# VocabGrowth: Vocabulary growth data In heplots: Visualizing Hypothesis Tests in Multivariate Linear Models

## Description

Data from the Laboratory School of the University of Chicago. They consist of scores from a cohort of pupils in grades 8-11 on the vocabulary section of the Cooperative Reading Test. The scores are scaled to a common, but arbitrary origin and unit of measurement, so as to be comparable over the four grades.

## Usage

 `1` ```data(VocabGrowth) ```

## Format

A data frame with 64 observations on the following 4 variables.

`grade8`

`grade9`

`grade10`

`grade11`

## Details

Since these data cover an age range in which physical growth is beginning to decelerate, it is of interest whether a similar effect occurs in the acquisition of new vocabulary.

## Source

R.D. Bock, Multivariate statistical methods in behavioral research, McGraw-Hill, New York, 1975, pp453.

## References

Friendly, Michael (2010). HE Plots for Repeated Measures Designs. Journal of Statistical Software, 37(4), 1-40. doi: 10.18637/jss.v037.i04.

Keesling, J.W., Bock, R.D. et al, "The Laboratory School study of vocabulary growth", University of Chicago, 1975.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29``` ```data(VocabGrowth) # Standard Multivariate & Univariate repeated measures analysis Vocab.mod <- lm(cbind(grade8,grade9,grade10,grade11) ~ 1, data=VocabGrowth) idata <-data.frame(grade=ordered(8:11)) Anova(Vocab.mod, idata=idata, idesign=~grade, type="III") ##Type III Repeated Measures MANOVA Tests: Pillai test statistic ## Df test stat approx F num Df den Df Pr(>F) ##(Intercept) 1 0.653 118.498 1 63 4.115e-16 *** ##grade 1 0.826 96.376 3 61 < 2.2e-16 *** heplot(Vocab.mod, type="III", idata=idata, idesign=~grade, iterm="grade", main="HE plot for Grade effect") ### doing this 'manually' by explicitly transforming Y -> Y M # calculate Y M, using polynomial contrasts trends <- as.matrix(VocabGrowth) %*% poly(8:11, degree=3) colnames(trends)<- c("Linear", "Quad", "Cubic") # test all trend means = 0 == Grade effect within.mod <- lm(trends ~ 1) Manova(within.mod) heplot(within.mod, terms="(Intercept)", col=c("red", "blue"), type="3", term.labels="Grade", main="HE plot for Grade effect") mark.H0() ```

### Example output

```Loading required package: car

Type III Repeated Measures MANOVA Tests: Pillai test statistic
Df test stat approx F num Df den Df    Pr(>F)
(Intercept)  1   0.65289  118.498      1     63 4.115e-16 ***
grade        1   0.82578   96.376      3     61 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Note: model has only an intercept; equivalent type-III tests substituted.

Type III MANOVA Tests: Pillai test statistic
Df test stat approx F num Df den Df    Pr(>F)
(Intercept)  1   0.82578   96.376      3     61 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

heplots documentation built on Oct. 7, 2021, 1:07 a.m.