layard: Test for homogeneity of variances of Layard

In ExpDes: Experimental Designs Package

Description

layard Performs the test for homogeneity of variances of Layard for Jackknife (1973).

Usage

layard(trat, resp, t, r)

Arguments

trat	Numeric or complex vector containing treatments.
resp	Numeric or complex vector containing the response variable.
t	Number of treatments.
r	Numeric or complex vector containing the number of replications of each treatment.

Value

Returns the p-value of the Layard test of homogeneity of variances and its practical interpretation for the significance level of 5%.

Author(s)

Eric B Ferreira, [e-mail] @author Denismar Alves Nogueira @author Marcos Costa de Paula @author Mateus Pimenta Siqueira Lima

References

LAYARD, M. N. J. Robust large-sample tests for homogeneity of variances. Journal of the American Statistical Association, v.68, n.341, p.195-198, 1973.

NOGUEIRA, D, P.; PEREIRA, G, M. Desempenho de testes para homogeneidade de variancias em delineamentos inteiramente casualizados. Sigmae, Alfenas, v.2, n.1, p. 7-22. 2013.

See Also

bartlett, samiuddin, levene, oneillmathews.

Examples

data(ex1)
attach(ex1)
crd(trat, ig, quali = FALSE, hvar = "layard")

Example output

Attaching package: ‘ExpDes’

The following object is masked from ‘package:stats’:

    ccf

------------------------------------------------------------------------
Analysis of Variance Table
------------------------------------------------------------------------
           DF     SS MS     Fc     Pr>Fc
Treatament  3 214.88  3 6.5212 0.0029622
Residuals  20 219.67  2                 
Total      23 434.55  1                 
------------------------------------------------------------------------
CV = 3.41 %

------------------------------------------------------------------------
Shapiro-Wilk normality test
p-value:  0.91697 
According to Shapiro-Wilk normality test at 5% of significance, residuals can be considered normal.
------------------------------------------------------------------------

------------------------------------------------------------------------
Homogeneity of variances test
p-value:  0.5906373 
According to the test of layard at 5% of significance, residuals can be considered homocedastic.
------------------------------------------------------------------------

Adjustment of polynomial models of regression
------------------------------------------------------------------------

Linear Model
==========================================
   Estimate Standard.Error   tc    p.value
------------------------------------------
b0 100.2878     1.1320     88.5938    0   
b1 -0.4136      0.1210     -3.4177 0.0027 
------------------------------------------

R2 of linear model
--------
0.597077
--------

Analysis of Variance of linear model
================================================
              DF    SS       MS     Fc   p.value
------------------------------------------------
Linear Effect 1  128.2987 128.2987 11.68 0.00273
Lack of fit   2  86.5794  43.2897  3.94  0.03605
Residuals     20 219.6710 10.9836               
------------------------------------------------
------------------------------------------------------------------------

Quadratic Model
==========================================
   Estimate Standard.Error   tc    p.value
------------------------------------------
b0 101.5728     1.3187     77.0229    0   
b1 -1.1846      0.4236     -2.7968 0.0111 
b2  0.0514      0.0271     1.8995  0.0720 
------------------------------------------

R2 of quadratic model
--------
0.781504
--------

Analysis of Variance of quadratic model
===================================================
                 DF    SS       MS     Fc   p.value
---------------------------------------------------
Linear Effect    1  128.2987 128.2987 11.68 0.00273
Quadratic Effect 1  39.6294  39.6294  3.61  0.07202
Lack of fit      1  46.9500  46.9500  4.27  0.05187
Residuals        20 219.6710 10.9836               
---------------------------------------------------
------------------------------------------------------------------------

Cubic Model
==========================================
   Estimate Standard.Error   tc    p.value
------------------------------------------
b0 102.1983     1.3530     75.5350    0   
b1 -3.1445      1.0383     -3.0286 0.0066 
b2  0.4267      0.1835     2.3250  0.0307 
b3 -0.0167      0.0081     -2.0675 0.0519 
------------------------------------------

R2 of cubic model
-
1
-

Analysis of Variance of cubic model
===================================================
                 DF    SS       MS     Fc   p.value
---------------------------------------------------
Linear Effect    1  128.2987 128.2987 11.68 0.00273
Quadratic Effect 1  39.6294  39.6294  3.61  0.07202
Cubic Effect     1  46.9500  46.9500  4.27  0.05187
Lack of fit      0     0        0       0      1   
Residuals        20 219.6710 10.9836               
---------------------------------------------------
------------------------------------------------------------------------

ExpDes documentation built on Oct. 5, 2021, 9:09 a.m.