ci_cramersv | R Documentation |

This function calculates CIs for the population Cramer's V. By default, a parametric approach based on the non-centrality parameter (NCP) of the chi-squared distribution is utilized. Alternatively, bootstrap CIs are available (default "bca"), also by boostrapping CIs for the NCP and then mapping the result back to Cramer's V.

```
ci_cramersv(
x,
probs = c(0.025, 0.975),
type = c("chi-squared", "bootstrap"),
boot_type = c("bca", "perc", "norm", "basic"),
R = 9999L,
seed = NULL,
test_adjustment = TRUE,
...
)
```

`x` |
The result of |

`probs` |
Lower and upper probabilities, by default |

`type` |
Type of CI. One of "chi-squared" (default) or "bootstrap". |

`boot_type` |
Type of bootstrap CI. Only used for |

`R` |
The number of bootstrap resamples. Only used for |

`seed` |
An integer random seed. Only used for |

`test_adjustment` |
Adjustment to allow for test of association, see Details.
The default is |

`...` |
Further arguments passed to |

A positive lower `(1 - \alpha) \cdot 100\%`

-confidence limit for the NCP goes
hand-in-hand with a significant association test at level `\alpha`

. In order to
allow such test approach also with Cramer's V, if the lower bound for the NCP is 0,
we round down to 0 the lower bound for Cramer's V as well.
Without this slightly conservative adjustment, the lower limit for V would always be
positive since the CI for V is found by
`\sqrt{(\textrm{CI for NCP} + \textrm{df})/(n \cdot (k - 1))}`

, where `k`

is the
smaller number of levels in the two variables (see Smithson, p.40).
Use `test_adjustment = FALSE`

to switch off this behaviour. Note that this is
also a reason to bootstrap V via NCP instead of directly bootstrapping V.

Further note that no continuity correction is applied for 2x2 tables,
and that large chi-squared test statistics might provide unreliable results with
method "chi-squared", see `stats::pchisq()`

.

An object of class "cint", see `ci_mean()`

for details.

Smithson, M. (2003). Confidence intervals. Series: Quantitative Applications in the Social Sciences. New York, NY: Sage Publications.

`cramersv()`

, `ci_chisq_ncp()`

```
# Example from Smithson, M., page 41
test_scores <- as.table(
rbind(
Private = c(6, 14, 17, 9),
Public = c(30, 32, 17, 3)
)
)
suppressWarnings(X2 <- stats::chisq.test(test_scores))
ci_cramersv(X2)
```

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