Analysis of Simple Randomised Trial (SRT).

Description

srtFREQ perfoms analysis of education trials under the assumption of independent errors between pupils. This can also be used with schools as fixed effects.

Usage

1
srtFREQ(formula, intervention, nBoot = NULL, nPerm = NULL, data)

Arguments

formula

specifies the model to be analysed. It is of the form y~x1+x2+..., where y is the outcome variable and X's are the predictors.

intervention

the name of the intervention variable as appeared in formula. This must be put in quotes. For example "intervention" or "treatment" or "group".

nBoot

number of bootstrap required to generate bootstrap confidence interval. Default is NULL.

nPerm

number of permutations required to generate permutation p-value. Default is NULL.

data

data frame containing the data to be analysed.

Value

S3 mcpi object; a list consisting of

  • Beta. Estimates and confidence intervals for the predictors specified in the model. It will be the slope for a continuous predictor and the mean difference for a dummy variable or a categorical predictor.

  • ES. Hedges' effect size for the intervention effect. If nBoot is not specified, the confidence intervals are classical 95 If nBoot is specified, they are non-parametric bootstrapped confidence intervals.

  • sigma2. Residual variance. Its square root will generate a pooled standard deviation.

  • Perm. A vector containing the distribution of effect size under the null hypothesis. It is produced only if nPerm is specified.

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
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
data(catcht)

###################################################################
## Analysis of simple randomised trials using Hedges Effect Size ##
###################################################################

output1 <- srtFREQ(Posttest~ Intervention+Prettest,
		intervention="Intervention",data=catcht )
ES1 <- output1$ES

###################################################################
## Analysis of simple randomised trials using Hedges Effect Size ## 
## with Permutation p-value                                      ##
###################################################################

output2 <- srtFREQ(Posttest~ Intervention+Prettest,
		intervention="Intervention",nPerm=1000,data=catcht )
ES2 <- output2$ES




#### Distribution under the null

perm <- output2$Perm


#### Permutation P-value using total variance


obsg <- output2$ES[1]


permPvalue <- ifelse(mean(perm$permES> obsg[1])==0,"<0.001",
		mean(perm$permES > obsg[1]) )
permPvalue 

## Distribution of ES under H0
hist(perm$permES, breaks=40, col="white", border="blueviolet", 
		xlab="Distribution Under Null Hypothesis", 
		main=paste("P(X|NULL)= ",permPvalue,sep=""),
		xlim=range(c(perm[,1],obsg),na.rm=TRUE));
abline(v=obsg[1],lwd=2,col=4)



###################################################################
## Analysis of simple randomised trials using Hedges Effect Size ##
## with non-parametric bootstrap CI                              ##
###################################################################

output3 <- srtFREQ(Posttest~ Intervention+Prettest,
		intervention="Intervention",nBoot=1000,data=catcht)
ES3 <- output3$ES


####################################################################
## Analysis of simple randomised trials using Hedges Effect Size. ##
## Schools as fixed effects                                       ##
####################################################################

output4 <- srtFREQ(Posttest~ Intervention+Prettest+as.factor(School),
		intervention="Intervention",data=catcht )
ES4 <- output4$ES

###################################################################
## Analysis of simple randomised trials using Hedges Effect Size ##
## with Permutation p-value. Schools as fixed effects            ##
###################################################################

output5 <- srtFREQ(Posttest~ Intervention+Prettest,
		intervention="Intervention",nPerm=1000,data=catcht )

ES5 <- output5$ES
ES5

####################################################################
## Analysis of simple randomised trials using Hedges Effect Size  ##
## with non-parametric bootstrap CI. Schools as fixed effects     ##
####################################################################

output6 <- srtFREQ(Posttest~ Intervention+Prettest,
		intervention="Intervention",nBoot=1000,data=catcht)
ES6 <- output6$ES
ES6