STEPS FOR PERFORMING A SIGNIFICANCE TESTA 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:AssumptionsEach 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).HypothesesEach significance test has two hypotheses about a population parameter. The null hypothesis and the alternative hypothesis.Test statisticThe 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.P-valueA 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.ConclusionThe conclusion of the significance test reports the P-value and interprets what is says about the question that motivated the test.SIGNIFICANCE TESTS ABOUT PROPORTIONSThe 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...
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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:Check whether or not 0 falls in the intervalIf it does, it could be that mean 1 is mean 2.Positive confidence interval suggests that mean 1 – mean 2 is positiveIf 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.Negative confidence interval suggests that mean 1 – mean 2 is negativeIf the confidence interval only contains negative numbers, this suggests...
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 INDEPENDENCEThe 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:Always positiveShape depends on degrees of freedomMean equals degrees of freedomAs degrees of freedom increases the distribution becomes more bell shapedLarge chi-square is evidence against independenceThe 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...
There are two historical examples of studies that violated several ethical criteria.Tuskegee Syphilis StudyThis 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. Milgram Obedience StudiesThis 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:Principle of respect for personsThis 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.The principle of beneficenceResearchers 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. The principle of justiceThis 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:Fidelity and...
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:ThreatWhat happens?When?SolutionMaturation threatA change in behaviour occurs more or less spontaneously over time. People adapt to changed environments. One-group, pre-test/post-test designUsing a comparison groupHistory threatA 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 designUsing a comparison groupRegression threatIf 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 designUsing a comparison groupAttrition threatA 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 designNot using the scores of participants that dropped outTesting threatThere is a change in the participants as a result of taking a test more than once (e.g: participants might become better at a test if they practice). Participants change over time.Pre-test/post-test designAbandoning the pre-test or using a comparison group.Instrumentation threatA measuring instrument changes over time (e.g: observers change the way they observe behaviour over time or two different instruments are used in the pre-test and the post-test that are...
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...
QUASI-EXPERIMENTSA 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:ThreatDefinitionSelection effectThe participants of one level of the independent variable are systematically different from other participants at another level of the independent variable.Design confoundsIn a design confound, some outside variable systematically varies the levels of the targeted independent variable.Maturation threatAn observed change has emerged more or less spontaneously over time.History threatAn 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 meanA measure is extreme and will thus (almost) always be less extreme and more closely to the mean on the next measurement.Attrition threatCertain kinds of participants drop out systematically (e.g: only the most depressed people drop out).Testing threatA testing threat is an...
TO BE IMPORTANT, A STUDY MUST BE REPLICATEDReplication gives a study credibility, and it is a crucial part of the scientific process. There are several types of replication:Direct replicationResearchers repeat an original study as closely as they can to see whether the effect is the same in the newly collected data. Conceptual replicationResearchers explore the same research question, but use different procedures. In this replication, the conceptual variables are the same, but the operationalizations are not.Replication-plus-extensionResearchers 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:Open scienceSharing one’s data and materials freely.Larger sample sizesMost studies and replications require much larger sample sizes nowadays.PreregistrationPreregistering 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...