# volleyball dataset In hyper2: The Hyperdirichlet Distribution, Mark 2

```set.seed(0)
knitr::opts_chunk\$set(echo = TRUE)
library("hyper2")
library("magrittr")
options("digits" = 5)
```

This short document discusses a dataset first presented by Hankin (2010), although here only the first 52 observations are used. A volleyball \dfn{set} is a Bernoulli trial between two disjoint subsets of the players. The two subsets are denoted (after the game) as the winners and the losers: these are denoted by `1` and `0` respectively.

```volleyball_table <- as.matrix(read.table("volleyball.txt",header=TRUE))
nrow(volleyball_table)
```

Each row of `volleyball_table` is a set. Thus the first line shows a game between a team comprising `p1`, `p4`, and `p8` against a team comprising `p5` and `p6`. Player `p9` did not play; team `p1 p4 p8` won.

We may use function `volley()` to convert this to a likelihood function:

```volleyball <- volley(volleyball_table)
(volleyball_maxp <- maxp(volleyball))
```

The original synthetic dataset was prepared using Zipf's law for the players' strengths, so we may test the hypothesis that this is the case; \$H_0\colon p_i\propto i^{-1}\$:

```zipf <- function(n){jj <- 1/(1:n); jj/sum(jj)}
zipf(9)
(null_support <- loglik(indep(zipf(9)),volleyball))
(alternative_support <- loglik(indep(volleyball_maxp),volleyball))
(Lambda <- 2*(alternative_support-null_support))
pchisq(Lambda,df=8,lower.tail=FALSE)
```

somewhat disappointingly rejecting the null with a \$p\$-value of about 4\% (and indeed--just---with a two units of support per degree of freedom criterion). However, it is not clear to me the extent to which Wilks's theorem is applicable here [Wilks is an asymptotic result; recall that we have only 52 observations here], nor whether the support criterion is appropriate with 8 degrees of freedom.

### Package dataset {-}

Following lines create `volleyball.rda`, residing in the `data/` directory of the package.

```save(volleyball_table,volleyball_maxp,volleyball,file="volleyball.rda")
```

## Try the hyper2 package in your browser

Any scripts or data that you put into this service are public.

hyper2 documentation built on March 4, 2021, 9:09 a.m.