This demonstration is designed to illustrate two of the theories of knowledge representation; Imagery Theory and Propositional Theory.   Imagery theorists have argued that our mental representation of objects in memory uses mental images. To support their theory they predicted there would be a Symbolic Distance Effect in our mental representations where the amount of time required to make judgements about objects would be faster or slower depending on whether the objects were similar or different in size. For example, it is easier, as reflected in faster reaction times, when mentally comparing two animals that are very different in size than for two that are of similar size (harder, slower reaction times). When a person sees two words like rabbit and camel, and is asked “which is the larger animal”; he or she calls up their mental images for rabbits and camels and compares them for size.  Thus, when there are large differences in the sizes of the memory images (e.g., which is larger, whales or mice?), much quicker decisions can be made.  Other researchers have argued that we store information as a series of propositions about the objects.  Propositions contain a series of facts about the object (such as camels have humps, live in the desert, smell bad, and so forth).  To answer the question “which is larger”, we compare the stored facts about the objects, instead of their images.  Propositional theory predicts no effect of animal sizes on reaction times (saying a whale is larger than a mouse would take the same time as saying a whale is larger than an elephant). Propositional theory would, however, predict a Congruity Effect; answering “which is larger” questions about small animals will be harder than for large animals because “largeness” isn’t one of the facts we have stored for those small animals. Thus “which is larger, a rabbit or a mouse” will take longer to answer than “which is larger, a whale or an elephant”, because “large” is not congruent with the information we have stored about small animals.

There are two hypotheses for this experiment. The first we will call the Symbolic Distance hypothesis and predict that participants will take longer to answer questions about which is larger/smaller for

animals that are closer together in size (and therefore will be faster for animals that are quite different is size).  The second hypothesis we will call the Congruity hypothesis and predict that it will take

longer to answer questions about “which is smaller” when both of the animals are large than it will

when both animals are small or when one of the animals is small and the other is large (mixed size

pairs). Similarly, this hypothesis also predicts that it will take longer to answer “which is larger” when both animals are small, or when the animal pairs are of mixed size (one small and one large).

To test our hypotheses,  each participant in this within-subject experiment (also called a repeated measures design) will complete 264 trials comparing the size of two animals.  Half the trials will ask the participant to judge which is larger, the other half will ask which is smaller.  Six small animals (fly, mouse, frog, ferret, cat, and dog, in ascending order of size) and six large animals (sheep, lion, horse, hippo, elephant, and whale) are used as stimulus words. On each trial the question is presented first (“Which is SMALLER?” or “ Which is LARGER?”). This is followed by two of the animal names, one above a fixation point (a plus sign) and the other below; like this:

HORSE

+

FROG

Participants will be instructed to press the left mouse button if the animal on top is the correct answer, and the right mouse button if the animal on the bottom is the correct answer. For example, in the example above, if the question had been “ Which is SMALLER?” the participant should respond by clicking the RIGHT mouse button, since a FROG is smaller than a HORSE.  After each trial the participant will be informed of their accuracy and response time.

Each animal will be paired with each other animal twice, for each question type. On one pairing the larger animal will be listed above the fixation point and on the other pairing it will be presented below the fixation point (to control for any effect of position).  Ten practice trials will be given to participants (to demonstrate the procedure) and will be repeated until they meet an 80% accuracy requirement before the experimental trials begin.  It is important to respond as accurately and quickly as possible to each pairing.  At the end of the experiment you will be presented with your individual results in two tables. In the first table you will see the Congruity data (mean reaction times for each type of animal pair by each type of judgement) and the second table will show you the Symbolic Distance data (the mean reaction time for animals that are 1 size different, 2 sizes different, 3 sizes different, etc all the way to 11 sizes different). The first table will look similar to this:

Average reaction times (msec):

Unfortunately, the software has an error that causes the first two column labels to be displayed in the wrong order. This means that the column that says Both Large should say Both Small and vice versa. (But the numbers are in the correct order).

You can just change the labels on the first two columns, or even better -- it is easiest to write down your individual data all in one line (as shown below), so that your data from your lab group can be combined with each participant on a separate row.

The second table will look like this and your lab group will be combined in this format:

Enter your data below

Use this one ↓

How to analyse your data

Once your group data has been entered into a spreadsheet, you can download it and use it for graphing and analysis.

There will be two parts and we will do them separately for each hypothesis in the following example. We will start with the Symbolic Distance Hypothesis. Your tutor will have calculated means for your lab group and put them in a column format. It should look something like this:

Our hypothesis was that reaction times (RTs) will be faster for animals that are much different in size (larger distances apart in size). To test this we will use a correlation. Whin one variable (RT) gets smaller as the other (distance) gets larger this is called a  negative  correlation.  First  let’s  make  a  graph  of  this relationship. 

In SPSS choose

Graphs,

then Legacy Dialogs,

then Scatter/Dot.

Like this:

Now, choose Simple Scatter,

And click on Define. Like this:

Next we tell SPSS which

variables we want on each axis

of the graph. Put Distance on

the X axis and RT on the Y

axis, like this:

After you click OK,

you will see a graph

like this:

As you can see, it looks as though the Symbolic Distance hypothesis is going to be supported, larger distances have smaller RTs. But we need to have SPSS calculate the correlation (called a Pearson’s correlation coefficient, sometimes abbreviated as “r”) to see whether it is statistically significant.

To do this, choose Analyze, then

Correlate, then Bivariate, like

this

Next, tell SPSS which variables

we want to correlate (since we

only have two variables, this is

pretty easy).

Click OK and SPSS will produce the correlation,

which will look something like this.

This table tells us that there is indeed a negative

correlation (-.958) for the two variables Distance and

Mean RT. We can also see that Sig (the likelihood

that these results are due to chance) is so low that

SPSS cannot calculate it. In fact we would be wrong

less than 1 time in 1000 in claiming that bigger

distances lead to faster RTs.  In other words, our

result supports the Symbolic Distance hypothesis,

with the finding of a significant negative correlation

between the difference in the size of the animals and

Mean RT. You can the statistical result in your

journal you can report the correlation like this: r = -

.958, n = 11, p < .001.

Now we are going to test the

Congruity hypothesis, that

answering congruent questions

such as “which is smaller?” for

small animals will be faster that

answering incongruent

questions such as “which is

smaller?” for large animals.

Your data set will look

something like this:

We need to start by graphing

the data. Select choose Graphs,

then Legacy Dialogs, then Bar.

Like this:

Now choose the type of bar

chart by clicking on Simple

and Summaries of separate

variables as shown here:

After clicking Define you will

need to tell SPSS which variables

we want to include, by moving the

names of the variables into the list

labelled “Bars Represent” like this:

Click on OK and you will see a graph like this:

The graph shows that two types of

questions appear to take longer to

answer  than  the  rest;  the  two

incongruent   questions   –   asking

which is smaller for large animals

and  asking  which  is  larger  for small animals.

We now need to see if these results are

statistically  significant.  We  will  do

this by comparing the Mean RTs for

incongruent  questions  to  the  Mean

RTs for congruent questions. Like our

last demonstration, we will use two t-

tests to do this.

Choose Analyze, then Compare

Means, and then Paired-Samples T-

Test (the samples are paired because

each participant answered each type

of question).