# Confidence interval for an (unstandardized) contrast in ANCOVA with one covariate

### Description

To calculate the confidence interval for an unstandardized contrast in the one-covariate ANCOVA.

### Usage

1 2 | ```
ci.c.ancova(Psi, adj.means, s.ancova = NULL, c.weights, n,
cov.means, SSwithin.x, conf.level = 0.95, ...)
``` |

### Arguments

`Psi` |
the unstandardized contrast of adjusted means |

`adj.means` |
the vector that contains the adjusted mean of each group on the dependent variable |

`s.ancova` |
the standard deviation of the errors from the ANCOVA model (i.e., the square root of the mean square error from ANCOVA) |

`c.weights` |
the contrast weights |

`n` |
either a single number that indicates the sample size |

`cov.means` |
a vector that contains the group means of the covariate |

`SSwithin.x` |
the sum of squares within groups obtained from the summary table for ANOVA on the covariate |

`conf.level` |
the desired confidence interval coverage, (i.e., 1 - Type I error rate) |

`...` |
allows one to potentially include parameter values for inner functions |

### Value

`lower.limit` |
the lower confidence limit of the (unstandardized) ANCOVA contrast |

`upper.limit` |
the upper confidence limit of the (unstandardized) ANCOVA contrast |

### Note

Be sure to use the standard deviation and not the error variance for `s.ancova`

, not the square of this value which would come from the source table (i.e., do not use the variance of the error but rather use the square root).

If `n`

receives a single number, that number is considered as the sample size *per group*. If `n`

receives a vector, the vector is considered as the sample size of each group.

Be sure to use fractions not the integers to specify `c.weights`

. For example, in an ANCOVA of four groups,
if the user wants to compare the mean of group 1 and 2 with the mean of group 3 and 4, `c.weights`

should
be specified as c(0.5, 0.5, -0.5, -0.5) rather than c(1, 1, -1, -1). Make sure the sum of the contrast weights
are zero.

### Author(s)

Keke Lai (University of California–Merced) and Ken Kelley (University of Notre Dame; kkelley@nd.edu)

### References

Kelley, K. (2007). Constructing confidence intervals for standardized effect sizes: Theory, application, and implementation. *Journal of Statistical Software, 20* (8), 1–24.

Maxwell, S. E., & Delaney, H. D. (2004). *Designing experiments and analyzing data: A model comparison perspective*. Mahwah, NJ: Erlbaum.

### See Also

`ci.c`

, `ci.sc.ancova`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
# Maxwell & Delaney (2004, pp. 428-468) offer an example that 30 depressive
# individuals are randomly assigned to three groups, 10 in each, and ANCOVA
# is performed on the posttest scores using the participants' pretest
# scores as the covariate. The means of pretest scores of group 1 to 3 are
# 17, 17.7, and 17.4, respectively, and the adjusted means of groups 1 to 3
# are 7.5, 12, and 14, respectively. The error variance in ANCOVA is 29,
# and the sum of squares within groups from ANOVA on the covariate is
# 313.37.
# To obtain the confidence interval for adjusted mean of group 1 versus
# group 2:
ci.c.ancova(adj.means=c(7.5, 12, 14), s.ancova=sqrt(29), c.weights=c(1, -1, 0),
n=10, cov.means=c(17, 17.7, 17.4), SSwithin.x=313.37)
``` |