, n2 for the sample size of 2, and conf.level for the desired confidence level:

ci_t2(x1 = 42, s1 = 8, n1 = 75, x2 = 36, s2 = 6, n2 = 50, conf.level = 0.95)
#> # A tibble: 1 × 4
#>   mean_diff    df lower upper
#>       <dbl> <dbl> <dbl> <dbl>
#> 1         6  121.  3.52  8.48

One-sample \chi^2-test

This has the form:

\frac{(n-1)s^2}{\chi^2_{\alpha/2,v}} < \sigma^2 < \frac{(n-1)s^2}{\chi^2_{1-\alpha/2,v}}

The function for computing it is ci_chisq, with arguments s for the sample standard deviation, n for the sample size, and conf.level for the desired confidence level:

ci_chisq(s = 0.535, n = 10, conf.level = 0.95)
#> # A tibble: 2 × 5
#>   stat  value    df lower upper
#>   <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 sd     0.54     9  0.37  0.98
#> 2 var    0.29     9  0.14  0.95

Two-sample F-test (Ratio of variances)

This has the form:

\frac{s^2_1}{s^2_2} \frac{1}{F_{\alpha/2(v_1,v_2)}} < \frac{\sigma^2_1}{\sigma^2_2} < \frac{s^2_1}{s^2_2} F_{\alpha/2(v_2,v_1)}

The function for computing it is ci_F, with arguments s1 for the sample 1 standard deviation, n1 for the sample size of 1, s2 for the sample 2 standard deviation, n2 for the sample size of 2, and conf.level for the desired confidence level:

ci_F(s1 = 3.1, n1 = 15, s2 = 0.8, n2 = 12, conf.level = 0.95)
#> # A tibble: 2 × 6
#>   stat  ratio   df1   df2 lower upper
#>   <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 sd     3.88    14    11  2.11  6.82
#> 2 var   15.0     14    11  4.47 46.5

P-values

There are homologous functions for calculating p-values, with the same arguments but adding either the population mean or population standard deviation for the respective cases.