Research methods in psychology by B. Morling (third edition) – Chapter 8 summary

INTRODUCING BIVARIATE CORRELATIONS
A bivariate correlation or bivariate association, is an association that involves exactly two variables. The nature of the association can be described with scatterplots and the correlation coefficient. Associations between categorical variables are usually presented in a bar graph.

INTERROGATING ASSOCIATION CLAIMS
The two most important validities to interrogate are construct validity and statistical validity with an association claim. The construct validity checks how well each variable was measured. The statistical validity checks how well the data supports the conclusion.

There are five questions that can be asked in order to interrogate the statistical validity:

  1. What is the effect size?
    The effect size is the strength of a relationship between two or more variables. Larger effect sizes allow more accurate predictions and large effect sizes are usually more important. Exceptions on this second rule depend on the context
  2. Is the correlation statistically significant?
    Statistical significance refers to the conclusion a researcher reaches regarding the likelihood of getting a correlation of that size just by chance, assuming there is no correlation in the real world. Statistical significance calculations depend on effect size and sample size.
  3. Could outliers be affecting the association?
    Outliers are extreme scores. Outliers matter the most when a sample is small.
  4. Is there restriction of range?
    If there is not a full range of scores on one of the variables in the association, it can make the correlation appear smaller than it really is. One of the solutions for this is the statistical technique called correction for restriction of range.
  5. Is the association curvilinear?
    A curvilinear association is an association in which the relationship between two variables is positive or negative up to some point and then changes.

INTERNAL VALIDITY: CAN WE MAKE A CAUSAL INFERENCE FROM AN ASSOCIATION?
The three requirements in order to establish causation are the following:

  1. Covariance of cause and effect
  2. Temporal precedence (directionality problem)
  3. Internal validity (third-variable problem)

A third-variable problem can be exposed by checking the correlation with that third variable between the original two variables. If there is a third-variable present, the original association is then called a spurious association.

EXTERNAL VALIDITY: TO WHOM CAN THE ASSOCIATION BE GENERALISED
The external validity interrogation asks whether the association can generalize to other people, places and times. When the relationship between two variables changes depending on the level of another variable, that variable is called a moderator.

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Research methods in psychology by B. Morling (third edition) – Book summary

Research methods in psychology by B. Morling (third edition) – Chapter 1 summary

Research methods in psychology by B. Morling (third edition) – Chapter 1 summary

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It is important to both produce and consume research. A research consumer is important, because to effectively know something or to put a theory or treatment in to use, it is imperative that the research consumer knows the evidence behind the evidence-based treatment. It is important to be able to decide how valuable and useful a research really is.

Both research producers and research consumers share an interest in psychological phenomena, such as behaviour or emotion. They also both share a commitment to the practice of empiricism: to answer psychological questions with systematic observations.

The cupboard theory is the idea that young animals (but also your dog) clings on to the caregiver because the caregiver provides food. The contact comfort theory is the idea that young animals (but also your dog) clings on to the caregiver because the caregiver provides warmth and contact comfort. These theories have been tested and followed the empirical cycle.

THE EMPIRICAL CYCLE

The empirical cycle always starts with an observation.

Induction -> Theory -> Deduction -> Prediction ->Testing -> Results -> Evaluation -> Observation - > Induction

  1. Observation
    You make an observation. This can be based on past research or an ‘every day method’.
  2. Induction
    This is the process of coming up with a theory that explains your observation. In this phase you research your research question.
  3. Theory
    After you’ve researched your research question you can find or come up with a theory. A theory is a set of statements that describe general principles about how variables relate to one another. A good theory is supported by data from previous studies, it should be falsifiable; it has to be possible to debunk the theory and a theory should not be unnecessarily complex. This is called parsimony. (preferring the simplest theory)
  4. Deduction
    This is the process of formulating a prediction that follows from your theory. You make an hypothesis: a predicted answer to your research question.
  5. Prediction
    A specific event that will occur if your hypothesis is true.
  6. Testing
    This is the process of verifying your prediction. You have to operationalize your test. This is determining how you will test your prediction.
  7. Results
    You have the results of your test.

Data are a set of observations. Depending on whether the data are consistent with hypotheses based on a theory data may either support or challenge a theory. The best theories should be supported by data from studies, should be parsimonious and falsifiable.

Basic research is used to enhance the general body of knowledge. Applied research is done with a practical problem in mind. Translational research is the dynamic bridge between basic and applied research. E.g: a basic research is about schizophrenia. Translational research is used to develop a new treatment for schizophrenia and applied research is used to see how people diagnosed with schizophrenia can fit better into today’s

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Research methods in psychology by B. Morling (third edition) – Chapter 2 summary

Research methods in psychology by B. Morling (third edition) – Chapter 2 summary

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EXPERIENCE
Experience is not a reliable source of information, because it has no comparison group. A comparison group in research is a group which isn’t affected by the controlled independent variable, so it is possible to really determine whether the independent variable has the effect people think it has.

E.g: Doctors used to take blood from an ill person, because they believed that it cured the illness. Some people recovered and they concluded that they recovered because they bled the patients. This is based on experience, they have experiences that some patients recovered, but they did not have a comparison group, so they had no way of knowing that the recovery was because of bleeding the patient. To make sure that it had this effect, they should have had a group with people who were ill, but were not bled, to see what would have happened.

When we are using personal experience to determine whether something works or not, we don’t have a comparison group as well. “My knee feels better with this tape”, but you don’t know how it would’ve felt if you didn’t use that tape. There is no comparison group, so it is not possible to give a conclusive answer, based on empirical evidence.

In real-world situation situations, there are several possible explanations for an outcome. In research, these alternative explanations are called confounds. Experience is confounded, because you do not know the cause of an effect, although you might think you do. When you use tape to lessen the pain in your knee, you don’t know whether the tape caused the pain to diminish. A researcher can see the situation from outside, but you can only see one condition and all you have is your experience.

Behavioural research is probabilistic. This means that it’s findings are not expected to explain all cases all the time. The conclusions of research are meant to explain a certain proportion of the cases. The two big problems with using experience as a source of information is that there is no comparison group and that experience is confounded.

INTUITION
People use their intuition to make decisions, although it is not a reliable source of information, because intuition is biased. There are ways our intuition is biased:

  1. Good Story bias
    People tend to believe a good story, but this doesn’t mean that is necessarily correct.
  2. Availability Heuristic
    Things that come to mind easily tend to guide our thinking. (e.g: Aeroflot is a bad airplane company, because the bad reports about Aeroflot come to mind easier than the good stories about Aeroflot) The availability heuristic occurs because sometimes things stand out more. (e.g: shark attacks stand out more than natural deaths, which causes us to believe that shark attacks are common)
  3. Present/Present bias
    This bias is the name for our failure to consider appropriate comparison groups. In this case there are comparison groups available, but you fail
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Research methods in psychology by B. Morling (third edition) – Chapter 4 summary

Research methods in psychology by B. Morling (third edition) – Chapter 4 summary

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There are two historical examples of studies that violated several ethical criteria.

  1. Tuskegee Syphilis Study
    This experiment involves black men diagnosed with syphilis, who were lied to, not told that the experiment was about syphilis and intentionally not treated. Participants in this study were not treated respectfully, they were harmed and the researcher targeted a disadvantaged social group in this study.
  2. Milgram Obedience Studies
    This experiment shows that ethical violations are often much more nuanced. Participants in this experiment were debriefed after the experiment. It also shows that balancing the potential risks to participants and the value of the knowledge gained is not an easy decision.

The Belmont Report outlines three main principles for guiding ethical decision making:

  1. Principle of respect for persons
    This includes two provisions. The participants should be treated as autonomous agents. Each person is entitled to the precaution of informed consent. People with less autonomy (e.g: children, mentally disabilities) should be protected. Coercion is an implicit or an explicit suggestion that those who do not participate will suffer a negative consequence.
  2. The principle of beneficence
    Researchers must take precautions to protect the participants of harm and to ensure their well-being. Valuable knowledge must be gained while inflicting as less as possible harm. To prevent harm by collecting personal data, the study can be conducted as an anonymous study. In a confidential study, researchers collect some identifying information, but prevent it from being disclosed.
  3. The principle of justice
    This calls for a fair balance between the kinds of people who participate in a study and the kinds of people who benefit from it.

The APA outlines five general principles for guiding individual aspects of ethical behaviour. Three of the give general principles are the same principles as in the Belmont Report. The other two are:

  1. Fidelity and responsibility
    Establish relationships of trust. Accept the responsibility for professional behaviour (e.g: a psychologist not treating a student or a professor not dating a student).
  2. Integrity
    Strive to be accurate, truthful and honest (e.g: professors are obligated to teach accurately).

The APA lists ten specific ethical standards. These standards are similar to enforceable rules or laws.

  1. Institutional review boards
    An institutional review board is a committee responsible for interpreting ethical principles and ensuring that research using human participants is conducted ethically.

Standard

Definition

Institutional review board

This is a committee responsible for interpreting ethical principles and ensuring that research using human participants is

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Research methods in psychology by B. Morling (third edition) – Chapter 5 summary

Research methods in psychology by B. Morling (third edition) – Chapter 5 summary

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Construct validity refers to how well a study’s variables are measured or manipulated. There are three common types of measurement: self-report, observational and physiological. The conceptual definition, or construct, is the researcher’s definition of the variable in question on a theoretical level. The operational definition represents a researcher’s specific decision about how to measure of manipulate the conceptual variable.

SELF-REPORT
A self-report measure operationalizes a variable by reporting people’s answers to questions about themselves in a questionnaire or an interview. In research on children, self-reports may be replaced with parent reports or teacher reports.     

The problems with self-reports are the demand characteristics: a participant wants to be  a ‘good’ participant. People their self-perception is not always correct and the social desirability: people want to give a good impression about themselves.

OBSERVATIONAL MEASURES
An observational measure is sometimes also called a behavioural measure and operationalizes a variable by recording observable behaviour or physical traces of behaviour.

The problems with observational measures are:

  1. Primacy effect
    The first observation sets the tone for the rest of the observations. (e.g: the first rated essay is very good, so the others that are not that good are automatically rated worse than they otherwise would have been rated)
  2. Recency effect
    The last observation will be remembered best. (e.g: the last person at a job interview will be remembered the best, because that person was the last)
  3. Halo effect
    A good rating on one dimension will influence the ratings on other dimensions. (e.g: if a person is friendly and that is rated first, then he will be more likely to receive higher ratings on other dimensions as well)

PHYSIOLOGICAL MEASURES
A physiological measure operationalizes a variable by recording biological data. The problem with physiological measurement is that not everything can be measured with biological data (at least not yet).

SCALES OF MEASUREMENT
All variables must have at least two levels. The levels of operational variables can be coded using different scales of measurement. 

  1. Categorical variables (nominal variables).
    This are categories in which the variable fit. (e.g: sex, species)
  2. Quantitative variables
    These variables are coded with meaningful numbers. (e.g: height, weight)

There are three kinds of quantitative variables.

  1. Ordinal scale
    A ranking. (e.g: top 10 best-selling books) The distance between the subsequent numerals might not be equal.
  2. Interval scale
    The interval between two ranked numbers means the exact same thing. The number ‘0’ doesn’t mean none. (e.g: the difference between IQ 105 and 110 is 5, so is the difference between IQ 110 and 115. The interval is the same)
  3. Ratio scale
    There are equal intervals and ‘0’ truly means none. (e.g: a knowledge test with amount of questions correct)

RELIABILITY
Reliability refers to how consistent the results of a measure are.

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Research methods in psychology by B. Morling (third edition) – Chapter 8 summary

Research methods in psychology by B. Morling (third edition) – Chapter 8 summary

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INTRODUCING BIVARIATE CORRELATIONS
A bivariate correlation or bivariate association, is an association that involves exactly two variables. The nature of the association can be described with scatterplots and the correlation coefficient. Associations between categorical variables are usually presented in a bar graph.

INTERROGATING ASSOCIATION CLAIMS
The two most important validities to interrogate are construct validity and statistical validity with an association claim. The construct validity checks how well each variable was measured. The statistical validity checks how well the data supports the conclusion.

There are five questions that can be asked in order to interrogate the statistical validity:

  1. What is the effect size?
    The effect size is the strength of a relationship between two or more variables. Larger effect sizes allow more accurate predictions and large effect sizes are usually more important. Exceptions on this second rule depend on the context
  2. Is the correlation statistically significant?
    Statistical significance refers to the conclusion a researcher reaches regarding the likelihood of getting a correlation of that size just by chance, assuming there is no correlation in the real world. Statistical significance calculations depend on effect size and sample size.
  3. Could outliers be affecting the association?
    Outliers are extreme scores. Outliers matter the most when a sample is small.
  4. Is there restriction of range?
    If there is not a full range of scores on one of the variables in the association, it can make the correlation appear smaller than it really is. One of the solutions for this is the statistical technique called correction for restriction of range.
  5. Is the association curvilinear?
    A curvilinear association is an association in which the relationship between two variables is positive or negative up to some point and then changes.

INTERNAL VALIDITY: CAN WE MAKE A CAUSAL INFERENCE FROM AN ASSOCIATION?
The three requirements in order to establish causation are the following:

  1. Covariance of cause and effect
  2. Temporal precedence (directionality problem)
  3. Internal validity (third-variable problem)

A third-variable problem can be exposed by checking the correlation with that third variable between the original two variables. If there is a third-variable present, the original association is then called a spurious association.

EXTERNAL VALIDITY: TO WHOM CAN THE ASSOCIATION BE GENERALISED
The external validity interrogation asks whether the association can generalize to other people, places and times. When the relationship between two variables changes depending on the level of another variable, that variable is called a moderator.

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Research methods in psychology by B. Morling (third edition) – Chapter 10 summary

Research methods in psychology by B. Morling (third edition) – Chapter 10 summary

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Experiments are the only way to investigate causal issues.

EXPERIMENTAL VARIABLES
An experiment means that the researchers manipulated at least one variable and measures another. A manipulated variable is a variable that is controlled. Measured variables take the forms of records of behaviour or attitudes. The manipulated variable is the independent variable. The conditions are the different levels of the independent variable. The measured variable is the dependent variable. Control variables are variables that are also controlled. These variables are controlled by holding all other factors constant. Any variable that an experimenter holds constant on purpose is called a control variable.

WHY EXPERIMENTS SUPPORT CAUSAL CLAIMS
There are three rules for something to be causal:

  1. Covariance
  2. Temporal precedence
  3. Internal validity

If independent variables did not vary, a study could not establish covariance, because you need a comparison group to establish covariance. It is impossible to establish internal validity if there are confounds, or alternative explanations. A design confound is an experimenter’s mistake in designing the independent variable. It is a second variable that happens to vary systematically along with the intended independent variable. Something is only a design confound if it shows systematic variability with the independent variable. It would not be a design confound if it shows unsystematic variability. If individual differences are distributed evenly in both groups, the are not a confound.

Selection effects are effects that are the result of two groups being systematically different from those in the other. This can also happen when the experimenters let participants choose in which group they want to be. The selection effects can be avoided by using random assignment, when assigning people to the conditions. Selection effects can also be avoided by using matched groups.

INDEPENDENT GROUP DESIGNS
In an independent group design both groups of participants are placed into different levels of the independent variable. This type of design is also called a between-subjects design or between-groups design. In a within-groups design or within-subjects design, there is only one group of participants and each person is pretended with all levels of the independent variable.

In the posttest-only design, also known as equivalent groups, participants are randomly assigned to independent variable groups. In a pretest/posttest design, participants are randomly assigned to at least two different groups and are tested on the key dependent variable twice, before and after exposure to the independent variable.

WITHIN-GROUPS DESIGNS
There are two basic types of within-groups design:

  1. Repeated-measures design
    In this design participants are measured on the dependent variable every time they are exposed to another level of the independent variable.
  2. Concurrent-measures design
    In this design participants are exposed to all the levels of an independent variable at roughly the same time.

The main advantage of a within-group design is that it ensures that participants in the two groups will be equivalent. The term

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Research methods in psychology by B. Morling (third edition) – Chapter 11 summary

Research methods in psychology by B. Morling (third edition) – Chapter 11 summary

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THREATS TO INTERNAL VALIDITY:
There are 12 threats to internal validity. Most of these threats can be prevented with a good experiment design and only occur in the so-called ‘really bad experiment’, also known as the one-group, pre-test/post-test design. The following twelve threats to internal validity exists:

Threat

What happens?

When?

Solution

Maturation threat

A change in behaviour occurs more or less spontaneously over time. People adapt to changed environments.

One-group, pre-test/post-test design

Using a comparison group

History threat

A specific event has occurred between the pre-test and the post-test that affects almost every participant systematically (e.g: a change of seasons).

One-group, pre-test/post-test design

Using a comparison group

Regression threat

If a group’s mean is unusually extreme at the pre-test, it is likely to be less extreme at the post-test, closer to the typical mean (e.g: depressed people have an extreme mean of sadness and this probably will be less extreme when it is tested again). Regression alone does not make an extreme group cross over the mean to the other extreme.

One-group, pre-test/post-test design

Using a comparison group

Attrition threat

A reduction in participant numbers that occurs when people drop out before the end. This is only a problem if attrition is systematic.

One-group, pre-test/post-test design

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Research methods in psychology by B. Morling (third edition) – Chapter 12 summary

Research methods in psychology by B. Morling (third edition) – Chapter 12 summary

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EXPERIMENTS WITH TWO INDEPENDENT VARIABLES CAN SHOW INTERACTIONS
Experiments with more than one independent variable allows researchers to look for an interaction effect. This is an effect where the effect of the original independent variable depends on the level of another independent variable. If the two lines of the independent variables cross, there is a crossover interaction, also known as “it depends”. If the lines are not parallel, there is an interaction and if the lines are parallel, there is no interaction. A spreading interaction occurs when the two lines spread out and can be labelled as an “only when..” interaction. An interaction is a difference in differences

FACTORIAL DESIGNS STUDY TWO INDEPENDENT VARIABLES
Testing for interactions is done with factorial designs. A factorial design is one in which there are two or more independent variables. In a factorial design, researchers study each possible combination of the independent variables. A participant variable is a variable whose levels are selected, but cannot be manipulated (e.g: age, the level for this variable can be selected, but not manipulated). Using factorial designs to test limits is called testing for moderators and it is a way to test the external validity of an experiment. Factorial designs can also test theories and hypotheses.

INTERPRETING FACTORIAL RESULTS: MAIN EFFECTS AND INTERACTONS
Researchers test each independent variable to look for main effects, the overall effect of one independent variable on another independent variable. Marginal means are the arithmetic means for each level of an independent variable, averaging over levels of the other independent variable. The main effect is not the most important effect, but the overall effect of one independent variable on another independent variable. The interaction itself is the most important effect. In a factorial design with two independent variables, the first to results obtained are the main effects for each independent variable. The third result is the interaction effect.

FACTORIAL VARIATIONS
In a mixed factorial design, one variable is manipulated as independent groups and the other is manipulated as within-groups (e.g: age and driving while on the phone. Age is independent groups and driving while on the phone is within-groups). When plotting a three-way factorial design and you want to check for three-way-interactions, you have to look for differences between the two states. If the lines are the same for both states in the three-way interaction, then there is a two-way interaction, but not a three-way interaction (unless the lines are parallel).

IDENTIFYING FACTORIAL DESIGNS IN YOUR READING
When looking for factorial designs in research articles it is important to look at the method part of the research description. When looking for factorial designs in regular articles it is important to look for the phrases it depends and only when.

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Research methods in psychology by B. Morling (third edition) – Chapter 13 summary

Research methods in psychology by B. Morling (third edition) – Chapter 13 summary

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QUASI-EXPERIMENTS
A quasi-experiment differs from a true experiment in that the researchers do not have full experimental control. In quasi-experiments, researchers might not be able to randomly assign participants to one level or the other. They are assigned by other things (e.g: teachers, political regulations or nature).

A non-equivalent control group design is a quasi-experiment in which there is a treatment group and a control group, but the participants have not been randomly assigned. A non-equivalent control group pretest/posttest design is a quasi-experiment in which participants are tested before and after the experiment, but are not randomly assigned to groups. An interrupted time-series design is a quasi-experiment that measures participants repeatedly on a dependent variable. A non-equivalent control group interrupted time-series design is a quasi-experiment in which the independent variable was studied as a repeated-measures variable and an independent groups variable.

There are several possible threats in quasi-experiments to internal validity:

Threat

Definition

Selection effect

The participants of one level of the independent variable are systematically different from other participants at another level of the independent variable.

Design confounds

In a design confound, some outside variable systematically varies the levels of the targeted independent variable.

Maturation threat

An observed change has emerged more or less spontaneously over time.

History threat

An external, historical event happens for everyone in a study at the same time as the treatment (e.g: a change of seasons).

Regression to the mean

A measure is extreme and will thus (almost) always be less extreme and more closely to the mean on the next measurement.

Attrition threat

Certain kinds of participants drop out systematically (e.g: only the most depressed people drop out).

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Research methods in psychology by B. Morling (third edition) – Chapter 14 summary

Research methods in psychology by B. Morling (third edition) – Chapter 14 summary

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TO BE IMPORTANT, A STUDY MUST BE REPLICATED
Replication gives a study credibility, and it is a crucial part of the scientific process. There are several types of replication:

  1. Direct replication
    Researchers repeat an original study as closely as they can to see whether the effect is the same in the newly collected data.
  2. Conceptual replication
    Researchers explore the same research question, but use different procedures. In this replication, the conceptual variables are the same, but the operationalizations are not.
  3. Replication-plus-extension
    Researchers replicate their original experiment and add variables to test additional questions.

The replication crisis refers to the fact that a lot of psychological studies don’t share the same results when they’re replicated. Replication studies might fail, because some original effect are contextually sensitive and when the replication context is too different, the replication is more likely to fail.

HARK-ing is hypothesising after the results are known. P-hacking is using more individuals and removing certain outliers if the results of the first experiment were not significant. The goal of this to find a p-value of under 0.05. There are three changes made to psychological research in order to increase the replication rate:

  1. Open science
    Sharing one’s data and materials freely.
  2. Larger sample sizes
    Most studies and replications require much larger sample sizes nowadays.
  3. Preregistration
    Preregistering the study’s methods, hypothesis and statistical analyses online, in advance of data collection. This can be useful for publication in journals.

In order to increase the replication rate in journals, journals now all devote a section to replicated articles. Meta-analysis is a way of mathematically averaging the results of all the studies that have tested the same variables to see what conclusion the whole body of evidence supports. This makes use of both published and unpublished articles. The file drawer problem refers to the idea that a meta-analysis might be overestimating the true size of an effect because null effects, or even opposite effects, have not been included in the collection of the process (unpublished studies are less likely to make it into a meta-analysis).

TO BE IMPORTANT, MUST A STUDY HAVE EXTERNAL VALIDITY?
The manner in which the participants are recruited is more important than the number of participants for getting external validity. Ecological validity is the generalizability of an experiment to real-world settings.

Researchers in the theory-testing mode are usually designing correlational or experimental research to investigate support for a theory. When investigating support for a theory, the generalizability is not always necessary (e.g: if a theory is false in one sample, it should be false in all samples). Researchers in the generalization mode want to generalize the findings from the sample in a previous study to a larger population. Frequency claims are always in the generalization mode and association and causal claims are usually in theory-testing mode, but can be in generalization mode. Many

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Research Methods & Statistics – Interim exam 2 (UNIVERSITY OF AMSTERDAM)

Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 3 summary

Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 3 summary

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THE ASSOCIATION BETWEEN TWO CATEGORICAL VARIABLES
When analysing data the first step is to distinguish between the response variable and the explanatory variable. The response variable is the outcome variable on which comparisons are made. If the explanatory variable is categorical, it defines the groups to be compared with respect to values for the response variable. If the explanatory variable is quantitative, it defines the change in different numerical values to be compared with respect to values for the response variable. The explanatory variable should explain the response variable (e.g: survival status is a response variable and smoking status is the explanatory variable).

An association exists between two variables if a particular value for one variable is more likely to occur with certain values of the other variable.

A contingency table is a display for two categorical variables. Conditional proportions are proportions which formation is conditional on ‘x’. A conditional proportion should be conditional to something. A conditional proportion is also a percentage. The proportion of the totals (e.g: percentage of total amount of ‘no’) is called a marginal proportion.

There is probably an association between two variables if there is a clear explanatory/response relationship, that dictates which way we compute the conditional proportions. Conditional proportions are useful in determining if there’s an association. A variable can be independent from another variable.

THE ASSOCIATION BETWEEN TWO QUANTITATIVE VARIABLES
We examine a scatterplot to study association. There is a difference between a positive association and a negative association. If there is a positive association, x goes up as y goes up. If there is a negative association, x goes up as y goes down.

Correlation describes the strength of the linear association. Correlation (r) summarizes th direction of the association between two quantitative variables and the strength of its linear trend. It can take a value between -1 and 1. A positive value for r indicates a positive association and a negative value for r indicates a negative association. The closer r is to 1, the closer the data points fall to a straight line and the stronger the linear association is. The closer r is to 0, the weaker the linear association is.

The properties of the correlation:

  • The correlation always falls between -1 and +1.
  • A positive correlation indicates a positive association and a negative correlation indicates a negative association.
  • The value of the correlation does not depend on the variables’ unit (e.g: euros or dollars)
  • Two variables have the same correlation no matter which is treated as the response variable and which is treated at the explanatory variable.
 

 

The correlation r can be calculated as following:

N is the number of points.  and ȳ are means and

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Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 7 summary

Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 7 summary

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HOW SAMPLE PROPORTIONS VARY AROUND THE POPULATION PROPORTION
The sample distribution of a statistic is the probability distribution that specifies probabilities for the possible values the statistic can take. The population distribution from which you take the sample. Values of its parameters are fixed, but usually unknown. Data distribution is the distribution of the sample data. It is also called sample proportion. Sampling distribution is the distribution of a sample statistic such as a sample proportion. Sampling distributions describe the variability that occurs from sample to sample.

For a random sample size n from a population with proportion p of outcomes in a particular category, the sampling distribution of the sample proportion in that category has:

 and 

For a large sample size n, the binomial distribution has a normal distribution. The central limit theorem states that the sampling distribution of the sample mean often has approximately a normal distribution. This result applies no matter what the shape of the population distribution from which the samples are taken. The standard deviation of the sampling distribution has the following formula:

The larger the sample, the closer the sample mean tends to fall to the population mean.

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Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 8 summary

Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 8 summary

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POINT AND INTERVAL ESTIMATES OF POPULATION PARAMETERS
A point estimate is a single number that is our best guess for the parameter (e.g: 25% of all Dutch people are above 1,80m). An interval estimate is an interval of numbers within which the parameter value is believed to fall (e.g: between 20% and 30% of the Dutch people are above 1,80m). The margin of error gives the lower border and the upper border of the margin.

A good estimator of a parameter has two properties:

  1. Unbiased
    A good estimator has a sampling distribution that is centred at the parameter. A mean from a random sample should fall around the population parameter and this is especially the case with multiple samples and thus a sampling distribution.
  2. Small standard deviation
    A good estimator has a small standard deviation compared to other estimators. The sample mean is preferred over the sample median, even in a normal distribution, because the sample mean has a smaller standard deviation.

An interval estimate is designed to contain the parameter with some chosen probability, such as 0.95. Confidence intervals are interval estimates that contain the parameter with a certain degree of confidence. A confidence interval is an interval containing the most believable values for a parameter. The probability that this method produces an interval that contains the parameter is called the confidence level. A sampling distribution of a sample proportion gives the possible values for the sample proportion and their probabilities and is a normal distribution if np is larger than 15 and n(1-p) is larger than 15. The margin of error measures how accurate the point estimate is likely to be in estimating a parameter.

CONSTRUCTING A CONFIDENCE INTERVAL TO ESTIMATE A POPULATION PROPORTION
The point estimate of the population proportion is the sample proportion. The standard error is the estimated standard deviation of a sampling distribution. The formula for the standard error is:

The greater the confidence level, the greater the interval. The margin of error decreases with bigger samples, because the standard error decreases with bigger samples. The larger the sample, the narrower the interval. If using a 95% confidence interval over time, then 95% of the intervals would give correct results, containing the population proportion.

CONSTRUCTING A CONDIFENCE INTERVAL TO ESTIMATE A POPULATION MEAN
The standard error for the population mean has the following formula:

The t-score is like a z-score, but a bit larger, and comes from a bell-shaped distribution that has slightly thicker tails than a normal distribution. The distribution that uses the t-score and the standard error, rather than the z-score and the standard deviation is called the t-distribution. The standard deviation of the t-distribution is a bit larger than 1, with the precise value depending on what is called the degrees of freedom. The t-score has

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Research methods in psychology by B. Morling (third edition) – Chapter 8 summary

Research methods in psychology by B. Morling (third edition) – Chapter 8 summary

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INTRODUCING BIVARIATE CORRELATIONS
A bivariate correlation or bivariate association, is an association that involves exactly two variables. The nature of the association can be described with scatterplots and the correlation coefficient. Associations between categorical variables are usually presented in a bar graph.

INTERROGATING ASSOCIATION CLAIMS
The two most important validities to interrogate are construct validity and statistical validity with an association claim. The construct validity checks how well each variable was measured. The statistical validity checks how well the data supports the conclusion.

There are five questions that can be asked in order to interrogate the statistical validity:

  1. What is the effect size?
    The effect size is the strength of a relationship between two or more variables. Larger effect sizes allow more accurate predictions and large effect sizes are usually more important. Exceptions on this second rule depend on the context
  2. Is the correlation statistically significant?
    Statistical significance refers to the conclusion a researcher reaches regarding the likelihood of getting a correlation of that size just by chance, assuming there is no correlation in the real world. Statistical significance calculations depend on effect size and sample size.
  3. Could outliers be affecting the association?
    Outliers are extreme scores. Outliers matter the most when a sample is small.
  4. Is there restriction of range?
    If there is not a full range of scores on one of the variables in the association, it can make the correlation appear smaller than it really is. One of the solutions for this is the statistical technique called correction for restriction of range.
  5. Is the association curvilinear?
    A curvilinear association is an association in which the relationship between two variables is positive or negative up to some point and then changes.

INTERNAL VALIDITY: CAN WE MAKE A CAUSAL INFERENCE FROM AN ASSOCIATION?
The three requirements in order to establish causation are the following:

  1. Covariance of cause and effect
  2. Temporal precedence (directionality problem)
  3. Internal validity (third-variable problem)

A third-variable problem can be exposed by checking the correlation with that third variable between the original two variables. If there is a third-variable present, the original association is then called a spurious association.

EXTERNAL VALIDITY: TO WHOM CAN THE ASSOCIATION BE GENERALISED
The external validity interrogation asks whether the association can generalize to other people, places and times. When the relationship between two variables changes depending on the level of another variable, that variable is called a moderator.

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Research methods in psychology by B. Morling (third edition) – Chapter 10 summary

Research methods in psychology by B. Morling (third edition) – Chapter 10 summary

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Experiments are the only way to investigate causal issues.

EXPERIMENTAL VARIABLES
An experiment means that the researchers manipulated at least one variable and measures another. A manipulated variable is a variable that is controlled. Measured variables take the forms of records of behaviour or attitudes. The manipulated variable is the independent variable. The conditions are the different levels of the independent variable. The measured variable is the dependent variable. Control variables are variables that are also controlled. These variables are controlled by holding all other factors constant. Any variable that an experimenter holds constant on purpose is called a control variable.

WHY EXPERIMENTS SUPPORT CAUSAL CLAIMS
There are three rules for something to be causal:

  1. Covariance
  2. Temporal precedence
  3. Internal validity

If independent variables did not vary, a study could not establish covariance, because you need a comparison group to establish covariance. It is impossible to establish internal validity if there are confounds, or alternative explanations. A design confound is an experimenter’s mistake in designing the independent variable. It is a second variable that happens to vary systematically along with the intended independent variable. Something is only a design confound if it shows systematic variability with the independent variable. It would not be a design confound if it shows unsystematic variability. If individual differences are distributed evenly in both groups, the are not a confound.

Selection effects are effects that are the result of two groups being systematically different from those in the other. This can also happen when the experimenters let participants choose in which group they want to be. The selection effects can be avoided by using random assignment, when assigning people to the conditions. Selection effects can also be avoided by using matched groups.

INDEPENDENT GROUP DESIGNS
In an independent group design both groups of participants are placed into different levels of the independent variable. This type of design is also called a between-subjects design or between-groups design. In a within-groups design or within-subjects design, there is only one group of participants and each person is pretended with all levels of the independent variable.

In the posttest-only design, also known as equivalent groups, participants are randomly assigned to independent variable groups. In a pretest/posttest design, participants are randomly assigned to at least two different groups and are tested on the key dependent variable twice, before and after exposure to the independent variable.

WITHIN-GROUPS DESIGNS
There are two basic types of within-groups design:

  1. Repeated-measures design
    In this design participants are measured on the dependent variable every time they are exposed to another level of the independent variable.
  2. Concurrent-measures design
    In this design participants are exposed to all the levels of an independent variable at roughly the same time.

The main advantage of a within-group design is that it ensures that participants in the two groups will be equivalent. The term

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