Explanation

Whilst we perceive a three-dimensional world, the sensory information available on the retina is only two-dimensional. The visual system partly achieves this by using depth cues available in the 2D retinal image to perceive size and distance. One example of a depth cue that conveys distance is linear perspective (e.g. roads, railway tracks), where converging lines make the wider part of the road look nearer to us than the narrower part. However, when applied to objects drawn on a flat 2D surface, size and depth information can "trick" our visual system into seeing three dimensions where it doesn't really exist, resulting in a visual illusion. The topic of the present study is the Ponzo illusion (or railway track illusion). Richard Gregory (Gregory, 1997) argues that this illusion is as the result of depth cues provided by the converging lines of the railway track. When the same sized line is further away it is perceived as smaller compared to the line in the foreground (see http://epsych.msstate.edu/descriptive/Vision/DepthValley/ponzo/index.html for an example). To test Gregory's prediction the study will investigate how strong this illusion is with depth cues both present and absent. The independent variable is the presence or absence of depth cues. The depth cues are the converging lines of the railway track. Two lines will be presented (line A is above line B). Subjects will be asked to adjust the length of line B until it looks equal in size to line A. The dependent variable is subjects mean estimation error between the two lines, which indicates the strength of the Ponzo illusion. This is measured in number of pixels. This is a between-subjects design. One group of subjects will adjust the length of the lines with the depth cues present, and the other with depth cues absent. It is hypothesised that the mean error will be higher in the depth cues present group and lower in the depth cues absent group. References Gregory, R.L. (1997) Eye and Brain: the psychology of seeing (6th Edition). Oxford: Oxford University Press. .

We will use the vocabulary of statistics, which can be confusing if you haven't seen it before, so here is an introduction to the study you will be working through and the words that are used to describe it.

The Data
Statistics are designed to help us understand things we observe in the world around us. To use statistics, we have to measure things in the real world and so produce data. Data can be expressed as words or numbers, and are plural - so you say "Here are my data."

So that we know which aspects of the data we are talking about, we use the following words:

• To generate data we take measurements or make observations of specific qualities of things;
• The things we are measuring are called the experimental units of the study. They might be referred to as 'people' or 'soil samples', whatever is being measured, but in this study, they are referred to as subjects;
• The qualities that we measure, or observe, are called variables. So if you measured a piece of string, the string would be the experimental unit and 'length' would be the variable;
• All variables take a range of values - the variable 'length' might take the values 3 or 10.5, for example. Generally, one measurement of a variable from a single experimental unit will produce a single value. If we say "Length = 5" then 'length' is the variable and '5' is the value.

Your study measured one variable: Estimation error , in two samples. Estimation error is measured in pixels.

The Study
Experiments often compare one set of measurements with another. The two sets of measurements could differ because they were each taken from different groups of experimental units, or because they were taken from the same experimental units under two different conditions. Each set of measurements is called a sample. Your study splits the subjects into two samples:

• The present sample
• The absent sample

Such studies always have two variables, each with its own role to play. They are:

• The independent variable discriminates between the two samples. Your independent variable is depth cues and it can take one of two values: present or absent.
• The dependent variable is whatever you are measuring in each sample. In the case of this study, the dependent variable is estimation error , so you expect estimation error to differ depending on depth cues (whether it is present or absent).

Such studies have an idea they wish to test. The idea is called the hypothesis. Each study actually has two versions of the hypothesis - one that says there is a difference between the two samples (the experimental hypothesis) and one that says that there is no difference (this is called the null hypothesis).

• The experimental hypothesis in this study is mean estimation error will be higher in the depth cues present group and lower in the depth cues absent group .
• The null hypothesis in this study is no difference in mean estimation error between depth cues present group and depth cues absent group..

Exploration

The table below shows estimation error for the both the present and the absent samples.

Estimation error (pixels)
Present	Absent
6	2
6	3
5	2
7	4
8	3
4	2
3	1
7	0
6	3
6	4
5	1
6	2
7	5
8	3
9	3
10	2
3	4
5	1
4	1
7	3

Application

We are measuring estimation error in your data. Which of the words in the box to the right best describes the role of estimation error ?	Choose..A valueA variableA sample
Depth cues can be either present or absent. What do these two words refer to?	Choose..VariablesSamplesHypotheses
Which of these is your null hypothesis?	Choose..No difference in mean estimation error between depth cues present group and depth cues absent group.Mean estimation error will be higher in the depth cues present group and lower in the depth cues absent group
Which variable is the independent variable?	Choose..Depth cuesEstimation error
Which variable is the dependent variable?	Choose..Depth cuesEstimation error
Imagine that you measured estimation error from a subject in the present sample and got a value of 6 pixels.
Which of these words best describes estimation error ?	Choose..A variableA valueA sample
Which of these words best describes present?	Choose..A variableA value and a sample
Which of these words best describes 6?	Choose..A variableA valueA sample