# Dyslexia and IQ Predicting Reading Accuracy

### Description

Data for assessing the contribution of non-verbal IQ to children's reading skills in dyslexic and non-dyslexic children.

### Usage

1 | ```
data("ReadingSkills")
``` |

### Format

A data frame containing 44 observations on 3 variables.

- accuracy
reading score scaled to the open unit interval (see below).

- dyslexia
factor. Is the child dyslexic? (A sum contrast rather than treatment contrast is employed.)

- iq
non-verbal intelligence quotient transformed to z-scores.

### Details

The data were collected by Pammer and Kevan (2004) and employed by
Smithson and Verkuilen (2006). The original reading accuracy score was transformed
by Smithson and Verkuilen (2006) so that `accuracy`

is in the open unit
interval (0, 1) and beta regression can be employed. First, the original accuracy
was scaled using the minimal and maximal score (`a`

and `b`

, respectively)
that can be obtained in the test: `(original_accuracy - a) / (b - a)`

(`a`

and `b`

are not provided). Subsequently, the scaled score is transformed
to the unit interval using a continuity correction: `(scaled_accuracy * (n-1) - 0.5) / n`

(either with some rounding or using `n = 50`

rather than 44).

### Source

Example 3 from http://psychology3.anu.edu.au/people/smithson/details/betareg/betareg.html

### References

Cribari-Neto, F., and Zeileis, A. (2010). Beta Regression in R.
*Journal of Statistical Software*, **34**(2), 1–24.
http://www.jstatsoft.org/v34/i02/.

Grün, B., Kosmidis, I., and Zeileis, A. (2012).
Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned.
*Journal of Statistical Software*, **48**(11), 1–25.
http://www.jstatsoft.org/v48/i11/.

Pammer, K., and Kevan, A. (2004).
The Contribution of Visual Sensitivity, Phonological Processing
and Non-Verbal IQ to Children's Reading.
*Unpublished manuscript*, The Australian National University, Canberra.

Smithson, M., and Verkuilen, J. (2006).
A Better Lemon Squeezer? Maximum-Likelihood Regression with
Beta-Distributed Dependent Variables.
*Psychological Methods*, **11**(7), 54–71.

### See Also

`betareg`

, `MockJurors`

, `StressAnxiety`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
data("ReadingSkills", package = "betareg")
## Smithson & Verkuilen (2006, Table 5)
## OLS regression
## (Note: typo in iq coefficient: 0.3954 instead of 0.3594)
rs_ols <- lm(qlogis(accuracy) ~ dyslexia * iq, data = ReadingSkills)
summary(rs_ols)
## Beta regression (with numerical rather than analytic standard errors)
## (Note: Smithson & Verkuilen erroneously compute one-sided p-values)
rs_beta <- betareg(accuracy ~ dyslexia * iq | dyslexia + iq,
data = ReadingSkills, hessian = TRUE)
summary(rs_beta)
## visualization
plot(accuracy ~ iq, data = ReadingSkills, col = as.numeric(dyslexia), pch = 19)
nd <- data.frame(dyslexia = "no", iq = -30:30/10)
lines(nd$iq, predict(rs_beta, nd))
lines(nd$iq, plogis(predict(rs_ols, nd)), lty = 2)
nd <- data.frame(dyslexia = "yes", iq = -30:30/10)
lines(nd$iq, predict(rs_beta, nd), col = 2)
lines(nd$iq, plogis(predict(rs_ols, nd)), col = 2, lty = 2)
## see demo("SmithsonVerkuilen2006", package = "betareg") for more details
``` |