Granularity of non-continuous scales — grim

grim_granularity() computes the minimal difference between two means or proportions of ordinal or interval data.

grim_items() is the reverse: It converts granularity values to the number of scale items, which might then be used for consistency testing functions such as grim().

Usage

grim_granularity(n, items = 1)

grim_items(n, gran, tolerance = .Machine$double.eps^0.5)

Arguments

n: Numeric. Sample size.
items: Numeric. Number of items composing the scale. Default is 1, which will hold for most non-Likert scales.
gran: Numeric. Granularity.
tolerance: Numeric. Any difference between x and a truncated version of x less than tolerance (in the absolute value) will be ignored. The default is close to 1 / (10 ^ 8). This avoids errors due to spurious precision in floating-point arithmetic.

Value

Numeric. Granularity or number of items.

Details

These two functions differ only in the names of their arguments — the underlying formula is the same (and it's very simple). However, for clarity, they are presented as distinct.

The output of grim_items() should be whole numbers, because scale items have a granularity of 1.

It would be wrong to determine a scale's granularity from the minimal distance between two values in a given distribution. This would only signify how those values actually do differ, not how they can differ a priori based on scale design. Also, keep in mind that continuous scales have no granularity at all.

References

Brown, N. J. L., & Heathers, J. A. J. (2017). The GRIM Test: A Simple Technique Detects Numerous Anomalies in the Reporting of Results in Psychology. Social Psychological and Personality Science, 8(4), 363–369. https://journals.sagepub.com/doi/10.1177/1948550616673876

Examples

# If a non-Likert scale ranges from 0 to 3
# and measures 16 cases:
grim_granularity(n = 16)   # `items = 1` by default
#> [1] 0.0625

# Same but Likert scale with 2 items:
grim_granularity(n = 16, items = 2)
#> [1] 0.03125

# If a scale is applied to a single case
# and has a granularity of 0.5:
grim_items(n = 1, gran = 0.5)
#> [1] 2

# With more cases, a warning appears
# because items can only be whole numbers:
grim_items(n = c(10, 15, 20), gran = 0.5)
#> Warning: 3 out of 3 item counts aren't whole numbers.
#> → This concerns `0.2`, `0.133`, and `0.1`.
#> ! Item counts have a granularity of 1, so they should be whole numbers. Are you
#>   sure about the `n` and `gran` values?
#> [1] 0.2000000 0.1333333 0.1000000