Few cases: grimmer()
To test if a reported mean of 7.3 on a granular scale is
GRIMMER-consistent with an SD of 2.51 and a sample size of 12, run
this:
grimmer(x = "7.3", sd = "2.51", n = 12)
#> 7.3
#> FALSE
Note that x, the reported mean, needs to be a string.
The reason is that strings preserve trailing zeros, which can be crucial
for GRIMMER-testing. Numeric values don’t, and even converting them to
strings won’t help. A workaround for larger numbers of such values,
restore_zeros(), is discussed in
vignette("wrangling").
grimmer() has some further parameters, but all of them
can be used from within grimmer_map(). The other parameters
will be discussed in that context because grimmer_map() is
often the more useful function in practice. Furthermore, although
grimmer() is vectorized, grimmer_map() is
safer and more convenient for testing multiple combinations of means,
SDs, and sample sizes.
Many cases: grimmer_map()
If you want to GRIMMER-test more than a handful of cases, the
recommended way is to enter them into a data frame and to run
grimmer_map() on the data frame. Two different ways to do
that are discussed in vignette("wrangling"), but here, I
will only describe an easily accessible solution for a single table.
Copy summary data from a PDF file and paste them into
tibble::tribble(), which is available via scrutiny:
flying_pigs1 <- tibble::tribble(
~x, ~sd, ~n,
"8.9", "2.81", 25,
"2.6", "2.05", 25,
"7.2", "2.89", 25,
"3.6", "3.11", 25,
"9.2", "7.13", 25,
"10.4", "2.53", 25,
"7.3", "3.14", 25
)
Use RStudio’s multiple cursors to draw quotation marks around all the
x and sd values, and to set commas at the end.
See vignette("wrangling"), section With copy and
paste, if you are not sure how to do that.
Now, simply run grimmer_map() on that data frame:
grimmer_map(flying_pigs1)
#> # A tibble: 7 × 5
#> x sd n consistency reason
#> <chr> <chr> <dbl> <lgl> <chr>
#> 1 8.9 2.81 25 FALSE GRIMMER inconsistent (test 3)
#> 2 2.6 2.05 25 FALSE GRIMMER inconsistent (test 3)
#> 3 7.2 2.89 25 TRUE Passed all
#> 4 3.6 3.11 25 TRUE Passed all
#> 5 9.2 7.13 25 TRUE Passed all
#> 6 10.4 2.53 25 TRUE Passed all
#> 7 7.3 3.14 25 TRUE Passed all
The x and n columns are the same as in the
input. By default, the number of items composing the mean
is assumed to be 1. The main result, consistency, is the
GRIMMER consistency of the former three columns.
The reason column says why a set of values was
inconsistent. To be GRIMMER-consistent, a value set needs to pass four
separate tests: the three GRIMMER tests by Allard
(2018) and the more basic GRIM test. Here, the two inconsistent
values passed GRIM as well as the first two GRIMMER tests, but failed
the third one. All consistent value sets are marked as
"Passed all" in the "reason" column.
Here is a quick reference for the three GRIMMER tests. See Allard (2018) for an explanation.
- The reconstructed sum of squared observations must be a whole
number.
- The reconstructed SD must match the reported one.
- The parity of the reconstructed sum of squared observations must
match the parity of the reconstructed sum of integers of which the
reported means are fractions; i.e., either both are even or both are
odd.
Scale items
If a mean is composed of multiple items, set the items
parameter to that number. Below are hypothetical means of a three-items
scale. With the single-item default, half of these are wrongly flagged
as GRIM-inconsistent (true GRIMMER example below):
flying_pigs2 <- tibble::tribble(
~x, ~sd, ~n,
"5.90", "2.19", 40,
"5.71", "1.42", 40,
"3.50", "1.81", 40,
"3.82", "2.43", 40,
"4.61", "1.92", 40,
"5.24", "2.51", 40
)
flying_pigs2 %>%
grimmer_map() # default is wrong here!
#> # A tibble: 6 × 5
#> x sd n consistency reason
#> <chr> <chr> <dbl> <lgl> <chr>
#> 1 5.90 2.19 40 TRUE Passed all
#> 2 5.71 1.42 40 FALSE GRIM inconsistent
#> 3 3.50 1.81 40 TRUE Passed all
#> 4 3.82 2.43 40 TRUE Passed all
#> 5 4.61 1.92 40 FALSE GRIM inconsistent
#> 6 5.24 2.51 40 FALSE GRIM inconsistent
Yet, all of them are consistent if the correct number of items is
stated:
flying_pigs2 %>%
grimmer_map(items = 3)
#> # A tibble: 6 × 5
#> x sd n consistency reason
#> <chr> <chr> <dbl> <lgl> <chr>
#> 1 5.90 2.19 120 TRUE Passed all
#> 2 5.71 1.42 120 TRUE Passed all
#> 3 3.50 1.81 120 TRUE Passed all
#> 4 3.82 2.43 120 TRUE Passed all
#> 5 4.61 1.92 120 TRUE Passed all
#> 6 5.24 2.51 120 TRUE Passed all
It is also possible to include an items column in the
data frame instead. This is helpful if the rows have different numbers
of items:
flying_pigs3 <- tibble::tribble(
~x, ~sd, ~n, ~items,
"6.92", "2.19", 30, 1,
"3.48", "1.42", 30, 1,
"1.59", "1.81", 30, 2,
"2.61", "2.43", 30, 2,
"4.04", "1.92", 30, 3,
"4.50", "2.51", 30, 3,
)
flying_pigs3 %>%
grimmer_map()
#> # A tibble: 6 × 5
#> x sd n consistency reason
#> <chr> <chr> <dbl> <lgl> <chr>
#> 1 6.92 2.19 30 FALSE GRIM inconsistent
#> 2 3.48 1.42 30 FALSE GRIM inconsistent
#> 3 1.59 1.81 60 FALSE GRIM inconsistent
#> 4 2.61 2.43 60 FALSE GRIM inconsistent
#> 5 4.04 1.92 90 TRUE Passed all
#> 6 4.50 2.51 90 TRUE Passed all
The items values are multiplied by the n
values. By default, the product is shown as n in the output
(merge_items = TRUE), but overriding this default won’t
affect the test results.
However, if we remove the items column, crucial
information is missing. As a consequence, the last two values are
wrongly flagged as inconsistent, one of them by GRIMMER:
flying_pigs3 %>%
dplyr::select(-items) %>%
grimmer_map()
#> # A tibble: 6 × 5
#> x sd n consistency reason
#> <chr> <chr> <dbl> <lgl> <chr>
#> 1 6.92 2.19 30 FALSE GRIM inconsistent
#> 2 3.48 1.42 30 FALSE GRIM inconsistent
#> 3 1.59 1.81 30 FALSE GRIM inconsistent
#> 4 2.61 2.43 30 FALSE GRIM inconsistent
#> 5 4.04 1.92 30 FALSE GRIM inconsistent
#> 6 4.50 2.51 30 FALSE GRIMMER inconsistent (test 3)
