Two‐tailed significance tests for 2 × 2 contingency tables: What is the alternative?

Abstract

Two‐tailed significance testing for 2 × 2 contingency tables has remained controversial. Within the medical literature, different tests are used in different papers and that choice may decide whether findings are adjudged to be significant or nonsignificant; a state of affairs that is clearly undesirable. In this paper, it is argued that a part of the controversy is due to a failure to recognise that there are two possible alternative hypotheses to the Null. It is further argued that, while one alternative hypothesis can lead to tests with greater power, the other choice is more applicable in medical research. That leads to the recommendation that, within medical research, 2 × 2 tables should be tested using double the one‐tailed exact probability from Fisher's exact test or, as an approximation, the chi‐squared test with Yates' correction for continuity.

Response to comments on “Two‐tailed significance tests for 2 × 2 contingency tables: What is the alternative?”

“…“What is the alternative?” That was the question asked as part of the title of my paper . This was not mere whimsy on my part nor was it a rhetorical question.…”

“…That was the question asked as part of the title of my paper. 1 This was not mere whimsy on my part nor was it a rhetorical question. It was a subtle play on words as a reminder of my key point that the inferential methods used to analyse a 2 × 2 contingency table should depend on the Alternative Hypothesis to the Null that is chosen.…”

Contemporary management of penetrating renal trauma - A national analysis

“…IO patients were more likely than NOM to have greater median ISS (25 [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] vs 18 [14][15][16][17][18][19][20][21][22][23][24][25][26], p < 0.001) and were more likely than NOM patients to suffer gunshot wounds as a mechanism of injury (88.9% vs 59.1%, p < 0.001). Additionally, IO patients tended to have higher grade (AAST IV & V) renal injuries (75.3% vs 48.8%, p < 0.001) and concomitant abdominal injuries (87.0% vs 56.7%, p < 0.001) than NOM patients ( Table 1).…”

“…Mean time to failure was 67.0 h (SD = 133.8) (median time, 24.8 h, IQR, 9.4-48.8). Compared to patients with s-NOM, f-NOM patients were more likely than s-NOM to have greater median ISS (26 [25][26][27][28][29][30][31][32][33][34] vs 18 [13][14][15][16][17][18][19][20][21][22][23][24][25][26], p < 0.001) and concomitant abdominal injuries (88.5% vs 53.9%, p < 0.001). Additionally, f-NOM patients were more likely than s-NOM patients to suffer gunshot wounds as a mechanism of injury (84.6% vs 56.9%, p < 0.001) and high grade (AAST IV & V) renal injuries (80.7% vs 46.0%, p < 0.001) ( Table 2).…”

“…As compared to IO, NOM patients had lower in-hospital complications (11.2% vs 31.9%, p < 0.001) and shorter median ICU (3 [2-5] vs 5 [3][4][5][6][7][8][9][10][11][12][13], p < 0.001) and hospital (6 [4][5][6][7][8][9][10][11][12] vs 14 [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], p < 0.001) lengths of stay. A similar trend was observed within the NOM groups, whereby s-NOM patients had less complications (8.9% vs 38.5%, p < 0.001) and shorter lengths of stay than f-NOM patients (Table 4).…”