Fusion Times for Random Dot Stereograms
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Story Name: Fusion Times for Random Dot Stereograms
Story Topics: Psychology
Datafile Name: Fusion Times
Methods: Boxplot , Two sample t-test , Pooled t-test , Transformation
Abstract: This dataset contains results from an experiment in visual perception using random dot sterograms, such as that shown below. Both images appear to be composed entirely of random dots. However, they are constructed so that a 3D image (of a diamond) will be seen, if the images are viewed with a stereo viewer, causing the separate images to fuse. Another way to fuse the images is to fixate on a point between them and defocus they eyes, but this technique takes some effort and practice.

An experiment was performed to determine whether knowledge of the form of the embedded image affected the time required for subjects to fuse the images. One group of subjects (group NV) received either no information or just verbal information about the shape of the embedded object. A second group (group VV) received both verbal information and visual information (e.g., a drawing of the object).

The investigators performed the usual two-sample pooled-variance t-test, giving t(76) = 1.9395, p-value = 0.0562, and concluded that, at the 0.05 significance level, no difference between the groups was demonstrated. However, analysis of these data using the unequal-variance t-test reveals a marginally significant result (p-value=0.0453). Note that the test of equality of variances gives a highly significant result.

                                TTEST PROCEDURE

Variable: TIME         Fusion Time                             

GROUP       N         Mean      Std Dev    Std Error
NV         43   8.56046465   8.08541161   1.23301371
VV         35   5.55142886   4.80173890   0.81164201

Variances        T       DF    Prob>|T|
Unequal     2.0384     70.0      0.0453
Equal       1.9395     76.0      0.0562

For H0: Variances are equal, F' = 2.84    DF = (42,34)    Prob>F' = 0.0023

Boxplots of the raw data show that the time values are positively skewed, longer fusion time in the NV group is accompanied by greater variability, and there is one very large potential outlier in the NV group.

These defects are all cured by transforming the data to log(time).

Image: Boxplots of the raw and log fusion time data

A t-test on the log data now shows equal variances, and a clearly significant difference in means, t(76) = 2.3190, p-value=0.0231.
Story Author: Michael Friendly