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Question 1 Researchers wanted to figure out what type of treatment was more effective in treating depression. A sample of 15 participants were randomly assigned to one of three groups: psychotherapy,...

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Question 1
Researchers wanted to figure out what type of treatment was more effective in treating
depression. A sample of 15 participants were randomly assigned to one of three groups:
psychotherapy, antidepressant medication, or no treatment. The treatment lasted 6 months. After
the 6-month treatment program, participants were asked to complete the Beck Depression
Inventory (Beck, Steer, Ball, & Ranieri, 1996) to determine if therapy type led to differences in
level of depression as measured by lower scores on Beck Depression Inventory. The scores
potentially range from 0-63. The researchers hypothesized a difference in levels of depression
across the three treatment groups. Write a paragraph describing and interpreting the results.
Participant #: 1
Age: 30
Gender: Mo. \e.
Therapy type:-p6,/C hoth:xCfP~
Beck Depression Inventory score out of63:;:;'S
- --- --- --- - -- - - - - ---
Participant #: 2
Age: L/5
Gender: ~C
tQ Ie:
Therapy type:?S'lc}-\O-thG(C(y~
Beck Depression Inventory score out of 63:~ I
- - - -- - -- - - - - - - --- -- -- - --
Participant #: 3
Age:;(3
Gender: S;c
u Ie
Therapytype:1'S"fCh6thcn~JP:J
Beck Depression Inventory score out of 63: 3d
- - - - - --- - --- --- - -- --- - --- - -- - --- -- ------------
Participant #: 4
Age: 1<6
Gender:tcrna Ie.
TherapytYPe:yS'{Chcth::rCfPBeckDepressionInventoryscoreoutof 63:30
- -- - - --- - --- -- -- - - -- --- --- --- -- -- --- --- -- -- -- - - -- - ---
Participant #: 5
Age: <0 ()
Gender: MQ k.
Therapytype:-pS'Jchothe(ap~
BeckDepressionInventoryscoreout of 63:,;zq
- - --- -- - --- -- - --- --- --- - - ---
Participant #: 6
Age: L-\l
Gender:.\ema \e.
Therapytype:o.f\bc\-e:W'(~Q0t '\Y'cChCQ-BOfl.
Beck Depression Inventory score out of63:,;(1
- --- - - - -- -- - -- --- -- - - - - ----
Participant #: 7
Age:3~
Gender:~C(Y'Q \-t:
Therapy type: On-bdeprC:~SQf\{ ~d;cai:100
Beck Depression Inventory score out of 63: 3d
- --- --- --- - -- - ---
Participant #: 8
Age: )Cj
Gender:
Therapy type: anbdC?x essClDt '((\edIcat\o n
Beck Depression Inventory score outof 63: 35
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -..;- - - - - - - - - - - - - - - - - - - - --
Participant #: 9
Age:SI
Gender: ma Ie
Therapytype:Qn6dcprC$Qnt m-ecJ,'C/JtJjn
Beck Depression Inventory score out of 63: 3~
- -- - - - -- - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - -- -- - - - - - - - - - - - - - - - - - - --
Participant #: 10
Age: ().1
Gender: YY\QIe
Therapy type: un-bcleprcSMtltma1i«()'bon
Beck Depression Inventory score out of 63:32
- - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - --
Participant #: 11
Age:Jlc
Gender: \?e ma Ie
Therapy type: no -treatmer}"t
Beck Depression Inventory score out of 63: CZ:>S
- - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - --
Participant #: 12
Age: 3q
Gender: ma \e
Therapytype:no -tre~-tvne n+
Beck Depression Inventory score out of63:Si
- - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - --
Participant #: 13
Age:~ ,
Gender: .t(
a Ie:
Therapytype: nO -treatment
Beck Depression Inventory score out of 63: Go
-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- -- - - - - - --
Participant #: 14
Age: 4'3
Gender: rY'Qle
Therapytype: no &ea&ncnt
Beck Depression Inventory score out of 63: S \
- - - - -- - - - - - - -- - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - --
Participant #: 15
Age: '"3 ~
Gender:~hlO \e
Therapy type: no {YCQ-tYnt:nt
Beck Depression Inventory score outof 63:51
- - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - --
Question 2
Researchers were interested in determining if different types of music and the color of a room
had an impact on relaxation. Forty participants were randomly assigned to one of four groups.
The four groups were a combination of blue or red walls and classical or heavy metal music. The
participants were randomly assigned to a room and music type for duration of 15 minutes. After
the 15 minutes, participants were asked to rate their level of relaxation using a 7-point scale (1 =
not at all relaxed to 7 = extremely relaxed). The following predictions were made. Participants in
the condition with blue walls will be more relaxed than participants in the condition with red
walls (main effect 1). Participants in the condition with classical music will be more relaxed than
participants in the condition with heavy metal music (main effect 2). When participants are in the
heavy metal music condition they will be more relaxed when in the blue room compared to the
ed room. In the classical music condition, the pattern will be the same but more pronounced
(interaction). Write a paragraph describing and interpreting the results.
Participant #: I
Age: ;);)
Gender: (Y\a Ie
Year in School:Sc:n W(
Room Color: Red ~
Genreof Music: Glassi~ HeavyMetal
Score out of7: 5
- - - -- - -- -- -- - - -- --- - -- - --- - - --- - - - - - -- -- - - - - -- -- -- - -- - ----
Participant #: 2
Age:d l
Gender: rY"OIl-e
Year in School: j IJ n io'{
Room Color: Red . ~
Genre of Music: ~ Heavy Metal
Score out of7: ~
- - - - - - - - - - - - - - -- --- - - -- - --- --- - - -- - - - -- -- - - - - - - - - - - - - - - - - - -- --
Participant #: 3
Age: \~
Gender: +-e rY\qI<:
Year in School:fresh ma n
Room Color: Red C!§V
Genreof Music: ~s~i~ HeavyMetal
Scoreout of7: (0
--------------------------------------------------------------
Participant #: 4
~ge: Iq
Gender:~e~1(
Year in School:.t-r <:5h (nQ 1
RoomColor: Red ~ui
Genre of Music: Glass~ Heavy Metal
Score out of 7: L\.
- - - - - -- - - - - -- - - - -- --- - - - - - -- -- - - - - -- - - - - - - - - - - - - - --
Participant #: 5
Age: d.6
Gender: tC.r11CtIe.
Year in School: ~6l*wY)O'(~
RoomColor: Red ~
Genre of Music: C~ssi;Y Heavy Metal
Score out of 7: S
--------------------------------------------------------------
Participant #: 6
Age: d:L
Gender: '(Y1C{(e
Year in School: J\Jn l' O(
Room Color: Red ~
GenreofMusic: ~s~ HeavyMetal
Score out of7: LI
-- -- -- - - -- -- - - - --- --- - - - - --- - - - -- - - - -- - - - -- - - - - - - -- --
Participant #: 7
Age:~
Gender: -+<:yY'Q\.e
Year in School:X'(1\O(
Room Color: Red ~
Genre of Music: (§as~ Heavy Metal
Score out of7: LP
--------------------------------------------------------------
Participant #: 8
Age:\q
Gender: -kxnu Ie:
Year in School: 5°1>'"TY\Ov-e
Room Color: Red @
Genre of Music:
~lassi~
Heavy Metal
Score out of 7: S
- - -- - - - --- -- -- -- - -- - - - -- - - - - --- - - --- - - - - - - - - - -- -- - -- - -- - - - - ---
Participant #: 9
Age: \q
Gender: rl'C\ I{'
Year in School: ~oy\1mO'(L
Room Color: Red ~
Genre of Music: €SSi~
Score out of 7: to
Heavy Metal
- -- - - - - - - - - - -- -- -- - --- - - - - - --- - - -- - -- - -- - - - - - - - - - - - - - - - ---
Participant #: 10
Age: 1<6
Gender: ~c:Y'Y'IQ\..e
Year in School: .+a:'Ch m<4 (\
Room Color: Red ~
Genre of Music: LClassi;;V
Score out of7: S
Heavy Metal
--------------------------------------------------------------
Participant #: 11
Age: dD
Gender: ~'('(\O,Ie
Year in School: Jun\O(
Room COlor:~ Blue
GenreofMusic: ~Si~
Score out of7: y
Heavy Metal
--------------------------------------------------------------
Participant #: 12
Age: \~
Gender: S;erY\QIe
Year in School:We6h met n
RoomColor:g Blue
Genre of Music:
Score out of7: L.\
Heavy Metal
--------------------------------------------------------------
Participant #: 13
Age: \ C1
Gender: mQ \{'
Year in School: s~\e
Room Color:@ Blue
Genre of Music: ~ssi~
Score out of 7: 11
Heavy Metal
--------------------------------------------------------------
Participant #: 14
Age: d-d-
Gender: ff'O..\e
Year in School: S-eniO{
Room Color: @ Blue
Genre of Music: ~ Heavy Metal
Score out of 7: 5
--------------------------------------------------------------
Participant #: 15
Age: d \
Gender: ~t:MQ If:
YearinSchool:Se" i 0 (
Room Color:~ Blue
Genre of Music: ~ssicaI) Heavy Metal
Score out of 7: Lt
- - - - - -- -- -- -- -- -- - - --- - - - - -- - - - -- - -- -- - - - - - - - - -- -- - - -- - --
Participant #: 16
Age: \~
Gender:+e Y'0C\l-e
Year in School:Suv'h'(Y1('-'e.
Room Color~g) Blue
Genre of Music: ~
Score out of 7: Y
Heavy Metal
--------------------------------------------------------------
Participant #: 17
Age: \ q
Gender: .t<:(YI~ l.e
Year in School:tTeShoon
Room Color:Gd> Blue
GenreofMusic: ~ HeavyMetal
Score out of7: S
--------------------------------------------------------------
Participant #: 18
Age: ,Ct
Gender: tc:ma Ie
Year in School: SD~hmo\('
Room Color: ~ Blue
Genre of Music: ~
Score out of 7: L\
Heavy Metal
- - - - - - - - - - - - -- - - - - - -
Answered Same Day Dec 04, 2021

Solution

Rajeswari answered on Dec 05 2021
120 Votes
48525 Assignment
Question No.1
One way anova:
Here no of elements selected = 15 participant
Groups = 3
Each group contained 5 persons in that
Since here are concerned about the various types of treatments and their effects we ignore the variable sex of the participant for time being.
We treat variables as the treatment programs, namely psychotherapy, antidepressant medication, or no treatment.
The results given individually is first consolidated as follows:
We set up hypotheses as
(two tailed anova test for three groups)
    Anova: Single Facto
    
    
    
    
    
    
    
    
    
    
    
    SUMMARY
    
    
    
    
    
    Groups
    Count
    Sum
    Average
    Variance
    
    
    Psycotherapy
    5
    143
    28.6
    7.3
    
    
    Antidepressent medication
    5
    168
    33.6
    18.3
    
    
    No treatment
    5
    280
    56
    11
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    ANOVA
    
    
    
    
    
    
    Source of Variation
    SS
    df
    MS
    F
    P-value
    F crit
    Between Groups
    2129.2
    2
    1064.6
    87.2623
    7.09E-08
    3.885294
    Within Groups
    146.4
    12
    12.2
    
    
    
    
    
    
    
    
    
    
    Total
    2275.6
    14
    Â 
    Â 
    Â 
    Â 
We are given sum of squares between groups is 2129.2 and degrees of freedom = no of groups -1 =2
Hence we get Mean squares between groups as 1064.6
Within groups we have sum of squares as 146.4 and degrees of freedom = total no of persons participated -1-df for no of groups = 12
Mean square = 12.2
F statistic = 87.2623 with p value very negligible
Since p <0.05 our significance level we reject H0. Atleast two means are unequal.
To find out pair wise comparison of the three groups
Post hoc test :
On scrunity of the summary we find that variances of the three groups are unequal.
Hence we do comparison of two means pairwise using unequal variances.
    t-Test: Two-Sample Assuming Unequal Variances
    
    
    
    Â 
    Psycotherapy
    Antidepressent medication
    Mean
    28.6
    33.6
    Variance
    7.3
    18.3
    Observations
    5
    5
    Hypothesized Mean Difference
    0
    
    df
    7
    
    t Stat
    -2.20971
    
    P(T<=t) one-tail
    0.031412
    
    t Critical one-tail
    1.894579
    
    P(T<=t) two-tail
    0.062824
    
    t Critical two-tail
    2.364624
    Â 
Comparing Psychotherapy and antidepressant medication we find that t statistic =...
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