Question

The data below represent scores from three different therapies used to treat depressive symptoms. Scores represent depressive symptoms on a scale of 1-10, with higher scores indicating greater depressive symptoms.

Treatment 1	Treatment 2	Treatment 3
0	1	4
0	4	3	G = 24
0	1	6	ΣX2 = 92
2	0	3	_______
T1 = 2	T2 = 6	T3 = 16
SS1 = 3	SS2 = 9	SS3 = 6

a.   SS_T is what?
b.   SS_W is what?
c.   SS_B is what?
d    df_T is what?
e.   df_W is what?
f.   df_B is what?
g.   MS_B is what?
h.   MS_W is what?
i.   F is what?
j.   η² is what?
k.   Statistically significant?
l.   Tukey HSD critical value is what?
m. APA Conclusion?

Answer 1

Answer :

By using Excel :

Path : data < data analysis < anova for single factor

SUMMARY
Groups	Count	Sum	Average	Variance
treatment 1	4	2	0.5	1
Treatment 2	4	6	1.5	3
Treatment 3	4	16	4	2
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	26	2	13	6.5	0.017914	4.256495
Within Groups	18	9	2
Total	44	11

a) SST = 26 = sum of square of treatment = also called between sum of square

b) SSW = Within sum of square = 18

c) SSB = between sum of square =26

d) Degrees of freedom of Treatment = dfT =2

e) Within Degrees of freedom = dfW=9

f) between Degrees of freedom= dfB=2

g) Between mean sum of square = MSB=13

h) within mean sum of square = MSW=2

i) F value= 6.5

j) η2 = F script = 4.2564

k) Here p-value = 0.017 is greater than 0.05 level of significance.

then we accept Ho at 5 % los.

Hence , There  is statistically significant .

l) we have to find Tukey HSD critical value :

From above analysis,

The value of the Tukey test is given by taking the absolute value of the difference between pairs of means and dividing it by the standard error of the mean (SE) as determined by a one-way ANOVA test.

		difference	n (group 1)	n (group 2)	SE	q
t1	t2	1	4	4	0.7071	1.414227
t2	t3	2.5	4	4	0.7071	3.535568
t3	t1	3.5	4	4	0.7071	4.949795

Hence , this are Tukey HSD critical values.

m) APA Conclusion:

ANOVA and post hoc tests ANOVAs are reported like the t test, but there are two degrees-of-freedom numbers to report. First report the between-groups degrees of freedom, then report the within-groups degrees.