Question

In R:

Consider dataset “juul” from library “ISwR”. (juul is a built in data set)

Are the means of igf1 equal among tanner groups at 5% level?

Please use the six step process to test statistical hypotheses for this research problem.

Note: You need to convert tanner from numeric to factor type and ignore all the NAs.

Answer 1

Solution :

Here , we have to consider the dataset “juul” from library “ISwR” in R software.

To test whether the means of "igf1" are equal among the 5 tanner groups at 5% level.

Step 1) Hypothesis :

Thus , here we are to test the hypothesis ,

where , is the mean of the i^th igf1 group.

Here , we are going to use the one - way ANalysis Of VAriance (ANOVA).

The complete ANOVA analysis is done in the R Statistical Software.

Step 2) Assumption :

The assumption of HOMOSCEDASTICITY or EQUAL VARIANCES is considered among the 5 tanner groups.

Step 3) Let the value of the level of significance () be 5% = 0.05.

The appropiate test statistic for testing the above hypothesis is given as ,

k = level of the tanners ; n = total number of observations

Step 4) Rejection Region : We reject the null hypothesis H₀ at 5% iff ,

Step 5) Calculations and Output :

The ANOVA table in R is given below.

Clearly , we can see that , the value of the test statistic and the p-value is ,

The critical value is given as ,

Step 6) Conclusion :

Since ,   and , we Reject the null hypothesis H₀ at 5% level of significance and conclude on the basis of the given data that the means of igf1 are not equal among tanner groups at 5% level.

The R codes are given below !!

library(ISwR)
attach(juul)
head(juul)
tanner=juul$tanner
igf1=juul$igf1
igf1[which(is.na(tanner))]=NA
tanner[which(is.na(igf1))]=NA
data.frame(igf1,tanner)
igf1=na.omit(igf1);igf1
tanner=na.omit(tanner);tanner
data.frame(igf1,tanner)
tanner=factor(tanner);tanner
fit=lm(igf1~tanner)
anova(fit)
qf(0.95,4,787)