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Historical categorical analysis of a binary Solomon outcome

Source: R/solomon_marginal.R
fisher_solomon.Rd

[Stable] Reproduces the categorical path described by El Karkri et al. (2025b) for qualitative outcomes: the treatment comparison is tested separately among pretested and unpretested participants with Fisher's exact test (Pearson's chi-square test is also reported), and pretest sensitization is "judged to exist if a significant effect is observed for pre-tested groups but not for non-pre-tested groups" (p. 7).

Usage

fisher_solomon(
  y_post,
  treat,
  pretested,
  alpha = 0.05,
  data = NULL,
  y = deprecated()
)

Arguments

y_post

Binary posttest outcome coded 0/1 (or logical).

treat

Treatment indicator coded 0/1 (or logical). Designs with several treatments are not supported; see fit_solomon_glm().

pretested

Pretest indicator coded 0/1 (or logical).

alpha

Significance level for the historical rule. Default 0.05.

data

Optional data frame. When supplied, the other data arguments are looked up in it first, as bare column names (y_post = post) or as strings (y_post = "post").

y

[Deprecated] Use y_post.

Value

An object of class solomon_fisher with tests (one row per pretest condition and for both combined: counts, proportions, the uncorrected Pearson chi-square, and Fisher's exact p-value) and sensitization (the historical rule's verdict).

Details

This is provided for teaching and replication. The rule compares significance, not effects: when the treatment effect is the same in both pretest conditions, it still declares sensitization whenever the pretested comparison reaches significance and the unpretested one does not. As Gelman and Stern (2006) put it, "even large changes in significance levels can correspond to small, nonsignificant changes in the underlying quantities" (p. 328). A test of sensitization compares the effects themselves; see marginal_solomon().

References

El Karkri, M., Quesada, A., & Romero-Ariza, M. (2025b). Methodological aspects of the Solomon four-group design: Detecting pre-test sensitisation and analysing qualitative and quantitative variables in education research. Review of Education, 13(1), Article e70050. https://doi.org/10.1002/rev3.70050

Gelman, A., & Stern, H. (2006). The difference between "significant" and "not significant" is not itself statistically significant. The American Statistician, 60(4), 328–331. https://doi.org/10.1198/000313006X152649

See also

marginal_solomon()

Examples

# Kvalem et al. (1996): condom use at most recent intercourse, 6 months.
kvalem <- data.frame(
  treat = c(1, 1, 0, 0), pretested = c(1, 0, 1, 0),
  events = c(51, 21, 76, 69), n = c(73, 49, 148, 133)
)
d <- kvalem[rep(1:4, kvalem$n), c("treat", "pretested")]
d$y <- unlist(lapply(1:4, function(i) {
  rep(c(1, 0), c(kvalem$events[i], kvalem$n[i] - kvalem$events[i]))
}))
fisher_solomon(y, treat, pretested, data = d)
#> Historical categorical Solomon analysis (El Karkri et al., 2025b)
#> 
#>    Condition Events (T) n (T) Events (C) n (C) Chi-square Fisher p
#>    Pretested         51    73         76   148       6.85   0.0095
#>  Unpretested         21    49         69   133       1.17   0.3180
#>     Combined         72   122        145   281       1.88   0.1922
#> 
#> Historical rule (significant among pretested, not among unpretested, alpha = 0.05): sensitization declared
#> Caution: this rule compares significance, not effects, and is not a test of
#> the Pretest x Treatment interaction. See marginal_solomon().