# Calculation of the Lowest Expected Value, kappaL for a fixed sample size in a Study of Interobserver Agreement with a Multinomial Outcome (3 Levels)

### Description

This function provides the potential lower bound for a 100(1 - *α*) % confidence interval
that can be calculated for a fixed sample size, n, and an anticipated
value of *κ*. This version assumes that the outcome has three categories.

### Usage

1 | ```
FixedN3Cats(kappa0, n, props, raters=2, alpha=0.05)
``` |

### Arguments

`kappa0` |
The preliminary value of |

`n` |
The total number of available subjects. |

`props` |
The anticipated prevalence of the desired trait. Note that the elements of the three element vector must be non-negative and sum to one. |

`raters` |
The number of raters that are available. This function allows between 2 and 6 raters. |

`alpha` |
The desired type I error rate. |

### Details

This function calculates the expected lower bound of a one-sided
confidence interval for a fixed sample size, n, and an anticipated
value of *κ*, kappa0. This function can illustrate the amount of precision
available in the estimation of *κ* for a fixed sample size. Note that a warning message is provided if any of the expected cell counts are less than 5.

### Value

`n` |
The specified sample size. |

`kappa0` |
The specified anticipated value of |

`kappaL` |
The calculated expected lower limit. |

`props` |
The anticipated proportion of individuals with the outcome. |

`raters` |
The number of raters. |

`alpha` |
The desired type I error rate. |

`ChiCrit` |
The critical value that is required for sample size estimation. It is typically not required and is not displayed in the summary output. |

### Author(s)

Michael Rotondi, mrotondi@uwo.ca

### References

Donner A, Rotondi MA. (2010). Sample Size Requirements for Interval Estimation of the Kappa Statistic for Interobserver Agreement Studies with a Binary Outcome and Multiple Raters. International Journal of Biostatistics 6:31.

Altaye M, Donner A, Klar N. (2001). Procedures for Assessing Interobserver Agreement among Multiple Raters. Biometrics 57:584-588.

Donner A. (1999). Sample Size Requirements for Interval Estimation of the Intraclass Kappa Statistic. Communication in Statistics 28:415-429.

Bartfay E, Donner A. (2001). Statistical Inferences for Interobserver Agreement Studies with Nominal Outcome Data. The Statistician 50:135-146.

Donner A, Eliasziw M. (1987) Sample size requirements for reliability studies. Statistics in Medicine 6:441-448.

### Examples

1 2 3 4 5 | ```
## Not run: Suppose an investigator would like to determine the expected lower bound for
kappa0=0.7 assuming he has access to 80 subjects and 5 raters. Further suppose that
the prevalence of the trait is 0.50.
## End(Not run)
FixedN3Cats(kappa0=0.7, n=80, props=c(0.33, 0.34, 0.33), alpha=0.05, raters=5);
``` |