EXPERIMENTS WITH TWO INDEPENDENT VARIABLES CAN SHOW INTERACTIONSExperiments 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 differencesFACTORIAL DESIGNS STUDY TWO INDEPENDENT VARIABLESTesting 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 INTERACTONSResearchers 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...


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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 3 (UNIVERSITY OF AMSTERDAM)

      Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 9 summary

      Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 9 summary

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      STEPS FOR PERFORMING A SIGNIFICANCE TEST
      A hypothesis is a statement about the population. A significance test is a method for using data to summarize the evidence about a hypothesis. The null hypothesis (H0) is a statement that the parameter takes a particular value (e.g: probability of getting a baby girl: p = 0.482). The alternative hypothesis (Ha) states that the parameter falls in some alternative range of values. A significance test has five steps:

      1. Assumptions
        Each significance test has certain assumptions or has certain condition under which it applies (e.g: an assumption is the assumption that random sampling has been used).
      2. Hypotheses
        Each significance test has two hypotheses about a population parameter. The null hypothesis and the alternative hypothesis.
      3. Test statistic
        The parameter to which the hypotheses refer has a point estimate. A test statistic describes how far that point estimate falls from the parameter value given in the null hypothesis. This is usually measured in number of standard errors between the point estimate and the parameter.
      4. P-value
        A probability summary of the evidence against the null hypothesis is used to interpret a test statistic. The P-value is the probability that the test statistic equals the observed value or a value even more extreme. It is calculated by presuming that the null hypothesis is true.
      5. Conclusion
        The conclusion of the significance test reports the P-value and interprets what is says about the question that motivated the test.

      SIGNIFICANCE TESTS ABOUT PROPORTIONS
      The steps for the significance test are the same for proportions. The biggest assumption made here is that the sample size is large enough that the sampling distribution is approximately normal. The hypotheses are the following for significance tests about proportions:

       and or

      This is called a one-sided alternative hypothesis, because it has values falling only on one side of the null hypothesis value. A two-sided alternative hypothesis has the form of:

      The test statistic of a significance test about proportions is:

       or

      The P-value of a test statistic of a significance test about proportions is the left- or right-tail probability of a test statistic value even more extreme than observed. Smaller P-values indicate stronger evidence against the null hypothesis, because the data would be more unusual if the null hypothesis were true. In a two-sides test, the P-value is the probability of a single tail doubled. The significance level is a number such that we reject H0 if the P-value is less than or equal to that number. The most common significance level is 0.05. If the data provide evidence to reject H0 and accept Ha, the data is called statistically significant. If Ha is rejected, this does not mean that

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      Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 10 summary

      Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 10 summary

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      CATEGORICAL RESPONSE: COMPARING TWO PROPORTIONS:
      Bivariate methods is the general category of statistical methods used when we have two variables. The outcome variable on which comparisons are made is called the response variable. The binary variable that specifies the groups is the explanatory variable. In an independent sample, observations in one sample are independent from observations in another sample. If two samples have the same subjects, they are dependent. If each subject in one sample is matched with a subject in another sample there are matched pairs and the data is dependent as well.

      The formula for the standard error for comparing two proportions is:

      A 95% confidence interval for the difference between two population proportions has the following formula:

      The proportion (p̂) is called a pooled estimate, since it pools the total number of successes and total number of observations from two samples. This uses the presumption p1=p2. The test statistic uses the following formula:

      The standard error for the test statistic uses the following formula:

      QUANTITATIVE RESPONSE: COMPARING TWO MEANS:
      The standard error for comparing two means has the following formula:

      A 95% confidence interval for the difference between two population means has the following formula:

      The confidence interval for the difference between two population means uses the t-distribution and not the z-distribution. Interpreting a confidence interval for the difference of means uses the following criteria:

      1. Check whether or not 0 falls in the interval
        If it does, it could be that mean 1 is mean 2.
      2. Positive confidence interval suggests that mean 1 – mean 2 is positive
        If the confidence interval only contains positive numbers, this suggests that mean 1 – mean 2 is positive. This suggests that mean 1 is larger than mean 2.
      3. Negative confidence interval suggests that mean 1 – mean 2 is negative
        If the confidence interval only contains negative numbers, this suggests that mean 1 -  mean 2 is negative. This suggests that mean 1 is smaller than mean 2.
      4. Group order is arbitrary
        It is arbitrary whether one group is group one or the other.

      The test statistic of a significance test comparing two population means uses the following formula:

      It uses minus zero because the null hypothesis is that there is no difference between the groups and is thus zero.

      OTHER WAYS OF COMPARING MEANS AND COMPARING PROPORTIONS
      If it is reasonable to expect that the variability as

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      Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 11 summary

      Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 11 summary

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      INDEPENDENCE AND DEPENDENCE (ASSOCIATION)
      Conditional percentages refer to a sample data distribution, conditional on a category. They form the conditional distribution. If the probabilities for two different categorical variables are the same in the same category, then these variables are independent. If the probabilities for two different categorical variables differ, then these variables are dependent. Dependence refers to the population, so if there is barely any difference between two categorical variables in a sample, it could be independent, even though they differ.

      TESTING CATEGORICAL VARIABLES FOR INDEPENDENCE
      The expected cell count is the mean of the distribution for the count in any particular cell. The formula for the expected cell count is the following:

      The chi-squared statistic summarizes how far the observed cell counts in a contingency table fall from the expected cell counts for a null hypothesis. It is the test statistic for the test of independence. The formula for the chi-squared statistic is:

      The sampling distribution using the chi-squared statistic is called the chi-squared probability distribution. The chi-squared probability distribution has several properties:

      1. Always positive
      2. Shape depends on degrees of freedom
      3. Mean equals degrees of freedom
      4. As degrees of freedom increases the distribution becomes more bell shaped
      5. Large chi-square is evidence against independence

      The degrees of freedom in a table with r rows and c columns can be calculated as following:

      If a response variable is identified and the population conditional distributions are identical, they are said to be homogeneous. The chi-squared test is then referred to as a test of homogeneity. The degrees of freedom value in a chi-squared test indicates how many parameters are needed to determine all the comparisons for describing the contingency table. The chi-squared test can test for independence, but it cannot provide information about the strength and the direction of the associations and provide information about the practical significance, only about the statistical significance. When testing particular proportion values for a categorical variable, the chi-squared statistic is referred to as a goodness-of-fit statistic. The statistic summarizes how well the hypothesized values predict what happens with the observed data.

      DETERMINING THE STRENGTH OF THE ASSOCIATION
      A measure of association is a statistic or a parameter that summarizes the strength of the dependence between two variables. The association can be measured by looking at the difference of two associations. The formula for the difference of the two proportions is the following:

      The ratio of two proportions is also a measure of association. This is also called the relative risk. The relative risk uses the following formula:

      The relative risk has several properties:

      1. The relative risk can equal any non-negative number
      2. When p1=p2, the variables
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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 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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