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().
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. In
grim_items(),toleranceis the maximal amount by which results may differ from being whole numbers. If they exceed that amount, a warning will be shown.
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. If they differ from the next whole number by more
than a numeric tolerance (which is determined by the argument by that
name), a warning will be shown.
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