‘What to do when?’ examples
Example 1 - The moon illusion
Why does the moon appear to be so much larger when it is near the horizon
than when it is directly overhead? This question has produced a wide
variety of theories from psychologists. An important early hypothesis was
put forth by Holway and Boring (1940) who suggested that the illusion was
due to the fact that when the moon was on the horizon, the observer looked
straight at it with eyes level, whereas when it was at its zenith, the observer
had to elevate his or her eyes as well as his or her head to see it. To test
this hypothesis, Kaufman and Rock (1962) devised an apparatus that
allowed them to present two artificial moons, one at the horizon and one at
the zenith…. Subjects were asked to adjust the variable horizon moon to
match the size of the zenith moon or vice versa. For each subject the ratio
of the perceived size of the horizon moon to the perceived size of the zenith
moon was recorded…. A ratio of 1.00 would represent no illusion. A ratio of
1.5 would mean the moon appears 1.5 times as large on the horizon as at its
zenith.
moon illusion (contd.)
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
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Question: Does the moon appear bigger at
its zenith, i.e., does the ratio differ from 1.0?
What kind of test would you use?
Options:




z-score test (C. 8)
single sample t-test (C. 9)
independent samples t-test (C. 10)
related samples t-test (C. 11)
Which analysis?
One sample t-test
Steps
A ratio of 1.0 = no illusion
1. State hypotheses:
H0: 1 = 1
H1: 1 <> 1
 =.05
2. Determine df
df = n - 1 = 10 - 1 = 9
Steps (contd.)





3. Obtain data
3a. Calc. SS
SS =1.045
s = SS/n-1
=.341
M= 1.46
Subject
ratio
1
1.73
2
1.06
3
2.03
4
1.4
5
0.95
6
1.13
7
1.41
8
1.73
9
1.63
10
1.56
sumX
ratio^2
sum X^2
Calculations (contd.)
M   1.463  1.00
t

 4.29
sM
1.08
sM 
t.05(9) = 2.262
Confidence intervals
2
s
.116

 .108
n
10
  M  tsM  1.46  2.262 * .108
 .244  1.462
upper  1.707
lower  1.219
Interpret your results


the moon does appear larger at its
horizontal position compared to its zenith
the probability is .95 that an interval such as
1.219 - 1.707 includes the true mean ratio
for the moon illusion. Note. the value of 1.00
is not included within this interval, which
represents no illusion.
SPSS output Analyze/Compare Means/One
Sample T
One-Sample Statistics
N
LEVEL
10
Mean
1.4630
Std. Deviation
.3407
Std. Error
Mean
.1077
One-Sample Test
Tes t Value = 1.0
LEVEL
t
4.298
df
9
Sig. (2-tailed)
.002
Mean
Difference
.4630
95% Confidence
Interval of the
Difference
Lower
Upper
.2193
.7067
Example 2 - The moon illusion
A different question
Why does the moon appear to be so much larger when it is near the horizon
than when it is directly overhead? This question has produced a wide
variety of theories from psychologists. An important early hypothesis was
put forth by Holway and Boring (1940) who suggested that the illusion was
due to the fact that when the moon was on the horizon, the observer looked
straight at it with eyes level, whereas when it was at its zenith, the observer
had to elevate his or her eyes as well as his or her head to see it. To test
this hypothesis, Kaufman and Rock (1962) devised an apparatus that
allowed them to present two artificial moons, one at the horizon and one at
the zenith, and to control whether the subjects elevated their eyes or kept
them level to see the zenith moon. The horizon, or comparison, moon was
always viewed with eyes level. Subjects were asked to adjust the variable
horizon moon to match the size of the zenith moon or vice versa. For each
subject the ratio of the perceived size of the horizon moon to the perceived
size of the zenith moon was recorded with eyes elevated and with eyes
level. A ratio of 1.00 would represent no illusion. If Holway and Boring were
correct, there should be a greater illusion in the eyes-elevated condition
than in the eyes-level condition. Is there a difference in the two conditions?
Which analysis?
Steps
1. State hypotheses:
H0: 1 -  2 = 0
H1: 1 -  2 <> 0
 =.05
2. Determine df
df = df1 + df2
=(n1 - 1) + (n2-1) = 9+9 = 18
Steps (contd.)






3. Obtain data
3a. Calc. SSD
=.169
sD2 = SSD/n-1
= .169/9=
= .0189
MD=.019
Subject Elevated
Level
1
1.65
1.73
2
1
1.06
3
2.03
2.03
4
1.25
1.4
5
1.05
0.95
6
1.02
1.13
7
1.67
1.41
8
1.86
1.73
9
1.56
1.63
10
1.73
1.56
Calculations (contd.)
sM D 
s2
.0189

 .0434
n
10
M D   D .019  0
t

 .438
sM D
.0434
Consult t-table =.05 2-tail
SPSS output
Paired Samples Statistics
Pair
1
ELEVATED
LEVEL
Mean
1.48
1.46
N
10
10
Std. Deviation
.37
.34
Std. Error
Mean
.12
.11
Paired Samples Correlations
N
Pair 1
ELEVATED & LEVEL
10
Correlation
.931
s
sM 
n
Sig.
.000
Paired Samples Test
Paired Differences
Pair 1
ELEVATED - LEVEL
Mean
1.90E-02
Std. Deviation
.14
Std. Error
Mean
4.34E-02
95% Confidence
Interval of the
Difference
Lower
Upper
-7.91E-02
.12
t
df
.438
9
Sig. (2-tailed)
.672
Example 3 - one group receives
Paxol and the other a placebo

See text p.338, #20
Tx1
Tx2
3
12
5
10
7
8
1
14