ItemAnalysis function

Compute traditional item analysis indices

Computes various traditional item analysis indices including difficulty, discrimination and item validity. For ordinal items, the function returns scaled values for some of the indices. See the details below.

ItemAnalysis(
  Data,
  minscore = NULL,
  maxscore = NULL,
  cutscore = NULL,
  criterion = NULL,
  k = NULL,
  l = NULL,
  u = NULL,
  bin = "deprecated"
)

Arguments

• Data: matrix or data.frame of items to be examined. Rows represent respondents, columns represent items.

• minscore, maxscore: integer, theoretical minimal/maximal score. If not provided, these are computed on observed data. Automatically recycled to the number of columns of the data.

• cutscore: integer If provided, the input data are binarized accordingly. Automatically recycled to the number of columns of the data.

• criterion: vector of criterion values.

• k, l, u: Arguments passed on to gDiscrim(). Provide these if you want to compute generalized upper-lower index along with a standard ULI (using k

  = 3, l = 1, u = 3), which is provided by default.

• bin: deprecated, use cutscore instead. See the Details .

Returns

A data.frame with following columns: - Difficulty: average score of the item divided by its range.

• Mean: average item score.

• SD: standard deviation of the item score.

• Cut.score: cut-score specified in cutscore.

• obs.min: observed minimal score.

• Min.score: minimal score specified in minscore; if not provided, observed minimal score.

• obs.max: observed maximal score.

• Max.score: maximal score specified in maxscore; if not provided, observed maximal score.

• Prop.max.score: proportion of maximal scores.

• RIT: item-total correlation (correlation between item score and overall test score).

• RIR: item-rest correlation (correlation between item score and overall test score without the given item).

• ULI: upper-lower index using the standard parameters (3 groups, comparing 1st and 3rd).

• Corr.criterion: correlation between item score and criterion criterion.

• gULI: generalized ULI. NA when the arguments k, l, and u

  were not provided.

• Alpha.drop: Cronbach's alpha without given item.

• Index.rel: Gulliksen's (1950) item reliability index.

• Index.val: Gulliksen's (1950) item validity index.

• Perc.miss: Percentage of missed responses on the particular item.

• Perc.nr: Percentage of respondents that did not reached the item nor the subsequent ones, see recode_nr() for further details.

Details

For calculation of generalized ULI index, it is possible to specify a custom number of groups k, and which two groups l and u are to be compared.

In ordinal items, difficulty is calculated as difference of average score divided by range (maximal possible score maxscore minus minimal possible score minscore).

If cutscore is provided, item analysis is conducted on binarized data; values greater or equal to cut-score are set to 1, other values are set to 0. Both the minscore and maxscore arguments are then ingored and set to 0 and 1, respectively.

Examples

## Not run:

# binary dataset
dataBin <- dataMedical[, 1:100]
# ordinal dataset
dataOrd <- dataMedicalgraded[, 1:100]
# study success is the same for both data sets
StudySuccess <- dataMedical[, 102]

# item analysis for binary data
head(ItemAnalysis(dataBin))
# item analysis for binary data using also study success
head(ItemAnalysis(dataBin, criterion = StudySuccess))

# item analysis for binary data
head(ItemAnalysis(dataOrd))
# item analysis for binary data using also study success
head(ItemAnalysis(dataOrd, criterion = StudySuccess))
# including also item analysis for binarized data
head(ItemAnalysis(dataOrd,
  criterion = StudySuccess, k = 5, l = 4, u = 5,
  maxscore = 4, minscore = 0, cutscore = 4
))
## End(Not run)

References

Martinkova, P., Stepanek, L., Drabinova, A., Houdek, J., Vejrazka, M., & Stuka, C. (2017). Semi-real-time analyses of item characteristics for medical school admission tests. In: Proceedings of the 2017 Federated Conference on Computer Science and Information Systems. https://doi.org/10.15439/2017F380

Gulliksen, H. (1950). Theory of mental tests. John Wiley & Sons Inc. https://doi.org/10.1037/13240-000

See Also

DDplot(), gDiscrim(), recode_nr()

Author(s)

Patricia Martinkova

Institute of Computer Science of the Czech Academy of Sciences

martinkova@cs.cas.cz

Jan Netik

Institute of Computer Science of the Czech Academy of Sciences

netik@cs.cas.cz

Jana Vorlickova

Institute of Computer Science of the Czech Academy of Sciences

Adela Hladka

Institute of Computer Science of the Czech Academy of Sciences

hladka@cs.cas.cz