Using the below data, can someone help me answer this two part question: Part On

Question

Using the below data, can someone help me answer this two part question:

Part One: in examining the treatment groups + depression scores, what is the value of Levene's Test and what does that value indicate?

Part Two: using the same data, provide the results of the Post-Hoc test and explain what that tells us in plain speech.

The data is treatment group in column 1, depression score in column 2, and age in column 3. You are asked to find Levene's Value, the ANOVA, and the Post-Hoc results to analyze the depression score and treatment groups.

1 19.25 1 1 22.25 2 1 20 3 1 24.25 1 1 24.75 2 1 26.25 3 1 19.25 1 1 22.25 2 1 20 3 1 24.25 1 1 24.75 2 1 26.25 3 2 13.25 1 2 15.25 2 2 20.25 3 2 19 1 2 17 2 2 13.25 3 2 15.25 1 2 20.25 2 2 19 3 2 17 1 3 29.25 2 3 26.75 3 3 23.25 1 3 27.75 2 3 25.25 3 3 26.75 1 3 23.75 2 3 29.25 3 3 26.75 1 3 23.25 2 3 27.75 3 3 25.25 1 3 26.75 2 3 23.75 3

Explanation / Answer

Here I write R-code for given problem. In which i creat vectors as y,v1,v2 insted
of treatment group,depression score and age.
The R-code is as:

y=c(19.25,22.25,20.00,24.25,24.75,26.25,19.25,22.25,20.00,24.25,24.75,26.25
,13.25,15.25,20.25,19.00,17.00,13.25,15.25,20.25,19.00,17.00,29.25,26.7
,23.25,27.75,25.25,26.75,23.75,29.25,26.75,23.25,27.75,25.25,26.75,23.75)
v1=rep(c(1,2,3),c(12,10,14))
v2=c(1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3)
x1=as.factor(v1)
x2=as.factor(v2)
d=data.frame(y,x1,x2)
a=aov(y~x1+x2,d)
summary(a)
TukeyHSD(a)
install.packages("Rcmdr")
library(Rcmdr)
leveneTest(y~x1,d)
leveneTest(y~x2,d)

The output is as:

> summary(a)
Df Sum Sq Mean Sq F value Pr(>F)   
x1 2 490.8 245.39 41.39 1.76e-09 ***
x2 2 12.3 6.16 1.04 0.365   
Residuals 31 183.8 5.93
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> TukeyHSD(a)
Tukey multiple comparisons of means
95% family-wise confidence level

Fit: aov(formula = y ~ x1 + x2, data = d)

$x1
diff lwr upr p adj
2-1 -5.841667 -8.4075084 -3.275825 0.0000112
3-1 3.311905 0.9544619 5.669348 0.0044491
3-2 9.153571 6.6724344 11.634708 0.0000000

$x2
diff lwr upr p adj
2-1 1.216369 -1.230065 3.662803 0.4484777
3-1 1.253869 -1.192565 3.700303 0.4271595
3-2 0.037500 -2.408934 2.483934 0.9992156

> leveneTest(y~x1,d)
Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 2 0.8693 0.4286
33
> leveneTest(y~x2,d)
Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 2 0.423 0.6586
33

Here age group are significant.
The Levene value is 0.8693 and 0.423
for treatment group and age group respectively.

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