# interval_statistics: Interval statistics In mosaicCore: Common Utilities for Other MOSAIC-Family Packages

## Description

Calculate coverage intervals and confidence intervals for the sample mean, median, sd, proportion, ... Typically, these will be used within `df_stats()`. For the mean, median, and sd, the variable x must be quantitative. For proportions, the x can be anything; use the `success` argument to specify what value you want the proportion of. Default for `success` is `TRUE` for x logical, or the first level returned by `unique` for categorical or numerical variables.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```coverage(x, level = 0.95, na.rm = TRUE) ci.mean(x, level = 0.95, na.rm = TRUE) ci.median(x, level = 0.9, na.rm = TRUE) ci.sd(x, level = 0.95, na.rm = TRUE) ci.prop( x, success = NULL, level = 0.95, method = c("Clopper-Pearson", "binom.test", "Score", "Wilson", "prop.test", "Wald", "Agresti-Coull", "Plus4") ) ```

## Arguments

 `x` a variable. `level` number in 0 to 1 specifying the confidence level for the interval. (Default: 0.95) `na.rm` if `TRUE` disregard missing data `success` for proportions, this specifies the categorical level for which the calculation of proportion will be done. Defaults: `TRUE` for logicals for which the proportion is to be calculated. `method` for `ci.prop()`, the method to use in calculating the confidence interval. See `mosaic::binom.test()` for details.

## Details

Methods: `ci.mean()` uses the standard t confidence interval. `ci.median()` uses the normal approximation method. `ci.sd()` uses the chi-squared method. `ci.prop()` uses the binomial method. In the usual situation where the `mosaic` package is available, `ci.prop()` uses `mosaic::binom.test()` internally, which provides several methods for the calculation. See the documentation for `binom.test()` for details about the available methods. Clopper-Pearson is the default method. When used with `df_stats()`, the confidence interval is calculated for each group separately. For "pooled" confidence intervals, see methods such as `lm()` or `glm()`.

## Value

a named numerical vector with components `lower` and `upper`, and, in the case of `ci.prop()`, `center`. When used the `df_stats()`, these components are formed into a data frame.

## Note

When using these functions with `df_stats()`, omit the `x` argument, which will be supplied automatically by `df_stats()`. See examples.

`df_stats()`, `mosaic::binom.test()`, `mosaic::t.test()`
 ```1 2 3 4 5 6 7 8``` ```# The central 95% interval df_stats(hp ~ cyl, data = mtcars, c95 = coverage(0.95)) # The confidence interval on the mean df_stats(hp ~ cyl, data = mtcars, mean, ci.mean) # What fraction of cars have 6 cylinders? df_stats(mtcars, ~ cyl, six_cyl_prop = ci.prop(success = 6, level = 0.90)) # Use without `df_stats()` (rare) ci.mean(mtcars\$hp) ```