‘What to do when?’ examples

Example 1 - The moon illusionWhy 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.)

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-testSteps

A ratio of 1.0 = no illusion1. State hypotheses: H0: 1 = 1

H1: 1 <> 1 =.05

2. Determine dfdf = 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 ratio^2

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 sum X^2

Calculations (contd.)

294081

0014631 ..

..

MsMt

108101162

..

nssM

t.05(9) = 2.262

Confidence intervals

2191

70714621244

1082622461

.

...

.*..

lower

upper

MtsM

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

10 1.4630 .3407 .1077LEVELN Mean Std. Deviation

Std. ErrorMean

One-Sample Test

4.298 9 .002 .4630 .2193 .7067LEVELt df Sig. (2-tailed)

MeanDifference Lower Upper

95% ConfidenceInterval of the

Difference

Test Value = 1.0

Example 2 - The moon illusionA 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 dfdf = df1 + df2

=(n1 - 1) + (n2-1) = 9+9 = 18

Steps (contd.) 3. Obtain data 3a. Calc. SSD

=.169 sD

2 = 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.)

4380434

0019 ..

.

DM

DD

sMt

043410

01892

..

nss

DM

Consult t-table =.05 2-tail

Paired Samples Test

1.90E-02 .14 4.34E-02 -7.91E-02 .12 .438 9 .672ELEVATED - LEVELPair 1Mean Std. Deviation

Std. ErrorMean Lower Upper

95% ConfidenceInterval of the

Difference

Paired Differences

t df Sig. (2-tailed)

Paired Samples Statistics

1.48 10 .37 .121.46 10 .34 .11

ELEVATEDLEVEL

Pair1

Mean N Std. DeviationStd. Error

Mean

Paired Samples Correlations

10 .931 .000ELEVATED & LEVELPair 1N Correlation Sig.

nssM

SPSS output

Example 3 - one group receives Paxol and the other a placebo

See text p.338, #20Tx1 Tx2

3 12

5 10

7 8

1 14