ANOVA #1
A study of the interaction between physician-directed drug treatment and family therapy support
for older patients with chronic depression
Background and Purpose: An HMO wants to research the effectiveness of
its family health maintenance program. This program coordinates the
services of the family physician and the psychotherapy arms of the health
services program to support vibrant, healthy, and satisfying marital
relationships for their patients (even older ones).
Research Design: The basic research design is experimental, in that the researcher will randomly
assign alternate cases to either one of three experimental conditions. Condition I will be that a
client reporting stress, unhappiness, anxiety, or illness related to marital adjustment issues will be
referred to the psychotherapy department for counseling therapy with a certified, trained, and
experienced psychotherapist, but not also referred to a physician for prescription drug treatments
such as Prozac or valium, for example. Condition II will be that a client reporting similar
symptoms or stress factors will be referred to the psychotherapy department, but also referred to
a physician for prescription drug treatment as well such as Prozac or valium. Condition III will
be that a client reporting similar symptoms or stress factors will be referred to the psychotherapy
department, but also referred to a physician for prescription of a placebo, that is, a salt pill with
no known medicinal benefit, although the patient will be told that this is an experimental mood
control drug.
The plan is that there will be twenty seven subjects randomly assigned to one of three treatment
conditions (therapy strategies) for the six-month duration of the study. Even if the therapy
continues after six months, the (fictitious) Marital Satisfaction Inventory posttest will be
administered at the conclusion of six months of the treatment program, so that duration of the
treatment is a minimum of six months. Should the client terminate treatment before the six
months has elapsed, the Marital Adjustment Inventory posttest will be administered at the
conclusion of the last visit.
The data collection will officially commence when the client has completed a pretest on the
HMO’s own Marital Adjustment Inventory (fictitious), and has been assigned to one of the three
treatment groups. The research psychologist is interested in the increased scores on the Marital
Adjustment Inventory between intake (Pretest) and exit (Posttest) from the treatment plan.
Increased scores (differences between pretest and posttest) will be interpreted as levels of
satisfaction in personal and social adjustment benefits for the patient.
Measurements: The (fictitious) HMO developed Marital Adjustment Inventory is an
organizationally developed brief 20 question scale of self-reported satisfaction checklist of
typical marital, familial, and healthy living criteria which, according to the HMO developers,
correlate well with general happiness with life. The guidelines for interpreting the Marital
Adjustment Inventory scores are: The average (mean) value for satisfaction is 50.00 with a
standard deviation of 10.00. A high marital adjustment score would be 65 or higher, which
indicates satisfactory adjustment and a low adjustment score would be under 45. A low score
indicates maladjustment with close personal relationships. Low scoring individuals also tend to
exhibit periods of depression and general discontent.
Counseling
only
Pretest
34
40
60
47
30
44
66
39
Posttest
40
48
62
55
26
40
55
48
Difference
-6
-8
-2
-8
4
4
11
-9
counseling and drug
Pretest
Posttest
40
50
50
60
38
44
52
65
39
50
42
52
30
50
26
44
28
36
42
46
44
55
Difference
-10
-10
-6
-13
-11
-10
-20
-18
-8
-4
-11
Pretest
50
44
49
66
30
27
47
62
Counseling and Placebo
Posttest
Difference
56
-6
38
6
60
-11
70
-4
38
-8
33
-6
55
-8
55
7
summary
Group A
-6
-8
-2
-8
4
4
11
-9
Group B
-10
-10
-6
-13
-11
-10
-20
-18
-8
-4
-11
Research Questions:
1.
2.
3.
4.
Please provide a critique of this research design.
Please discuss any measurement issues.
What are your findings?
What are your conclusions? (Is there a difference in the results of these various treatments? Let the level of statistical
significance, alpha level be set at .05)
Group C
-6
6
-11
-4
-8
-6
-8
7
ANOVA #2
Craik and Lockhart (1972) proposed as a model of memory that the degree to which the subject
remembers verbal material is a function of the degree to which it was processed when it was
initially presented. Thus, for example, if you are trying to memorize a list of words, repeating a
word to yourself (a low level of processing) would not lead to good recall compared to thinking
about the word and trying to form associations between that word and some other word.
Fifty subjects aged between 55 and 65 years were randomly assigned to one of five groups. The
five groups included four incidental learning groups and one intentional learning group. Where
incidental learning is learning in the absence of expectation that the material will later need to be
recalled. The Counting group was asked to read through a list of words and simply count the
number of letters in each word. This involved the lowest level of processing, since subjects did
not need to deal with each word as anything more than a collection of letters.
The Rhyming group was asked to read each word and think of a word that rhymed with it. This
task involved considering the sound of each word, but not its meaning. The Adjective group had
to process the words to the extent of giving an adjective that could reasonably be used to modify
each word on the list. The imagery group was instructed to try to form vivid images of each
word. This was assumed to require the deepest level of processing of the four incidental
conditions. None of these four groups were told that they would later be asked for recall of the
items.
Finally, the Intentional group was told to read through the list and to memorize the words for
later recall.
After subjects had gone through the list of 27 items three times, they were given a sheet of paper
and asked to write down all the words they could remember. If learning involves nothing more
than being exposed to the material then the five groups should show equal recall. If the level of
processing of the material is important, then there should be noticeable differences among the
group means. The data (number of words recalled) are presented below.
Research question
The research question is obviously whether the level of processing required when material is
processed affects how much material is remembered.
Counting
Rhyming
Adjective
Imagery
Intentional
9
7
11
12
10
8
9
13
11
19
6
6
8
16
14
8
6
6
11
5
10
6
14
9
10
4
11
11
23
11
6
6
13
12
14
5
3
13
10
15
7
8
10
19
11
7
7
11
11
11
Figure 1.1 Data for one-way between groups ANOVA.
Hypotheses:
Ho : µ 1 = µ 2 = µ 3 = µ 4 = µ 5
H1: µ s not all equal
Assumptions
The between groups ANOVA requires the same assumptions as the between groups t-test. These
are:
1. All observations must be independent of each other
2. The dependent variable must be measured on an interval or ratio scale.
3. The dependent variable must be normally distributed in the population (for each group
being compared). (NORMALITY ASSUMPTION)
4. The distribution of the dependent variable for one of the groups being compared must
have the same variance as the distribution for the other group being compared.
(HOMOGENEITY OF VARIANCE ASSUMPTION)
1. Enter these data into SPSS and save the data as a file.
Note: The way in which the data for this problem is entered into SPSS is not the same as
it is displayed in the table provided (see figure below).
2. Run the 'Compare Means' procedure with the appropriate options.
3. Conduct a post hoc analysis (Tukey's) on these data.
4. Graph results using a bar graph.
Format of data entry
Notice two columns only. One for the Grouping variable (IV) and one for the Test variable (DV).
There are 50 lines of data, one line per case (i.e., thing being measured Ð in this situation,
people).
The answer! i.e., The Summary Table. Note that the DFs are correct. The Between Groups DF is
k-1 (i.e., the number of groups minus one) and the Total DF is 49 (i.e., one less than the total
number of observations). The Summary Table contains the main information we need to answer
our research question. Here we can deduce that a significant result has been found
F(4,45) = 9.09, p < .001. This result is (highly) significant.
Note the significance is given as ".000". Normally I recommend quoting the probability exactly,
but in the case of all zeros, it doesn't make sense to say p = .000. A probability of zero means
that the result is impossible! What is really meant of course is that the probability rounded to
three decimal places is zero. In reality, the probability is really something like .000257 (say). The
most accurate way to report this is by referring to p < .001. That is, use the same number of
decimal places, change the last digit to 1, and use the < sign.
Because we have a significant F-value, we now know that all the means are not equal (i.e., reject
Ho in favour of H1). However, we do not yet know exactly which means are significantly
different to which other means. For this we need Tukey's.
Multiple Comparisons
Here are the results of all pair-wise comparisons using Tukey's. I find the "Matrix of Ordered
Means" described earlier as an easier way of working out which means are significantly different
to which other ones. But all the information is here (plus extra that you don't really need). From
the table we can see that Group 1 differed from Group 2 by .1 (notice that .1 = 1.000E-01) and
that this difference was not significant.
However, Group 1 was significantly different to Group 3 (only just) and Groups 4 and 5. Group
2 is significantly different to Groups 3, 4, and 5. Group 3 is significantly different to Group 1 and
2 only. Group 4 is significantly different to 1 and 2 only. Group 5 is significantly different to 1
and 2 only.
Practice Problems: ANOVA
A research study was conducted to examine the clinical efficacy of
a new antidepressant. Depressed patients were randomly
assigned to one of three groups: a placebo group, a group that
received a low dose of the drug, and a group that received a
moderate dose of the drug. After four weeks of treatment, the
patients completed the Beck Depression Inventory. The higher
the score, the more depressed the patient. The data are
presented below. Compute the appropriate test.
Placebo Low Dose Moderate Dose
38
22
14
1.
2.
3.
4.
5.
6.
7.
8.
47
19
26
39
8
11
25
23
18
42
31
5
What is your computed answer?
What would be the null hypothesis in this study?
What would be the alternate hypothesis?
What probability level did you choose and why?
What is your Fcrit?
Is there a significant difference between the groups?
If there is a significant difference, where specifically are the differences?
Interpret your answer.
ANOVA Vignette
Patients with advanced cancers of the stomach, bronchus, colon, ovary or breast were treated
with ascorbate. The purpose of the study was to determine if patient survival differed with
respect to the organ affected by the cancer.
Survival
124
42
25
45
412
51
1112
46
103
876
146
340
396
81
461
20
450
246
166
63
64
155
859
151
166
37
223
138
72
245
248
377
189
1843
180
537
519
455
406
365
942
776
372
163
101
Organ
Stomach
Stomach
Stomach
Stomach
Stomach
Stomach
Stomach
Stomach
Stomach
Stomach
Stomach
Stomach
Stomach
Bronchus
Bronchus
Bronchus
Bronchus
Bronchus
Bronchus
Bronchus
Bronchus
Bronchus
Bronchus
Bronchus
Bronchus
Bronchus
Bronchus
Bronchus
Bronchus
Bronchus
Colon
Colon
Colon
Colon
Colon
Colon
Colon
Colon
Colon
Colon
Colon
Colon
Colon
Colon
Colon
20
283
1234
89
201
356
2970
456
1235
24
1581
1166
40
727
3808
791
1804
3460
719
Colon
Colon
Ovary
Ovary
Ovary
Ovary
Ovary
Ovary
Breast
Breast
Breast
Breast
Breast
Breast
Breast
Breast
Breast
Breast
Breast