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How IV's Interact to produce effects on DV's

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This is the text of the in-class lecture which accompanied the Authorware visual graphics on this topic. You may print this text out and use it as a textbook. Or you may read it online. In either case it is coordinated with the online Authorware teaching program.

Studying the effect of one IV on a DV. So far we have have limited ourselves to a simple question in experimental research: Does an IV cause changes in a DV? Does Psychotherapy improve mental health? Does a new keyboard increase typing speed? Does imagining perfect runs down a ski slope decrease the elapsed time of elite skiers?

Studying the effect of two IV's on a DV. Frequently we have more than one IV whose effects on a DV interest us. Often we want to study the effect of two IV's on one DV in the same experiment. We will now consider that case. But to understand that idea fully, we must learn about INTERACTION EFFECTS.

Variables and Levels

Memory Example. To talk about the idea of an interaction we need a concrete example that includes two IV's and one DV. Let's say you want to study memory. You are wondering how memory is affected by two different independent variables. One IV is type of memory strategy people use to memorize materials. You can buy memory books that teach you different strategies for remembering things. A very common memory strategy, much researched in the psychological literature, is the use of mental imagery.

Dependent Variable (DV). Suppose people have a list of nouns (more or less like a long shopping list) that they are supposed to learn during a study period so they can remember it later. The dependent variable will be how many nouns they remember after studying this list. Usually the list is rather long (but in the examples below we will use short lists to keep the discussion simple). Top

IV1: MEMORY STRATEGY

Level 1: Mental Imagery Instructions. One group of volunteers could be given a Mental Imagery strategy to use while studying the list of nouns. A common imagery technique is to make an internal picture in which all the things on the list are integrated into an interacting mental image. If the list contains the nouns "soup, boat, tennis racket, bear, and notebook," people can be trained to put all these nouns into a single image in which they interact. And example of such an image might be a mental picture of an open notebook on which is drawn a boat floating in a lake with a bear paddling it with a tennis racket. It doesn't matter that the image is unrealistic or absurd. So long as all the items on the list are integrated into the image in a way that they interact, memory will be improved.

Our first group of research participants then will be given instructions to integrate the nouns on a list into interacting images. This is what we call the first level of our IV.

Level 2: Interference Instructions. A second group of people might be asked to count backwards by "7's" from 10,019 while they are studying the list of nouns. So the person is engaging in the mental strategy of calculating 10,019, 10,011, 10,004, 9,997, and so on. If a person is doing that strategy, it would interfere with memory for the list nouns they are studying at the same time. This, of course, would be a very poor memory strategy.

Level 3: Control. A third group of people might be given no special strategy instructions. They simply would be told to study the list during the study period so that they could remember the list later.

So let's say that the first independent variable is the instructions given to research participants on how to study a list of nouns. IV1 has three levels: Memory instructions, Interference Instructions, and Control (no instructions).

IV2: STUDY TIME

Let's say that the second independent variable, IV2, is the amount of time the participants are given to study each noun on a long list. Let's say that IV2 has two levels: 5 seconds to study each item and 1/10th of a second to study each item. It is well known that people can remember a long list of nouns better if they have more time to study the list.

Let's go over the two independent variables and the levels of each.

Levels of the first IV

The first IV is Type of Memory Strategy. It has three levels: Imagery, Interference, and Control (No Strategy).

Levels of the second IV

The second independent variable in our study is amount of study time per item on the list. The levels of Study Time are 1/10 of a second per item and 5 seconds per item.

Summary. Okay, so now we've established an example with two independent variables. You can imagine that both of these independent variables are going to have a potent effect on memory. We've also developed some vocabulary we are going to use--the levels of IV's.

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Verbal Definition of Interaction

Two independent variables, IV1 and IV2, are said to interact if the effect of IV1 upon the dependent variable depends on the level of IV2.

What this means is that there is no simple way to describe the effect of IV1 because the effect of IV1 changes at different levels of IV2.

Let's look at the memory example so that we can be more concrete about the meaning of the term "interaction."

Assume that there is an interaction between Memory Strategy and Study Time

The first IV is Memory Strategy; the second IV is amount of Study Time. The dependent variable is number of items recalled from the study list.

Pattern of Results for an Interaction

Table of Cell Means. The current figure shows that we can create a table that has the three levels of IV1, Memory Strategy, across the top and the two levels of IV2, Study Time down the side. Since the table has three columns and two rows, it has six cells.

The table in the current figure shows the mean of each of the six groups in the experiment in one cell of the table. For example, the group that used an Imagery Strategy and had 5 seconds of Study Time per item recalled 45 items from the list. The group that used an Interference Strategy and had 5 seconds to study each item recalled an average of 10 items from the list. And so on for each of the possible six conditions of the experiment.

Sometimes results are presented in table such as this one. But other times the cell means are graphed to make the pattern of results more apparent.

Graph of Cell Means. Look at the pattern of results shown on the graph below the table. On the horizontal axis we have laid out the three levels of Memory Strategy--imagery, interference, and control. The two levels of Study Time (the 5 second level and the 1/10 second level) are shown as separate lines on the graph. The 5 seconds per item level is the upper (red) line; the 1/10th second per item is the lower (blue) line.

Simple effect of Memory Strategy at 1/10th of a second. Look at the the lower line, the 1/10th of a second per item line. That line is nearly flat; there's basically no difference between memory strategies on that line. All three strategies lead to very low levels of recall. You could say that Memory Strategy has no effect when people have only 1/10 of a second to study each item. Sometimes scientists call this the simple effect of Memory Strategy at 1/10th second level of Study Time.

Simple effect of Memory Strategy at 5 seconds. In contrast, the 5 seconds per item line shows large effects of Memory Strategy. The Imagery Strategy group recalls many more nouns from the list than do the Interference or Control Groups. And the Control Group appears to recall more items than does the Interference Group. You could say that Memory Strategy has a large effect when people are given 5 seconds to study (using the strategy) each item. Sometimes scientists call this the simple effect of Memory Strategy at the 5 seconds level of Study Time.

Interaction of Strategy (IV1) and Study Time (IV2). Let's return to our idea of interaction. Notice that the effect of Memory Strategy on memory (number of items recalled) depends on which level of Study Time you're talking about. At 1/10th of a second study time per item, Memory Strategy has essentially no effect. But at 5 seconds per item, Memory Strategy does have an effect.

The thing that you should see on the graph is that the effect of Memory Strategy on recall is different for different levels of study time. Strategy has no effect at one level of study time, while it has a strong effect at another level of study time. This is what we mean by an interaction. There is an interaction between two IV's when the effect of one independent variable on the dependent variable depends on the level of the other. In this example, the effect of memory strategy depends on amount of study time. That's pretty much the whole idea of interaction.

As a contrast, let's reexamine the memory example assuming there is no interaction between Strategy and Study Time.

Assume NO interaction between Memory Strategy and Study Time

How would the the graph look if there was NO interaction between the two IV's? Look at the graph. The effect of Memory Strategy on number of items recalled is exactly the same for the 1/10th second and 5 second levels of Study Time.

Pattern of Results for NO Interaction

Table of Cell Means. In the current graphic some of the cell means are different than they were in first table, above.

Graph of Cell Means. Let's graph them and see how this difference looks.

Simple effect of Memory Strategy at 5 seconds. Look at the top (red) line (5 seconds Study Time). The number of items recalled is the highest for the Imagery group and drops down from 45 items recalled to its lowest (10 items recalled) for the Interference Group and then rises up to 25 items recalled for the Control Group. There is a 35 item drop from Imagery to Interference (45 minus 10). There is a 15 item rise (25 minus 10) from Interference to Control.

Simple effect of Memory Strategy at 1/10th of a second. Now look at the bottom (blue) line (1/10 second level of Study Time). You see the same pattern. The number of items recalled drops exactly the same amount (35 items) from the Imagery condition to the Interference condition on the 1/10 th second line as it did on the 5 second line. Also, the number of items recalled rises exactly the same amount (15 items) from the Interference condition to the Control condition on the 1/10th second line as it did on the 5 second line. The lines are parallel.

Let's describe the graph in words. The effect of Memory Strategy is exactly the same at different levels of Study Time. Granted, the 5 second study time line overall is higher (more items recalled) than is the 1/10 second study time line. But, the effect of memory strategy is exactly the same on the red line as it is on the blue line. You lose just as much (35 items recalled) by switching from an Imagery strategy to an Interference strategy on the 5 second line as you do on the 1/10 second line.

In short, on the current figure, the graph shows no interaction of Strategy and Study Time. For there to be an interaction the effects of one IV (Strategy) must be different at different levels of the second IV (Study Time). But on the current graph the effects of Strategy are the same at both levels of Study Time. So there is no interaction.

Two independent variables are said to interact if the effect of one independent variable upon the dependent variable depends on the level of the other independent variable.

More Examples

For the purpose of developing fluency with the concept of interaction, lets examine three more examples.

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Interaction of Pollutants

Let's say we're studying the effects of pollutants on health. Suppose that we have two IV's (pollutants) we are interested in--sulfur dioxide and carbon monoxide. Our DV is some measurement of health. Let's keep our DV measurement operations simple, perhaps some kind of rating scale from 0 to 100, where 100 is perfect health, and 0 is very bad health.

IV1 is sulfur dioxide. To keep the example simple we'll only have two levels of sulfur dioxide--level 1 will be the absence of sulfur dioxide; level 2 will be the presence sulfur dioxide. IV2 is carbon monoxide. Level 1 will be the absence of carbon monoxide and level 2 will be the presence carbon monoxide in the air. Logically, this yields 4 combinations--the absence of both pollutants, the presence of one but not the other, the presence of the other but not the one, and the presence of both.

What we have is a four-group study. One group breathes clear air, no carbon monoxide and no sulfur dioxide. Another group breathes no carbon monoxide, but does breathe some sulfur dioxide. A third group does breathe carbon monoxide but no sulfur dioxide, and finally a fourth group breathes both gases.

You'll notice that it's a nice study, we have a control group with clean air, we have a group that breathes only sulfur dioxide, we have a group that breathes only carbon monoxide, and we have a group that breathes both.

All data patterns below are hypothetical. Their purpose is to demonstrate either a lack of an interaction or the presence of interaction. They do not report actual research data.

No Interaction between pollutants

The current graph shows no interaction between sulfur dioxide and carbon monoxide on health. IV1--the absence or presence of sulfur dioxide--is along the horizontal axis. IV2--the absence or presence of carbon monoxide--is indicated by the two lines (green and blue). The top (green) line is for the absence of CO. The bottom (blue) line is for the presence of CO.

Since one of the skills we are practicing in this course is reading graphs, let's look at the four groups. 1) The group who gets neither carbon monoxide nor sulfur dioxide has the highest health rating. 2) The group breathing sulfur dioxide alone shows a drop in health. 3) There's also a drop in health for breathing carbon monoxide alone without sulfur dioxide. 4) The group who breathes both has the poorest health.

Is there an interaction? Two independent variables are said to interact if the effect of one independent variable upon the dependent variable depends on the level of the other independent variable. Notice that the effect of sulfur dioxide on health is exactly the same at both levels of carbon monoxide. The drop from No SO2 to SO is exactly the same on the green (no CO) line as it is on the blue (CO) line. The lines are parallel. The fact that the effect of SO2 does NOT depend on the level of CO would indicate no interaction.

Interaction of two pollutants. In contrast then, let's look at a data pattern that shows an interactions between the two pollutants. For the purpose of examining the interaction effect more clearly, the graphic this time includes a table of means.

Table of Group Means. Look at the table of mean health ratings for the four groups. Along the top of the table is the absence or presence of SO2. Down the rows of the table is the absence or presence of CO. The arrows on the graphic point to the four cell means, 96, 80, 68, and 08, which we will graph.

Let's graph the cell means to see the interaction effect. SO2 (absence or presence) is along the horizontal axis. The absence or presence of carbon monoxide is indicated by the green and blue lines.

On the graph we can see all four of our groups. 1) The the group who breathees clean air, neither carbon monoxide nor sulfur dioxide, has a 96 health rating. 2) On the same (green) line the group who's breatheing sulfur dioxide but not carbon monoxide has a mean health rating of 80. 3) If we drop down to the lower (blue) line, the group that breathes no sulfur dioxide but is breathing carbon monoxide has a mean health rating of 68. 4) Finally, the group who breathes both gases has a mean health rating of 8. It appears that the combination of gases is much more harmful than you would think from looking at either gas alone.

Is there an interaction? Yes, the effect of SO2 depends on the level of CO. When no CO is present (green line), the effect of breathing SO2 is a moderate drop of 16 health points (96 minus 80). In contrast, when CO is present (blue line), the effect of breathing SO2 is a precipitous drop of 60 health points (68 minus 8). SO2 is much more damaging to health when it is combined with CO than when it is acting alone. Another way to say this is that there is a synergy in which the combined health risk of the two pollutants is much greater than you would think from simply adding up their individual effects.

The possibility of interactions has important implications. Many times the effects of environmental contaminants is measured for each contaminant alone, and these may appear relatively minor. But in everyday life, the air contains not just contaminants in isolation, but contaminants interacting in combination. The effects of these complex interactions is largely unknown.

Drug Interactions

Another situation where there are important implications of interaction effects is in the use of drugs. Whether the drugs are part of the health care system or not, whether the drugs be socially sanctioned or socially punished makes no difference. Drugs ingested in combination may have effects that are unpredictable from the effects of the individual drugs acting alone. For this reason it is important that your doctor or pharmacist be advised of other medications you are taking when they give you a new one.

The example we will use is the suppression of basal metabolism by alcohol and barbiturates. The DV will be a measure of basal metabolism. The two IV's will be the levels of Alcohol and Barbiturates in a person's bloodstream. Some years ago barbiturates were used as sleeping pills.

No Drug Interaction

Suppose that there were no drug interaction between alcohol and barbiturates. The first figure shows how this might work. Both alcohol and barbiturates are metabolic suppressants. If there were no interaction between barbiturates and alcohol then combining sleeping pills with alcohol would simply add their effects.

Alcohol alone. On the green line (No Barbiturates) we can see that alcohol depresses the basal metabolism a certain amount. The difference between no alcohol and some alcohol will result in a lower the basal metabolism.

Barbiturates alone. Look at the two left hand end points of the green and blue lines. The left hand end of both lines is where there is no alcohol present. The difference between the green line and the blue line (on the left end where no alcohol is present) shows the difference between basal metabolism with and without several barbiturates. As you can see, taking several sleeping pills reduces metabolism.

Is there an interaction? No, as the graph is drawn, the effect of alcohol is exactly the same whether barbiturates are present or not. The combination of the several drinks and several pills simply adds the effects of the two drugs. That's what would happen if there were no interaction.

An interaction between Alcohol and Barbiturates

The actual case is that there seems to be an interaction between these two drugs, at least for many people.

The current graph shows an interaction. The effect of several drinks without barbiturates (green line) results in a moderate decrease of metabolism. But the effect of several drinks in combination with several pills (blue line) can produce a disastrous drop in metabolism, possibly below the survival threshold.

Several years ago, before this drug interaction was well known, people who were very experienced with both drinking alcohol and taking sleeping pills, died by taking them in combination. They thought that the combination of the two drugs would just add up their individual effects. But, as you can see from the graph, that is not the case. The combination produces effects much larger than merely adding up the individual effects.

Interaction of Type of Problem and Therapeutic Technique

In the final example, we will examine how two types of psychotherapy, cognitive versus behavioral psychotherapy, might be differentially effective depending on the type of clinical problem to be healed. IV1 will be Type of Therapy. The two levels will be Cognitive Therapy and Behavioral Therapy. IV2 will be Type of Problem. The two levels will Learning Difficulties in school and undesirable Habits. Learning Difficulties might include inability to concentrate on school work, inability to organize school work, and so on. Undesirable Habits might include things like chewing nails. The DV is some measure of mental health after psychotherapy.

We do a four-group psychotherapy outcome study. One group has learning difficulties and is given Cognitive Therapy. A second group has learning difficulties and is given Behavioral Therapy. A third group has a habit problem and is given Cognitive Therapy. A fourth group has a habit problem and is given Behavioral Therapy.

No interaction

The first graph has a data pattern showing no interaction between type of problem and type of therapy. There is little if any effect of therapy at either level of learning difficulty.

The way the graph is drawn it appears that learning difficulties are easier to handle therapeutically than are habit problems. That is, for both types of therapy, the mental health outcome is higher for learning difficulties than it is for habit problems. But one type of therapy does not appear to be better than the other for either type of problem.

Is there an interaction? No, what little effects of therapy there are are the same for both types of problems. There is no effect of therapy for learning difficulties and there is no effect of therapy for habit problems.

Interaction

The current graph shows a classic case of interaction--the X-shaped crossed lines. In this case the effects of one IV are reversed at two different levels of another IV.

For learning difficulties (red line) Cognitive Therapy is much more successful than Behavioral Therapy. But it's just the opposite for habit problems. On the blue line Behavioral Therapy is much more successful than Cognitive Therapy.

So, in this hypothetical data, cognitive therapy is much better for learning difficulties while behavior therapy is much better for breaking habits. The effect of therapeutic choice depends on what kind of problem you have.

That finishes our introduction to the concept of interaction effects. We will return to this concept when we take up 2-way ANOVA's much later in the course.

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