10. The median test for independent samples Aa Aa A teacher wants to see which a

Question

10. The median test for independent samples Aa Aa A teacher wants to see which activity best improves second grade students' arithmetic scores. She randomly selects 30 second grade students and randomly splits them into three groups, each of which will perform a different activity for 15 minutes. One group plays math games that involve arithmetic. Another group uses flash cards to memorize math facts. The last group reads a book about dinosaurs. At the end of the 15-minute activity, she has each student take an arithmetic test with 40 addition and subtraction problems. The table below contains the scores for the 30 students. Flash Cards Silent Reading Math Games 20 34 34 36 38 18 26 36 34 24 24 40 20 30 26 22 34 24 36 20 32 28 34 27 38 38 32 The teacher wants to find out if there is a significant relationship between which 15-minute activity the children do and their scores on the subsequent arithmetic test. She uses a median test to evaluate whether these three groups share a common median score The overall median for the 30 students is 29. Using the information in the table above, fill out the table below with the observed frequencies of the number of students above and below the median in each of the three groups. Flash Cards Silent Reading Math Games Above Median Below Median The expected re Flash Cards Silent Reading Math Games 2.5 0.4 0.8 0.48 Above Median Below Median , with df-2 and -.05, the critical value for the chi-square is 5.99. Given The chi-square test statistic is this critical value, the teacher decides to not reject the null hypothesis and conclude that: O These data do not provide sufficient evidence that there are significant differences among the scores of the three groups O The median scores of these three groups are different. O There is a difference in the distribution of the scores in these three groups O The median scores of these three groups are the same.

Explanation / Answer

### R Program for ref

Flash = c(40,20,26,22,24,36,30,32,34,22)

Silent = c(20,34,38,26,34,34,36,18,36,24)

Math = c(22,20,32,28,34,24,16,27,38,38)

m1 = median(Flash)

m2 = median(Silent)

m3 = median(Math)

length(which(Flash>m1))

length(which(Silent>m2))

length(which(Math>m3))

data = data.frame(Flash,Silent,Math)

# Empty dataframe

expDat <- data.frame()

# Loop that makes i = 1, then i = 2, then i = 3

for (i in 1:10){

   for(j in 1:3){

  

expDat[i,j] <- (sum(data[i,]) * sum(data[,j])) / sum(data)

}

}

expDat

m1 = median(expDat[,1])

m1

m2 = median(expDat[,2])

m2

m3 = median(expDat[,3])

m3

length(which(expDat[,1]>m1))

length(which(expDat[,2]>m2))

length(which(expDat[,3]>m3))

> kruskal.test(list(Flash, Silent, Math))

   Kruskal-Wallis rank sum test

data: list(Flash, Silent, Math)
Kruskal-Wallis chi-squared = 0.42396, df = 2, p-value = 0.809

Conclusion -

### These data do not provide the sufficient evidence that there are significatn differences among the scores of the three goups

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