Question

Diagnosis Category

affective disorders	cognitive disorder	drug-related conditions
7	12	8
6	8	10
5	9	12
6	11	10

Conduct Tukey's HSD post hoc test to determine where there is a difference in the three groups.

5% level of significance

Answer 1

Conduct one way ANOVA and then post Hoc test Tukey kramer

in R studio:

Rcode:

df1 =read.table(header = TRUE, text ="
category pats
1 7
1 6
1 5
1 6
2 12
2 8
2 9
2 11
3 8
3 10
3 12
3 10
"
)
df1
df1$category <- ordered(df1$category ,
levels = c("1", "2", "3"))

summary(df1)
res.aov <- aov(pats ~ category , data = df1)
summary(res.aov)
TukeyHSD(res.aov)

Output:

res.aov <- aov(pats ~ category , data = df1)
> summary(res.aov)
Df Sum Sq Mean Sq F value Pr(>F)   
category 2 42.67 21.333 9.6 0.00586 **
Residuals 9 20.00 2.222   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> TukeyHSD(res.aov)
Tukey multiple comparisons of means
95% family-wise confidence level

Fit: aov(formula = pats ~ category, data = df1)

$category
diff lwr upr p adj
2-1 4 1.056968 6.943032 0.0106731
3-1 4 1.056968 6.943032 0.0106731
3-2 0 -2.943032 2.943032 1.0000000

Intrepretation:

ANOVA one way

Ho:

Ha:atleast one of the

F=9.6

p=0.00586

p<0.05

Reject Ho

Accept Ha

Conclusion:
There is suffcient statistical evdidence at 5% level of significance to conclude that atleast one of the group means are different.

Conduct Tukey kramer to know which group means are different

$category
diff lwr upr p adj
2-1 4 1.056968 6.943032 0.0106731
3-1 4 1.056968 6.943032 0.0106731
3-2 0 -2.943032 2.943032 1.0000000

P>0.05 means that group means are not different

p<0.05,means that group means are different

For

2-1 p=0.0106731,p<0.05

affective disorders

cognitive disorder

are different

3-1 ,p= 0.0106731,p<0.05

drug-related conditions and affective disorders group means are different