A factor is a discrete variable used to classify experimental units. Such designs are classified by the number of levels of each factor and the number of factors. So a 2x2 factorial will have two levels or two factors and a 2x3 factorial will have three factors each at two levels.
These often need to be investigated in order to determine the generality of a response. It may be important to know whether a response is only seen in, say, females but not males. One way to do this would be to do separate experiments in each sex. A much better alternative is to include both sexes or more than one strain etc. Such designs can include several factors without using excessive numbers of experimental subjects.
Split plot designs are considered at the end of this section. They are like a cross between a factorial and a randomised block design.
They were derived from agricultural research in which is was sometimes impossible to irrigate, say, a small plot without affecting the adjacent plots. So irrigated plots were large and covered several smaller plots comparing, say, planting distance. Indeed in a wide class of cases by using factorial designs an experimental investigation, at the same time as it is made more comprehensive, may also be made more efficient if by more efficient we mean that more knowledge and a higher degree of precision are obtainable by the same number of observations.
Fisher RA. The design of experiments. Unfortunately, although such designs are widely used, they are often incorrectly analysed.
A survey found the following:. Niewenhuis et al. Assuming that the animal is the experimental unit, the experiment on the right has two factorsthe treatment Control ve rsus Treated represented by the two columns and the colour White versus Green. This might represent the two sexes, or two strains or two diets or any other factor of possible interest.
This is a 2x2 factorial because there are two factors each at two levels. This assumes that the males and females respond in the same way to the treatment, an assumption that is tested in the statistical analysis using a two-way analysis of variance with interaction. However, this would be useful information which could not be obtained by doing separate experiments on each sex. A 3x3 Factorial design 3 factors each at 3 levels is shown below. A 3x3x2 factorial is shown on the right. So it is a 3x3x2 factorial design.
As E is between 10 and 20 it is probably an appropriate number of experimental units. Strain means will be based on 18 animals averaged across both diets and treatments. So although there are subgroups consisting of just two animals, the means are based on much larger numbers.
A real example. This is a 2 strains x 2 dose levels factorial design. We want to know:. The treatment appears to reduce red blood cell RBC counts. There is no overlap between treated and control individuals. Whether or not there is an interaction can best be seen graphically. So there is no interaction between strain and chloramphenicol in this case. This should, of course, be confirmed by a two-way analysis of variance with interaction as described in section In contrast, here are the results with two different strains C3H and outbred CDThis would be called a 2 x 2 two-by-two factorial design because there are two independent variables, each of which has two levels.
If the first independent variable had three levels not smiling, closed-mouth, smile, open-mouth smilethen it would be a 3 x 2 factorial design. Note that the number of distinct conditions formed by combining the levels of the independent variables is always just the product of the numbers of levels.
In a 2 x 2 design, there are four distinct conditions. In a 3 x 2 design, there are 6. The table below represents a 2 x 2 factorial design in which one independent variable is the type of psychotherapy used to treat a sample of depressed people behavioural vs cognitive and the other is the duration of that therapy short vs long.
The dependent variable, which is not actually shown in this table is a measure of improvement. Each cell in the table, therefore, represents one of the four distinct conditions, short behavioural therapy, short cognitive therapy, long behavioural therapy, and long cognitive therapy.
Inside the cells, you can put different things. In this example, it is the number of participants in each condition. The symbol n generally refers to the number of subjects in a condition. You could also put expected results or actual results e. In a factorial design, each independent variable can be manipulated between subjects or within subjects and this decision must be made separately for each one.
In the design above, it makes sense that participants will receive only one kind of psychotherapy. They will receive either behavioral or cognitive, not both. And they will receive either short or long, not both. Tags: Ba Psychology Graduation Programs. You must be logged in to post a comment. February 23, We will be happy to hear your thoughts. Leave a reply Cancel reply You must be logged in to post a comment.
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Contacts Ua. Register New Account. Password Minimum 6 symbols. Confirm password. Sign up. Already have an account? Log In. Password Lost Password? Remember me. Don't have an account? Sign Up.Dickson, K. Authorized crib cards do not improve exam performance. Teaching of Psychology, 32 For each of the four examinations, half of the students were randomly assigned to the crib card use condition and half to the no crib card use condition.
The percentage of correct answers on each exam constituted the data. An ANCOVA, with crib card use and question type higher order and lower order as factors and student GPA as a covariate, revealed no significant main effects for either crib card use or question type. However, the main effect of the covariate, student GPA, was significant. In a separate analysis, students rated on the final day of the course the effects of crib card use on their studying, test performance, and test anxiety.
The authors discuss the implications of their findings for test performance and for how students study for examinations. Strange, D. A photo, a suggestion, a false memory. Applied Cognitive Psychology, 22 These researchers examined the susceptibility of children to simple suggestion and the resulting creation of false memories — that is, believing they had experienced something that actually had never happened.
When asked about their memories of the scenes in the photos, the children in the false-photo family balloon condition reported remembering that family outing. Since that outing had never happened, they were reporting a false memory. The research suggests how easily false memories in children can be encouraged and the need to be cautious about using photos in child sexual abuse cases. King, L.Introduction to Two Way ANOVA (Factorial Analysis)
What makes a life good? Journal of Personality and Social Psychology, 75 This study used a factorial design to investigate how factors, such as happiness with one's job, degree of meaning one obtains from one's job, and the amount of money one makes, affect the ratings from others of the person's desirability and moral goodness. Each subject was assigned the task of reading a career satisfaction questionnaire and rating the person who filled out the questionnaire on several dimensions.
The questionnaires were all fictitious. They were prepared by the researcher to represent one of eight conditions, represented by a 2 high vs.
They found that the factors of happiness in one's job and the amount of meaning one derived from one's job influenced the ratings of desirability and moral goodness, but that income did not have an effect. Quality of life ratings were influenced by all three independent variables. Lee, A. Improving learning from examples through reflection.A factorial design is often used by scientists wishing to understand the effect of two or more independent variables upon a single dependent variable.
Traditional research methods generally study the effect of one variable at a time, because it is statistically easier to manipulate. However, in many cases, two factors may be interdependent, and it is impractical or false to attempt to analyze them in the traditional way. Social researchers often use factorial designs to assess the effects of educational methods, whilst taking into account the influence of socio-economic factors and background.
Agricultural science, with a need for field-testingoften uses factorial designs to test the effect of variables on crops. In such large-scale studies, it is difficult and impractical to isolate and test each variable individually.
Factorial experiments allow subtle manipulations of a larger number of interdependent variables. Whilst the method has limitations, it is a useful method for streamlining research and letting powerful statistical methods highlight any correlations. Imagine an aquaculture research group attempting to test the effects of food additives upon the growth rate of trout. However, as any fish farmer knows, the density of stocking is also crucial to fish growth; if there are not enough fish in a tank, then the wasted capacity costs money.
If the density is too high, then the fish grow at a slower rate. Rather than the traditional experiment, the researchers could use a factorial design and co-ordinate the additive trial with different stocking densities, perhaps choosing four groups. The factorial experiment then needs 4 x 2, or eight treatments.
The traditional rules of the scientific method are still in force, so statistics require that every experiment be conducted in triplicate. This means 24 separate treatment tanks. Of course, the researchers could also test, for example, 4 levels of concentration for the additive, and this would give 4 x 4 or 16 tanks, meaning 48 tanks in total. Each factor is an independent variable, whilst the level is the subdivision of a factor. Assuming that we are designing an experiment with two factors, a 2 x 2 would mean two levels for each, whereas a 2 x 4 would mean two subdivisions for one factor and four for the other.
It is possible to test more than two factors, but this becomes unwieldy very quickly. In the fish farm example, imagine adding another factor, temperature, with four levels into the mix. It would then be 4 x 4 x 4, or 64 runs. In triplicate, this would be tanks, a huge undertaking. There are a few other methods, such as fractional factorial designs, to reduce this, but they are not always statistically valid. This lies firmly in the realm of advanced statistics and is a long, complicated and arduous undertaking.
Factorial designs are extremely useful to psychologists and field scientists as a preliminary study, allowing them to judge whether there is a link between variables, whilst reducing the possibility of experimental error and confounding variables. The factorial design, as well as simplifying the process and making research cheaper, allows many levels of analysis. As well as highlighting the relationships between variablesit also allows the effects of manipulating a single variable to be isolated and analyzed singly.
The main disadvantage is the difficulty of experimenting with more than two factors, or many levels. A factorial design has to be planned meticulously, as an error in one of the levels, or in the general operationalizationwill jeopardize a great amount of work. Other than these slight detractions, a factorial design is a mainstay of many scientific disciplines, delivering great results in the field.
Check out our quiz-page with tests about:.By Saul McLeodupdated Experimental design refers to how participants are allocated to the different conditions or IV levels in an experiment. Probably the commonest way to design an experiment in psychology is to divide the participants into two groups, the experimental group, and the control group, and then introduce a change to the experimental group and not the control group.
For example, if there are 10 participants, will all 10 participants take part in both conditions e. This type of design is also known as between groups.
Different participants are used in each condition of the independent variable. This means that each condition of the experiment includes a different group of participants. This should be done by random allocation, which ensures that each participant has an equal chance of being assigned to one group or the other.
Independent measures involve using two separate groups of participants; one in each condition. For example:.
Repeated Measures: 2. Repeated Measures: This type of design is also known as within groups.
The same participants take part in each condition of the independent variable. This means that each condition of the experiment includes the same group of participants. Counterbalancing Counterbalancing Suppose we used a repeated measures design in which all of the participants first learned words in 'loud noise' and then learned it in 'no noise.
However, a researcher can control for order effects using counterbalancing. The sample would split into two groups experimental A and control B. Although order effects occur for each participant, because they occur equally in both groups, they balance each other out in the results.
Each condition uses different but similar participants. An effort is made to match the participants in each condition in terms of any important characteristic which might affect performance, e. One member of each matched pair must be randomly assigned to the experimental group and the other to the control group.
Matched pairs : Each condition uses different participants, but they are matched in terms of important characteristics, e. Read about each of the experiments below.We have usually no knowledge that any one factor will exert its effects independently of all others that can be varied, or that its effects are particularly simply related to variations in these other factors.
In a different but related study, Schnall and her colleagues investigated whether feeling physically disgusted causes people to make harsher moral judgments Schnall et al. They also used a self-report questionnaire to measure the amount of attention that people pay to their own bodily sensations. Finally, the researchers asked participants to rate their current level of disgust and other emotions. The primary results of this study were that participants in the messy room were in fact more disgusted and made harsher moral judgments than participants in the clean room—but only if they scored relatively high in private body consciousness.
The research designs we have considered so far have been simple—focusing on a question about one variable or about a statistical relationship between two variables. But in many ways the complex design of this experiment undertaken by Schnall and her colleagues is more typical of research in psychology. Fortunately, we have already covered the basic elements of such designs in previous chapters.
In this chapter, we look closely at how and why researchers combine these basic elements into more complex designs. We start with complex experiments—considering first the inclusion of multiple dependent variables and then the inclusion of multiple independent variables. Finally, we look at complex correlational designs. Imagine that you have made the effort to find a research topic, review the research literature, formulate a question, design an experiment, obtain research ethics board REB approval, recruit research participants, and manipulate an independent variable.
It would seem almost wasteful to measure a single dependent variable. Even if you are primarily interested in the relationship between an independent variable and one primary dependent variable, there are usually several more questions that you can answer easily by including multiple dependent variables.
Often a researcher wants to know how an independent variable affects several distinct dependent variables. She conducted an experiment in which the independent variable was whether participants were tested in a room with no odor or in one scented with lemon, lavender, or dimethyl sulfide which has a cabbage-like smell.
When an experiment includes multiple dependent variables, there is again a possibility of carryover effects. So the order in which multiple dependent variables are measured becomes an issue. One approach is to measure them in the same order for all participants—usually with the most important one first so that it cannot be affected by measuring the others. Another approach is to counterbalance, or systematically vary, the order in which the dependent variables are measured.
When the independent variable is a construct that can only be manipulated indirectly—such as emotions and other internal states—an additional measure of that independent variable is often included as a manipulation check. This is done to confirm that the independent variable was, in fact, successfully manipulated. For example, Schnall and her colleagues had their participants rate their level of disgust to be sure that those in the messy room actually felt more disgusted than those in the clean room.
Manipulation checks are usually done at the end of the procedure to be sure that the effect of the manipulation lasted throughout the entire procedure and to avoid calling unnecessary attention to the manipulation.
Manipulation checks become especially important when the manipulation of the independent variable turns out to have no effect on the dependent variable. Imagine, for example, that you exposed participants to happy or sad movie music—intending to put them in happy or sad moods—but you found that this had no effect on the number of happy or sad childhood events they recalled.
This could be because being in a happy or sad mood has no effect on memories for childhood events. But it could also be that the music was ineffective at putting participants in happy or sad moods. Another common approach to including multiple dependent variables is to operationally define and measure the same construct, or closely related ones, in different ways.
Imagine, for example, that a researcher conducts an experiment on the effect of daily exercise on stress. The dependent variable, stress, is a construct that can be operationally defined in different ways. For this reason, the researcher might have participants complete the paper- and-pencil Perceived Stress Scale and measure their levels of the stress hormone cortisol.
This is an example of the use of converging operations.Note that, in this context, an IV is often referred to as a factor. The factorial design is very popular in the social sciences. It has a few advantages over single variable designs. The most important of these is that it can provide some unique and relevant information about how variables interact or combine in the effect they have on the DV. Let's look at these design issues in more detail with a concrete example and then consider the unique information that this design provides.
Design Our example involves the effects of maternal consumption of ethanol on the behavior of the offspring of rats. The human literature had shown that children diagnosed with Fetal Alcohol Syndrome FAS were more active and impulsive than children not receiving this diagnosis.
They also seemed to have a more difficult time controlling themselves i. These problems typically become less severe as the child ages. The human literature is difficult to interpret however, because questions remain as to the cause and effect relationships involved.
Were the behavioral abnormalities observed in the children with FAS due to the fact that their mothers consumed alcohol while they were pregnant? Another possible causal factor of the abnormalities observed is spousal abuse. Ethically, we cannot conduct the experiments necessary to determine the causal relations involved in humans. Earlier literature had demonstrated that rats can be used as an animal model of FAS. Offspring of rodents given alcohol when pregnant show similar morphological and behavioral changes to that observed in humans.
So, we will have two IVs or factors and each will have two levels or possible values. The table below illustrates the design. This is an example of a 2x2 factorial design with 4 groups or cellseach of which has 5 subjects. This is the simplest possible factorial design. Rats are nocturnal, burrowing creatures and thus, they prefer a dark area to one that is brightly lit.
The PA task uses this preference to test their learning ability. The apparatus has two compartments separated by a door that can be lifted out. One of the compartments has a light bulb which is controlled by the experimenter. Furthermore, the floor can be electrified.
In this case, the rat receives a brief, mild electric shock. Finally, there is also a holding cage separate from the experimental apparatus available. The learning takes place over a series of trials. The first trial goes something like this: The rat is placed in the compartment with the light bulb as shown below. When the trial begins, three things happen. The door is raised, the light is turned on, and a stopwatch is started see the diagram below. Within a few seconds of the door being raised, the rat will typically sniff around and begin to move into the darker compartment without the light.
When the rat has completely entered the darker compartment, the door is closed and the brief, mild shock is administered. The goal is for the rat to learn not to move into the darker compartment. In other words, by remaining passivethe rat can avoid the shock, hence the term passive avoidance. For our purposes, we will use a criteria of seconds as our operational definition of learning PA. That is, when the rat remains in the brightly lit compartment for 3 minutes, we will say that it has learned the task and what we measure is the number of trials it takes the rat to do this.
Note that a "smart" rat will take less trials to learn. Thus, the PA task was chosen as the DV because it can be thought of as a measure of "self restraint.