What are the assumptions of a repeated measures t-test?
The common assumptions made when doing a t-test include those regarding the scale of measurement, random sampling, normality of data distribution, adequacy of sample size, and equality of variance in standard deviation.
Which assumption of the linear model is automatically violated in repeated measures designs?
The sphericity assumptionThe sphericity assumption was violated in these data.
What happens if normality assumption is violated repeated measures ANOVA?
If this assumption is violated, then this is a serious issue because the values of each individual may be related to each other in some way. Often the only remedy in this scenario is to recruit individuals for a new study using a random sampling method.
Which assumption of ANOVA is not needed in repeated measures ANOVA?
Repeated-measures ANOVA should not be conducted when the assumption of normality of difference scores is violated. Repeated-measures ANOVA should only be conducted on normally distributed continuous outcomes.
How do you know if a homoscedasticity assumption is violated?
A scatterplot in a busted homoscedasticity assumption would show a pattern to the data points. If you happen to see a funnel shape to your scatter plot this would indicate a busted assumption. Once again transformations are your best friends to correct a busted homoscedasticity assumption.
Does repeated measures ANOVA assume normality?
Finally, repeated measures ANOVA has assumptions of normality within each factor. Sure, it's robust to small departures of this assumption. And if the outcome variable is continuous, unbounded, and measured on an interval or ratio scale, you may be able to solve non-normality with a transformation.
What happens when normality assumption is violated?
If the assumption of normality is violated, or outliers are present, then the t test may not be the most powerful test available, and this could mean the difference between detecting a true difference or not. A nonparametric test or employing a transformation may result in a more powerful test.
What happens if linear regression assumptions are violated?
Violating multicollinearity does not impact prediction, but can impact inference. For example, p-values typically become larger for highly correlated covariates, which can cause statistically significant variables to lack significance. Violating linearity can affect prediction and inference.
What happens if sphericity is violated?
The violation of sphericity occurs when it is not the case that the variances of the differences between all combinations of the conditions are equal. If sphericity is violated, then the variance calculations may be distorted, which would result in an F-ratio that is inflated.
What are the 3 assumptions of ANOVA?
There are three primary assumptions in ANOVA: The responses for each factor level have a normal population distribution. These distributions have the same variance. The data are independent.
Is repeated measures ANOVA robust to violations of normality?
These assumptions need to be tested before you can run a repeated measures ANOVA. Fortunately, the repeated measures ANOVA is fairly "robust" to violations of normality. "Robust", in this case, means that the assumption can be violated (a little) and still provide valid results.
When the assumption of sphericity is violated what action is needed?
Answer: 8. When the assumption of sphericity is violated, what action is needed? Correct the model degrees of freedom and correct the error degrees of freedom.
What are the assumptions of the linear regression model?
There are four assumptions associated with a linear regression model: Linearity: The relationship between X and the mean of Y is linear. Homoscedasticity: The variance of residual is the same for any value of X. Independence: Observations are independent of each other.
What happens if independence assumption is violated?
In simple terms, if you violate the assumption of independence, you run the risk that all of your results will be wrong.
How do you check if a linear regression model violates the independence assumption?
To test for non-time-series violations of independence, you can look at plots of the residuals versus independent variables or plots of residuals versus row number in situations where the rows have been sorted or grouped in some way that depends (only) on the values of the independent variables.
What are the four assumptions of linear regression?
Assumptions in RegressionThere should be a linear and additive relationship between dependent (response) variable and independent (predictor) variable(s). ... There should be no correlation between the residual (error) terms. ... The independent variables should not be correlated. ... The error terms must have constant variance.More items...•
Variability and its sources
Variability is actually one of the cornerstones of statistics. We can very well estimate average effect sizes, but without a measure of variability these averages won’t tell us much.
Between- vs. within-subject effects
Consider a study where we have two measurements, baseline and follow-up (5 years later), of cognitive health scores (response) and the covariates sex and blood pressure. We can summarize this design as follows:
Variance of B and W
WARNING: compared to the previous sections, this one is quite mathy… It practically just contains derivations to arrive at two insightful equations that illustrate how the between- and within-subjects variability depend on the correlation between responses. Fasten your seatbelt!
Illustrative example
Remember the expressions for the between- and within-subjects variance:
What is repeated measure analysis?
Repeated measure analysis involves a ‘within subject’ design. The true ‘within subject’ design in this repeated measure analysis is a design in which each subject is measured under each treatment condition. Similar analyses include a repeated measures ANOVA, MANOVA, and dependent sample t -test, as well as the non-parametric Wilcoxon signed rank test. The repeated measures design in this repeated measure analysis is a design in which each subject is measured at two or more points with respect to time. The profile analysis design in this repeated measure analysis is that which involves the comparison of the scores of the different tests that are comparably scaled.
How does repeated measure design work?
The repeated measure design mechanically removes the individual differences from the between treatments variability as the same subjects are being used in every condition. In the case of the ANOVA/MANOVA, individual differences are removed from the denominator of the F-test.
What happens if the value of F statistic is violated?
If this assumption of sphericity is violated, then the value of F statistic will come out with severely biased results. In other words, if the assumption of sphericity is violated, then the researcher might end up committing Type I error.
What happens if you violate the assumption of sphericity?
If this assumption of sphericity is violated, then the value of F statistic will come out with severely biased results. In other words, if the assumption of sphericity is violated, then the researcher might end up committing Type I error.
How to measure effect size?
The common technique for measuring an effect size in this type of repeated measure analysis is to compute the percentage of variance that has been explained by the treatment effects. For a dependent sample t -test, the effect size is measured by cohen’s d . For ANOVA/MANOVA, the effect size is identified as parital eta squared. The researcher should keep in mind that before computing the effect size it is necessary to eliminate the individual differences between the subjects.
What is repeated measures ANOVA?
Repeated-measures ANOVA refers to a class of techniques that have traditionally been widely applied in assessing differences in nonindependent mean values.6In the most simple case, there is only 1 within-subject factor (one-way repeated-measures ANOVA; see Figures Figures11and and22for the distinguishing within- versus between-subject factors).19In the situation where there are only 2 related means, the repeated-measures ANOVA provides identical results as the paired ttest. As noted in a previous tutorial, the tested null hypothesis is that the mean of all the differences between the 2 related measurements is zero.20
Which class of analysis is historically prevalent and comprises the repeated-measures ANOVA type of analysis?
The second class is historically prevalent and comprises the repeated-measures ANOVA type of analysis.6
What is a multivariate ANOVA?
Multivariate ANOVA (MANOVA) does not assume a specific correlation structure or sphericity and is therefore a popular alternative to repeated-measures ANOVA. 23Similarly to ANOVA, MANOVA also tests for main effects as well as for the interaction.6,24However, MANOVA also shares many of the limitations of ANOVA described in the next paragraph. Note that the term “multivariate” is commonly misused in literature to describe models with multiple independent (predictor) variables. In reality, multivariate means that there are multiple (correlated) outcomes—like an outcome repeatedly measured over time.
What is a two way mixed ANOVA?
Schematic representation of a two-way (two-factor) mixed ANOVA. The model includes a within-subject factor (Figure (Figure1),1), but also a between-subject factor. Factors that vary between subjects are between-subject factors (here: a part of the subjects are assigned to treatment A, but other subjects are assigned to treatment B). A two-way mixed ANOVA tests for differences in the mean values of the outcome variable between the factor levels of the within-subject factor, between the factor levels of the between-subject factor, as well as the interaction of the 2. ANOVA indicates analysis of variance.
What are the advantages and disadvantages of using a condensed number?
A main advantage to this approach is that it is very simple but yet provides valid results, and the technique and results are easily understood by clinicians with a limited statistical background. Obviously, a major drawback is that a substantial amount of information is lost when all individual measurements are condensed in a single number.
What is the difference between independent and dependent variables?
The factors that are considered to have an effect on an outcome in a statistical model are commonly termed independent variables (or explanatory variables, predictor variables, or covariates), whereas the outcome variable is termed the dependent variable. 5,11This has nothing to do with dependent or independent in the sense whether observations of the outcome variable have been made in the same individuals. Most statistical analysis techniques assume observed or measured values of the dependent variable to be independent from each other,5and this tutorial describes techniques that can be used when this key assumption is violated.
What does "repetitio est mater studiorum" mean?
Repetitio est mater studiorum[Repetition is the mother of learning].
What are the assumptions in repeated measures ANOVA?
In repeated measures ANOVA containing repeated measures factors with more than two levels, additional special assumptions enter the picture: The compound symmetry assumption and the assumption of sphericity. Because these assumptions rarely hold (see below), the MANOVA approach to repeated measures ANOVA has gained popularity in recent years (both tests are automatically computed in ANOVA/MANOVA).
When the compound symmetry or sphericity assumptions have been violated, the univariate A?
When the compound symmetry or sphericity assumptions have been violated, the univariate ANOVA table will give erroneous results. Before multivariate procedures were well understood, various approximations were introduced to compensate for the violations (e.g., Greenhouse & Geisser, 1959; Huynh & Feldt, 1970), and these techniques are still widely used (therefore, ANOVA/MANOVA and GLM provide those methods).
What does it mean to repeat the point?
To repeat the point, this means that the differences between the levels of the respective repeated measures factors are in some way correlated across subjects. Sometimes, this insight by itself is of considerable interest.
How to look at ANOVA?
One general way of looking at ANOVA is to consider it a model fitting procedure. In a sense we bring to our data a set of a priori hypotheses; we then partition the variance (test main effects, interactions) to test those hypotheses. Computationally, this approach translates into generating a set of contrasts (comparisons between means in the design) that specify the main effect and interaction hypotheses. However, if these contrasts are not independent of each other, then the partitioning of variances runs afoul. For example, if two contrasts A and B are identical to each other and we partition out their components from the total variance, then we take the same thing out twice. Intuitively, specifying the two (not independent) hypotheses "the mean in Cell 1 is higher than the mean in Cell 2" and "the mean in Cell 1 is higher than the mean in Cell 2" is silly and simply makes no sense. Thus, hypotheses must be independent of each other, or orthogonal (the term orthogonality was first used by Yates, 1933).
Can MANOVA be used for univariate tests?
ANOVA/MANOVA will detect those instances and only compute the univariate tests.
What happens if you violate assumptions in an analysis?
Violations of the assumptions of your analysis impact your ability to trust your results and validly draw inferences about your results. For a brief overview of the importance of assumption testing, check out our previous blog. When the assumptions of your analysis are not met, you have a few options as a researcher.
What is the problem when assumptions are not met?
When the assumptions of your analysis are not met, you have a few options as a researcher. Data transformation: A common issue that researchers face is a violation of the assumption of normality. Numerous statistics texts recommend data transformations, such as natural log or square root transformations, to address this violation (see Rummel, 1988).
What is non-parametric analysis?
Non-parametric analysis: You may encounter issues where multiple assumptions are violated, or a data transformation does not correct the violated assumption. In these cases, you may opt to use non-parametric analyses.
Is a non-parametric analysis more powerful than a parametric analysis?
There are non-parametric alternatives to the common parametric analyses so you will not be limited in the type of analysis you can conduct. However, although non- parametric analyses are beneficial because they are free of the assumptions of parametric analyses, they are generally considered less powerful than parametric analyses.
What is the error rate of a type 1 ANOVA?
The simulated type 1 error rate for the univariate ANOVA with a Greenhouse-Geisser correction is now 4.82% and it is 5.36% with a Huynh-Feldt correction. After we determine which analysis approach best preserves the Type 1 error rate, given assumptions about the data generation model (e.g., the standard deviations and correlations) we could then re-run the simulation with the pattern of means we want to detect and estimate the power for the given design. This way, we control our Type 1 error rate, and can estimate our statistical power for an analysis that handles violations of the sphericity assumption.
What is the purpose of superpower in ANOVA?
We can also use Superpower to estimate the impact of violating the assumption of sphericity on the type 1 error rate for a simple one-way repeated measures ANOVA . The sphericity assumption entails that the variances of the differences between all possible pairs of within-subject conditions (i.e., levels of the independent variable) are equal. This assumption is often tenuous at best in real life, and is typically “adjusted” for by applying a sphericity correction (e.g, Greenhouse-Geisser or Huynh-Feldt adjusted output).
Can simulations be used for power analyses?
So far we have shown how simulations can be useful for power analyses for ANOVA designs where all assumptions of the statistical tests are met. An ANOVA is quite robust against violations of the normality assumption, which means the Type 1 error rate remains close to the alpha level specified in the test. Violations of the homogeneity of variances assumption can be more impactful, especially when sample sizes are unequal between conditions. When the equal variances assumption is violated for a one-way ANOVA, Welch’s F -test is a good default.
Does ANOVA have type 1 error?
As we saw above, the unadjusted repeated measures ANOVA has an elevated type I error rate, but the MANOVA analysis and corrections control Type 1 error rates well.
