Claritin

Description

From Example 4.3

A 2×2 contingency table for a clinical trial comparing Claritin (active drug) vs. placebo, cross-tabulated against whether patients reported nervousness as a side effect.

	nervous	not nervous
claritin	4	184
placebo	2	260

Small counts in the “nervous” column make this dataset a canonical example for Fisher’s exact test — the chi-squared expected-count assumption (all cells > 5) is violated.

Bar chart

From Bar charts

A side-by-side bar chart of proportions highlights the relative difference in nervousness rates between the two arms.

Python code

import numpy as np
import pandas as pd
 
claritin_tab = np.array([[4, 184], [2, 260]])
claritin_prop = claritin_tab / claritin_tab.sum(axis=1).reshape((2,1))
 
xx = pd.DataFrame(claritin_prop,
                  columns=['nervous', 'not_nervous'],
                  index=['claritin', 'placebo'])
 
ax = xx.plot(kind='bar', stacked=False, rot=1.0, figsize=(10,4),
             title='Nervousness by drug')
ax.legend(loc='upper left');

Proportions are small in absolute terms (~2% vs ~1%) but the relative difference looks noteworthy — hence the need for a formal test.

Fisher’s exact test

From Fisher’s Exact Test

Used when expected cell counts are < 5 (chi-squared’s approximation fails). Models the top-left cell count as hypergeometric under fixed marginals.

R code

y <- matrix(c(4, 2, 184, 260), nrow=2)
dimnames(y) <- list(c("claritin", "placebo"), c("nervous", "not nervous"))
claritin_tab <- as.table(y)
fisher.test(claritin_tab)

Python code

from scipy import stats
 
fe_output = stats.fisher_exact(claritin_tab)
print(f"The p-value for the test is {fe_output.pvalue:.4f}.")
# The p-value for the test is 0.2412.

Conclusion: p-value = 0.2412. Do not reject $H_0$; no significant association between drug group and nervousness.

Verifying the chi-squared test was not appropriate:

chisq.test(claritin_tab)$expected

confirms at least one expected count is below 5.

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See also: L4 Exploring Categorical Data · Chi-Square & Fisher