Explain a DEBIT test step by step

debit_explain() tests a single mean and SD of binary data like debit() does, but also lays out the calculation in plain words: which numbers of ones the mean allows, and whether the SD of any of them would be reported as the given one.

The text is built from the numbers that decide the test itself, so it always agrees with debit().

Usage

debit_explain(
  x,
  sd,
  n,
  digits_x,
  digits_sd,
  data_type,
  sd_meaning = c("sd_sample", "sd_pop", "sd_sample_or_pop", "se"),
  formula = c("exact", "mean_n"),
  rounding = "up_or_down",
  threshold = 5,
  symmetric = FALSE
)

Arguments

x

Numeric. The reported mean of the binary data, between 0 and 1.

sd

Numeric. The reported standard deviation, between 0 and 1.

n

Integer. The reported sample size.

digits_x, digits_sd

Integer. The number of decimal places in x and sd, including trailing zeros. There are no defaults, since a numeric value does not keep them (1.40 is 1.4).

data_type

String. As in grim(): "integer" or "continuous". No default. For DEBIT, "integer" means the binary values 0 and 1 that the test assumes. Continuous data can have any mean and SD from 0 to 1, so the result is TRUE, but a single value can only have an SD of 0. Values outside of 0 to 1 are an error for either data type.

sd_meaning

String. What sd really is: the sample SD, "sd_sample" (the default); the population SD, "sd_pop"; either one, "sd_sample_or_pop"; or the standard error of the mean, "se". As in grimmer(), whose sections Defaults and SD meaning say why the sample SD is the default and when to choose another.

formula

String. Only "exact", the default, can be explained.

rounding

String. The rounding method assumed to have produced x and sd. Default is "up_or_down". See grim() for the others.

threshold, symmetric

The same as in grim().

Value

An object of class scrutiny_explain: a list with the result as consistency (TRUE, FALSE, or NA), the explanation's paragraphs, and the test and its inputs. It prints as the explanation.

Examples

debit_explain(
  x = 0.36,
  sd = 0.11,
  n = 20,
  digits_x = 2,
  digits_sd = 2,
  data_type = "integer"
)
#> DEBIT test: x = 0.36, sd = 0.11, n = 20, data_type = "integer"
#> 
#> DEBIT is about binary data, where every value is 0 or 1. The mean is then the
#> share of ones, and the SD follows from the number of ones and the sample size.
#> 
#> The mean was reported as 0.36, with 2 decimal places. Before rounding (assuming
#> either rounding up from 5 or down from 5), it could have been anything from
#> 0.355 to 0.365.
#> 
#> With 20 values, the mean is the number of ones divided by 20, so that number
#> must be from 0.355 * 20 = 7.1 to 0.365 * 20 = 7.3. But it has to be an integer,
#> and there is none in this range. So no number of ones fits the mean, whatever
#> the SD is.
#> 
#> ==> Inconsistent

debit_explain(
  x = 0.35,
  sd = 0.49,
  n = 20,
  digits_x = 2,
  digits_sd = 2,
  data_type = "integer"
)
#> DEBIT test: x = 0.35, sd = 0.49, n = 20, data_type = "integer"
#> 
#> DEBIT is about binary data, where every value is 0 or 1. The mean is then the
#> share of ones, and the SD follows from the number of ones and the sample size.
#> 
#> The mean was reported as 0.35, with 2 decimal places. Before rounding (assuming
#> either rounding up from 5 or down from 5), it could have been anything from
#> 0.345 to 0.355.
#> 
#> With 20 values, the mean is the number of ones divided by 20, so that number
#> must be from 0.345 * 20 = 6.9 to 0.355 * 20 = 7.1. It has to be an integer, so
#> it can only be 7.
#> 
#> The SD was reported as 0.49, with 2 decimal places. Before rounding, it could
#> have been anything from 0.485 to 0.495.
#> 
#> With k ones among 20 values, the SD is sqrt(k * (20 - k) / (20 * 19)). For
#> k = 7, that is sqrt(7 * 13 / 380) = 0.4894, which is in that range.
#> 
#> ==> Consistent