Covariates are characteristics of the participants in an experiment. These are characteristics outside of the actual treatment. If a researcher wants to compare means of multiple groups using the additional predictors, the covariates, then the ANCOVA is used. Examples of covariates could be love for puppies, softness of puppy fur. Covariates can be included in an ANOVA for two reasons:Reduce within-group error varianceThe unexplained variance is attributed to other variables, the covariates, which reduces the total error variance. This allows for a more sensitive test for the difference of group means.Elimination of confoundsBy adding other variables, covariates, in the analysis, confounds are eliminated. If there are covariates, the b-values represent the differences between the means of each group and the control adjusted for the covariate. ASSUMPTIONS AND ISSUES WITH ANCOVAThere are two new assumptions for ANCOVA that are not present with ANOVA. These assumptions are independence of the covariate and treatment effect and homogeneity of regression slopes. The ideal case is that the covariate is independent from the treatment effect. If the covariate is not independent from the treatment effect, then the covariate will reduce the experimental effect because it explains some of the variance that would otherwise be applicable to the experiment. The ANCOVA does not control for or balance out the differences caused by the covariate. The problem of covariates potentially explaining a bit of the data and wanting to filter these confounds is using randomizing participants to experimental groups or matching experimental groups on a covariate. Another assumption of the ANCOVA is that the relationship between covariate and outcome variable holds true for all groups of participants and not only for a few groups of participants (e.g. for both males and females and not only males). This assumption can be checked by checking the regression line...

Repeated-measures refers to when the same entities (e.g. people) participate in all conditions of an experiment or provide data at multiple points of time. One of the assumptions of the standard linear model is that residuals are independent, which is not true for repeated-measures designs. The residuals are affected by both between-participant factors and within-participant factors. There are two solutions to this:Model within-participant variabilityApply additional assumptions to make a simpler, less flexible model fitOne of these assumptions is sphericity (circularity). This assumption states that the relationship between scores in pairs of treatment conditions is similar (e.g. the level of dependence between means is roughly equal). It states that variation within conditions are similar and that no two conditions are any more dependent than any other two. Local sphericity refers to when some conditions do have equal variance and some do not. Sphericity is not relevant if there are only two groups. It becomes relevant when there are at least three conditions. The assumption of sphericity can be tested using Mauchly’s test. The degree of sphericity can be estimated using the Greenhouse-Geisser estimate or the Huyn-Feldt estimate. If the assumption of sphericity is not met, then there is a loss of power and the F-statistic doesn’t have the distribution it is supposed to have. In order to do post-hoc tests when you worry about whether the assumption of sphericity is violated, Bonferonni method can be used, if it is not violated, Tukey’s test can be used.If the assumption of sphericity is violated, the degrees of freedom has to be adjusted. The degrees of freedom is multiplied by the estimate of sphericity to calculate the adjusted degrees of freedom. F-STATISTIC OF REPEATED MEASURES DESIGNIn repeated measured designs, the within-groups variance consists of within-participant variance, as there is only one group of participants. This...

A multivariate analysis is used when there is more than one dependent (outcome) variable. It is possible to use several F-tests when there are several dependent variables, but this inflates the type-I error rate. A MANOVA can detect whether groups differ along a combination of dimensions. MANOVA has a greater potential power to detect an effect.A matrix is a grid of numbers arranged in columns and rows. The values within a matric are called components or elements and the rows and columns are vectors. A square matrix has an equal number of columns and rows. An identity matrix is a matrix where the diagonal numbers are ‘1’ and the non-diagonal numbers are ‘0’. The sum of squares and cross-products (SSCP) matrices are a way of operationalize multivariate versions of the sums of squares. The matrix that represents the systematic variance (model sum of squares) is denoted by the letter ‘H’ and is called the hypothesis sum of squares and cross-products matrix (hypothesis SCCP). The matrix that represents the unsystematic variance (residual sum of squares) is denoted by the letter ‘E’ and is called the error sums of squares and cross-products matrix (error SSCP). The matrix that represents the total sums of squares for each outcome (total SSCP) is denoted by the letter ‘T’.The cross-product is the total combined error between two variables. THEORY BEHIND MANOVAThe total sum of squares is calculated by calculating the difference between each of the scores and the mean of those scores, then squaring those differences and adding them together. The degrees of freedom is N-1. The model sum of squares is calculated by taking the difference between each group mean and the grand mean, squaring it, multiplying by the number of scores in the group and then adding it all together. The degrees of freedom is the sample size of each group minus one multiplied by the number of groups. The SST and the SSM then have to be divided by their own degrees of...

People can get more polarized opinions after they have read the same article if they started off with opposing beliefs. This can be due to misinterpreting the evidence (1), different motivation (2) or other cognitive malfunctions (3). Psychologists need to be critical thinkers, because they want to know the field and want to keep up with what is going on in the field of psychology. Critical thinking requires to check for scientific soundness and not whether a paper matches with pre-existing beliefs, assumptions or other forms of bias. Scepticism of scientists towards their own work is valuable, as they then do not show the confirmation bias. There are several expectations a critical reader should have:The research question flows naturally from the previous literature and the context.The literature review and the statement of the problem relate to the hypotheses.The hypotheses set up research design expectancies and suggest what variables should be manipulated, measured or controlled for.The hypotheses, appropriate design and type of data dictate the method of data analysis.The analysis influences the kind of conclusions, inferences and generalizations that can be made....

There is a publication bias in research. Mostly positive results – that is significant – are being published and non-significant results are often not published. This leads to researchers only trying to find significant results instead of genuine effects or non-effects. Researchers are more likely to find significant results because of flexible analysis options (1), the confirmation bias (2) and the drive to find significant results (3). It is possible to find significant results everywhere if you search hard enough. Direct replications do not occur often in research and are almost never published. There are several practices that can increase publishability but can decrease the validity of the results:Leveraging chance by running many low-powered studies instead of a few high-powered ones.Uncritically dismissing “failed” studies as pilot studies but uncritically accepting “successful” studies.Selectively reporting studies with positive results and not studies with negative results (cherry picking).Stopping data collection as soon as a reliable effect is obtained.Continuing data collection until a reliable effect is obtained.Including multiple independent and/or dependent variable and reporting the subset that “worked”.Maintaining flexibility in design and analytical models (attempt to exclude data)Reporting a discovery as if it had been the result of a confirmatory testNot doing a direct replication once a reliable effect is obtainedConceptual replication involves deliberately changing the operationalization of the key elements of the design such as the independent variable, dependent variable or both. Demonstrating the same effects with multiple operationalizations provides confidence in its conceptual interpretation. Conceptual replication is not an effective replacement for direct replication.The peer review process offers a way to detect false results. Not publishing articles without replications would also be effective in...