Question

A researcher wanted to test the effectiveness of three different doses of medication on depression levels, so she recruited 60 people and split them evenly into the 3 groups. Below an ANOVA summary table from his hypothetical experiment. Use this table to answer questions below.

Source	SS	df	MS	F
Between	(A)	(C)	(F)	3.50
Within	570	(D)	(G)
Total	(B)	(E)

Using the information in the table (be sure to fill in, see other ANOVA table based essay question), test for significance (α=0.05). Please state the null hypothesis, research hypothesis, F obtained, F critical, df used, and conclusion of the study.

Answer 1

Solution:

Given:

Source	SS	df	MS	F
Between	(A)	(C)	(F)	3.5
Within	570	(D)	(G)
Total	(B)	(E)

k = number of groups ( treatments) = 3

N = total observations = 60

i) Find (C):

df_between = k - 1

df_between = 3 - 1

df_between = 2

ii) Find (E):

df_total = N - 1

df_total = 60 -1

df_total = 59

iii) Find (D) :

df_within = df_total - df_between

df_within = 59 - 2

df_within = 57

iv) Find (G):

MSW = SSW / df_within

MSW = 570 / 57

MSW = 10

v) Find (F):

MSB = .......?

We have F test statistic = 3.5

F = MSB / MSW

3.5 = MSB / 10

MSB = 3.5 * 10

MSB = 35

vi) Find (A):

SSB =........?

we have:

MSB = 35

MSB = SSB / df_between

35 = SSB / 2

SSB = 35 * 2

SSB = 70

vi) Find (B):

SST = SSB + SSW

SST = 70 + 570

SST = 640

Thus we get:

Source	SS	df	MS	F
Between	70	2	35	3.50
Within	570	57	10
Total	640	59

Null hypothesis:

Vs

research hypothesis:

H₁: Three different doses of medication have effect on depression levels,

That is:

H1: At least one mean is different.

F obtained = 3.50

F critical and df:

df_numerator = df_between = 2

df_denominator = df_error = 57

α = 0.05

Use F table:

F critical at 0.05 significance level = 3.16

conclusion of the study:

Since F obtained = 3.50 > F critical = 3.16,we reject null hypothesis H0.

Thus we conclude that:Three different doses of medication have effect on depression levels.