GRIM-testing with hypothetical group sizes

When reporting group means, some published studies only report the total sample size but no group sizes corresponding to each mean. However, group sizes are crucial for GRIM-testing.

In the two-groups case, grim_map_total_n() helps in these ways:

It creates hypothetical group sizes. With an even total sample size, it incrementally moves up and down from half the total sample size. For example, with a total sample size of 40, it starts at 20, goes on to 19 and 21, then to 18 and 22, etc. With odd sample sizes, it starts from the two integers around half.
It GRIM-tests all of these values together with the group means.
It reports all the scenarios in which both "dispersed" hypothetical group sizes are GRIM-consistent with the group means.

All of this works with one or more total sample sizes at a time. Call audit_total_n() for summary statistics.

Usage

grim_map_total_n(
  data,
  x1 = NULL,
  x2 = NULL,
  dispersion = 0:5,
  n_min = 1L,
  n_max = NULL,
  constant = NULL,
  constant_index = NULL,
  ...
)

Arguments

data: Data frame with string columns x1 and x2, and numeric column n. The first two are group mean or percentage values with unknown group sizes, and n is the total sample size. It is not very important whether a value is in x1 or in x2 because, after the first round of tests, the function switches roles between x1 and x2, and reports the outcomes both ways.
x1, x2: Optionally, specify these arguments as column names in data.
dispersion: Numeric. Steps up and down from half the n values. Default is 0:5, i.e., half n itself followed by five steps up and down.
n_min: Numeric. Minimal group size. Default is 1.
n_max: Numeric. Maximal group size. Default is NULL, i.e., no maximum.
constant: Optionally, add a length-2 vector or a list of length-2 vectors (such as a data frame with exactly two rows) to accompany the pairs of dispersed values. Default is NULL, i.e., no constant values.
constant_index: Integer (length 1). Index of constant or the first constant column in the output tibble. If NULL (the default), constant will go to the right of n_change.
...: Arguments passed down to grim_map().

Value

A tibble with these columns:

x, the group-wise reported input statistic, is repeated in row pairs.
n is dispersed from half the input n, with n_change tracking the differences.
both_consistent flags scenarios where both reported x values are consistent with the hypothetical n values.
case corresponds to the row numbers of the input data frame.
dir is "forth" in the first half of rows and "back" in the second half. "forth" means that x2 from the input is paired with the larger dispersed n, whereas "back" means that x1 is paired with the larger dispersed n.
Other columns from grim_map() are preserved.

Summaries with `audit_total_n()`

You can call audit_total_n() following up on grim_map_total_n() to get a tibble with summary statistics. It will have these columns:

x1, x2, and n are the original inputs.
hits_total is the number of scenarios in which both x1 and x2 are GRIM-consistent. It is the sum of hits_forth and hits_back below.
hits_forth is the number of both-consistent cases that result from pairing x2 with the larger dispersed n value.
hits_back is the same, except x1 is paired with the larger dispersed n value.
scenarios_total is the total number of test scenarios, whether or not both x1 and x2 are GRIM-consistent.
hit_rate is the ratio of hits_total to scenarios_total.

Call audit() following audit_total_n() to summarize results even further.

References

Bauer, P. J., & Francis, G. (2021). Expression of Concern: Is It Light or Dark? Recalling Moral Behavior Changes Perception of Brightness. Psychological Science, 32(12), 2042–2043. https://journals.sagepub.com/doi/10.1177/09567976211058727

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

# Run `grim_map_total_n()` on data like these:
df <- tibble::tribble(
  ~x1,    ~x2,   ~n,
  "3.43", "5.28", 90,
  "2.97", "4.42", 103
)
df
#> # A tibble: 2 × 3
#>   x1    x2        n
#>   <chr> <chr> <dbl>
#> 1 3.43  5.28     90
#> 2 2.97  4.42    103

grim_map_total_n(df)
#> # A tibble: 48 × 8
#>    x         n n_change consistency both_consistent probability  case dir  
#>    <chr> <int>    <int> <lgl>       <lgl>                 <dbl> <int> <fct>
#>  1 3.43     45        0 FALSE       FALSE                  0.55     1 forth
#>  2 5.28     45        0 FALSE       FALSE                  0.55     1 forth
#>  3 3.43     44       -1 TRUE        TRUE                   0.56     1 forth
#>  4 5.28     46        1 TRUE        TRUE                   0.54     1 forth
#>  5 3.43     43       -2 FALSE       FALSE                  0.57     1 forth
#>  6 5.28     47        2 TRUE        FALSE                  0.53     1 forth
#>  7 3.43     42       -3 TRUE        FALSE                  0.58     1 forth
#>  8 5.28     48        3 FALSE       FALSE                  0.52     1 forth
#>  9 3.43     41       -4 FALSE       FALSE                  0.59     1 forth
#> 10 5.28     49        4 FALSE       FALSE                  0.51     1 forth
#> # ℹ 38 more rows

# `audit_total_n()` summaries can be more important than
# the detailed results themselves.
# The `hits_total` column shows all scenarios in
# which both divergent `n` values are GRIM-consistent
# with the `x*` values when paired with them both ways:
df %>%
  grim_map_total_n() %>%
  audit_total_n()
#> # A tibble: 2 × 8
#>   x1    x2        n hits_total hits_forth hits_back scenarios_total hit_rate
#>   <chr> <chr> <int>      <int>      <int>     <int>           <int>    <dbl>
#> 1 3.43  5.28     90          3          2         1              12     0.25
#> 2 2.97  4.42    103          0          0         0              12     0   

# By default (`dispersion = 0:5`), the function goes
# five steps up and down from `n`. If this sequence
# gets longer, the number of hits tends to increase:
df %>%
  grim_map_total_n(dispersion = 0:10) %>%
  audit_total_n()
#> # A tibble: 2 × 8
#>   x1    x2        n hits_total hits_forth hits_back scenarios_total hit_rate
#>   <chr> <chr> <int>      <int>      <int>     <int>           <int>    <dbl>
#> 1 3.43  5.28     90          6          3         3              22   0.273 
#> 2 2.97  4.42    103          2          0         2              22   0.0909