L_1way_ANOVA: Likelihood Supports for One-way Independent Samples ANOVA

In likelihoodR: Likelihood Analyses for Common Statistical Tests

Likelihood Supports for One-way Independent Samples ANOVA

Description

This function calculates supports for independent samples ANOVA. One support is for the model of group means against the null (no grouping), for the first contrast versus the group means model, and the other for 2 contrasts. Both contrasts should be either NULL or specified. If the contrasts use the default of NULL, then it calculates a linear versus a quadratic contrast. The corrected support is given for groups versus null, using Akaike's correction (Hurvich & Tsai (1989)). No correction is necessary for the two contrasts' support since they both involve 1 parameter. Conventional frequentist F and p value statistics are given for the overall analysis and for contrast 1. Unequal group sizes are accommodated.

Usage

L_1way_ANOVA(data, group, contrast1=NULL, contrast2=NULL, verb=TRUE)

Arguments

data	a (non-empty) numeric vector of data values.
group	an integer vector the same length as data, coding for k groups.
contrast1	first contrast, default = NULL.
contrast2	second contrast, default = NULL.
verb	show output, default = TRUE.

Value

$S.12c - corrected support for groups hypothesis versus null.

$S.12 - uncorrected support for groups hypothesis versus null.

S.1mc - support for contrast 1 versus the group means model.

$S.1m = uncorrected support for contrast 1 vs group means.

$S.cont.12 - support for contrast 1 versus contrast 2.

$contrast1 - first contrast.

$contrast2 - second contrast.

$gp.means - group means.

$df - degrees of freedom for groups and error.

$F.val - F value for overall ANOVA analysis.

$P.val - p value for overall analysis.

$eta.sq - eta-squared.

$Fval.c1 - F value for contrast 1.

$df.1 - degrees of freedom for contrast.

$P.val1 - p value for contrast 1.

References

Cahusac, P.M.B. (2020) Evidence-Based Statistics, Wiley, ISBN : 978-1119549802

Hurvich CM, Tsai C-L. Regression and time series model selection in small samples. Biometrika. 1989; 76(2):297.

Dixon P. The effective number of parameters in post hoc models. Behavior Research Methods. 2013; 45(3):604.

Dixon P. The p-value fallacy and how to avoid it. Canadian Journal of Experimental Psychology/Revue canadienne de psychologie expérimentale. 2003; 57(3):189.

Glover S, Dixon P. Likelihood ratios: a simple and flexible statistic for empirical psychologists. Psychonomic Bulletin and Review. 2004; 11(5):791.

Examples

# fitness example, p 81
dat <- c(7,	5,	9,	8,	3,	12,	10,	8,	7,	9,
5,	7,	7,	6,	4,	8,	12,	9,	7,	8,
3,	2,	7,	6,	8,	6,	5,	3,	4,	3,
4,	3,	3,	1,	2,	5,	7,	6,	8,	7)
gp <- as.factor(rep(1:4,each=10))
gp = gl(4,10,40, labels=c("6 hr",	"3 hr",	"Sports club",	"Video games"))
contrast1 <- c(-3, -1, 1, 3)  # linear
contrast2 <- c(1, -1, -1, 1)  # quadratic
contrast3 <- c(1, 1, -1, -1)
L_1way_ANOVA(dat,gp,contrast3, contrast1)

likelihoodR documentation built on Sept. 14, 2023, 9:08 a.m.