what does a research need to do when conducting a repeated measures design?

Repeated Measures Blueprint

Repeated measures analysis of variance (rANOVA) is one of the almost commonly used statistical approaches to repeated measures designs.

Learning Objectives

Evaluate the significance of repeated measures blueprint given its advantages and disadvantages

Key Takeaways

Cardinal Points

• Repeated measures design, as well known as within-subjects blueprint, uses the same subjects with every status of the inquiry, including the control.
• Repeated measures design can exist used to conduct an experiment when few participants are bachelor, carry an experiment more efficiently, or to study changes in participants' behavior over time.
• The master strengths of the repeated measures blueprint is that it makes an experiment more efficient and helps keep the variability low.
• A disadvantage of the repeated measure out blueprint is that it may not be possible for each participant to be in all conditions of the experiment (due to time constraints, location of experiment, etc.).
• One of the greatest advantages to using the rANOVA, as is the case with repeated measures designs in general, is that you are able to partition out variability due to individual differences.
• The rANOVA is still highly vulnerable to furnishings from missing values, imputation, unequivalent time points between subjects, and violations of sphericity — factors which tin lead to sampling bias and inflated levels of type I fault.

Key Terms

• longitudinal study: A correlational research study that involves repeated observations of the aforementioned variables over long periods of time.
• sphericity: A statistical supposition requiring that the variances for each fix of deviation scores are equal.
• society effect: An outcome that occurs when a participant in an experiment is able to perform a chore and then perform information technology over again at some afterward time.

Repeated measures design (also known as "within-subjects design") uses the same subjects with every condition of the research, including the command. For instance, repeated measures are collected in a longitudinal study in which change over fourth dimension is assessed. Other studies compare the same measure under two or more different conditions. For case, to test the effects of caffeine on cognitive function, a subject's math ability might be tested once later on they consume caffeine and another time when they swallow a placebo.

Repeated Measures Pattern: An example of a examination using a repeated measures design to exam the effects of caffeine on cognitive function. A subject area'south math ability might be tested once subsequently they consume a caffeinated cup of coffee, and once more when they consume a placebo.

Repeated measures design can be used to:

• Conduct an experiment when few participants are available: The repeated measures blueprint reduces the variance of estimates of treatment-effects, allowing statistical inference to be fabricated with fewer subjects.
• Bear experiment more than efficiently: Repeated measures designs let many experiments to be completed more quickly, as but a few groups need to be trained to complete an entire experiment.
• Study changes in participants' beliefs over time: Repeated measures designs permit researchers to monitor how the participants change over the passage of time, both in the example of long-term situations like longitudinal studies and in the much shorter-term case of order furnishings.

Advantages and Disadvantages

The principal strengths of the repeated measures pattern is that it makes an experiment more efficient and helps keep the variability depression. This helps to go on the validity of the results higher, while still allowing for smaller than usual subject area groups.

A disadvantage of the repeated measure out design is that it may not be possible for each participant to be in all conditions of the experiment (due to time constraints, location of experiment, etc.). At that place are also several threats to the internal validity of this blueprint, namely a regression threat (when subjects are tested several times, their scores tend to regress towards the hateful), a maturation threat (subjects may change during the class of the experiment) and a history threat (events outside the experiment that may change the response of subjects between the repeated measures).

Repeated Measures ANOVA

Repeated measures assay of variance (rANOVA) is one of the about commonly used statistical approaches to repeated measures designs.

Partitioning of Error

One of the greatest advantages to using the rANOVA, as is the case with repeated measures designs in general, is that you are able to partition out variability due to individual differences. Consider the general structure of the [latex]\text{F}[/latex]– statistic:

[latex]\text{F} = \dfrac{\text{MS}_{\text{treatment}}}{\text{MS}_{\text{error}}} = \dfrac{\text{SS}_{\text{treatment}} / \text{df}_{\text{treatment}}}{\text{SS}_{\text{error}} / \text{df}_{\text{error}}}[/latex]

In a between-subjects design at that place is an element of variance due to individual divergence that is combined in with the treatment and error terms:

[latex]\text{SS}_{\text{full}} = \text{SS}_{\text{treatment}} + \text{SS}_{\text{error}}[/latex]
[latex]\text{df}_{\text{full}} = \text{northward}-1[/latex]

In a repeated measures design information technology is possible to account for these differences, and partition them out from the treatment and error terms. In such a instance, the variability can be cleaved downward into between-treatments variability (or inside-subjects effects, excluding private differences) and inside-treatments variability. The within-treatments variability can exist farther partitioned into between-subjects variability (individual differences) and error (excluding the individual differences).

[latex]\text{SS}_{\text{full}} = \text{SS}_{\text{treatment}} + \text{SS}_{\text{subjects}} + \text{SS}_{\text{fault}}[/latex]

[latex]\begin{align} \text{df}_{\text{full}} &= \text{df}_{\text{treatment}} + \text{df}_{\text{betwixt subjects}} + \text{df}_{\text{error}}\\ &= (\text{k}-1) + (\text{due north}-ane) + ((\text{north}-\text{k})-(\text{n}-ane)) \terminate{align}[/latex]

In reference to the general structure of the [latex]\text{F}[/latex]-statistic, information technology is clear that by segmentation out the between-subjects variability, the [latex]\text{F}[/latex]-value will increase considering the sum of squares mistake term volition exist smaller resulting in a smaller [latex]\text{MS}_{\text{error}}[/latex]. It is noteworthy that partitioning variability pulls out degrees of liberty from the [latex]\text{F}[/latex]-test, therefore the between-subjects variability must be significant enough to offset the loss in degrees of freedom. If between-subjects variability is small this process may actually reduce the [latex]\text{F}[/latex]-value.

Assumptions

Every bit with all statistical analyses, there are a number of assumptions that should be met to justify the employ of this test. Violations to these assumptions tin moderately to severely affect results, and often lead to an inflation of blazon one fault. Univariate assumptions include:

1. Normality: For each level of the within-subjects cistron, the dependent variable must take a normal distribution.
2. Sphericity: Deviation scores computed betwixt two levels of a within-subjects factor must take the same variance for the comparison of any two levels.
3. Randomness: Cases should be derived from a random sample, and the scores between participants should be independent from each other.

The rANOVA also requires that certain multivariate assumptions are met considering a multivariate test is conducted on difference scores. These include:

1. Multivariate normality: The deviation scores are multivariately normally distributed in the population.
2. Randomness: Private cases should be derived from a random sample, and the divergence scores for each participant are independent from those of another participant.

[latex]\text{F}[/latex]-Test

Depending on the number of within-subjects factors and supposition violates, it is necessary to select the most advisable of three tests:

1. Standard Univariate ANOVA [latex]\text{F}[/latex]-test: This test is unremarkably used when there are only two levels of the inside-subjects cistron. This test is not recommended for use when there are more than 2 levels of the inside-subjects cistron considering the assumption of sphericity is usually violated in such cases.
2. Alternative Univariate examination: These tests account for violations to the assumption of sphericity, and can be used when the within-subjects factor exceeds 2 levels. The [latex]\text{F}[/latex] statistic will be the same as in the Standard Univariate ANOVA F test, merely is associated with a more than accurate [latex]\text{p}[/latex]-value. This correction is done past adjusting the [latex]\text{df}[/latex] downward for determining the critical [latex]\text{F}[/latex] value.
3. Multivariate Examination: This test does not assume sphericity, but is also highly conservative.

While there are many advantages to repeated-measures blueprint, the repeated measures ANOVA is non always the best statistical analyses to conduct. The rANOVA is however highly vulnerable to effects from missing values, imputation, unequivalent time points betwixt subjects, and violations of sphericity. These issues can consequence in sampling bias and inflated rates of type I error.

Farther Discussion of ANOVA

Due to the iterative nature of experimentation, preparatory and follow-up analyses are often necessary in ANOVA.

Learning Objectives

Contrast preparatory and follow-up analysis in constructing an experiment

Key Takeaways

Key Points

• Experimentation is frequently sequential, with early experiments often beingness designed to provide a mean -unbiased estimate of treatment effects and of experimental fault, and later experiments often being designed to test a hypothesis that a treatment effect has an important magnitude.
• Power analysis is often practical in the context of ANOVA in guild to assess the probability of successfully rejecting the zilch hypothesis if we assume a sure ANOVA design, effect size in the population, sample size and significance level.
• Effect size estimates facilitate the comparison of findings in studies and beyond disciplines.
• A statistically significant effect in ANOVA is often followed upwardly with ane or more than different follow-up tests, in order to assess which groups are different from which other groups or to test various other focused hypotheses.

Primal Terms

• iterative: Of a process that involves repetition of steps (iteration) to achieve the desired outcome.
• homoscedasticity: A property of a set of random variables where each variable has the same finite variance.

Some assay is required in back up of the design of the experiment, while other analysis is performed subsequently changes in the factors are formally found to produce statistically significant changes in the responses. Because experimentation is iterative, the results of one experiment alter plans for following experiments.

Preparatory Assay

The Number of Experimental Units

In the design of an experiment, the number of experimental units is planned to satisfy the goals of the experiment. Most often, the number of experimental units is called so that the experiment is within budget and has adequate ability, among other goals.

Experimentation is often sequential, with early experiments often existence designed to provide a mean-unbiased judge of treatment effects and of experimental fault, and later experiments often beingness designed to test a hypothesis that a treatment issue has an important magnitude.

Less formal methods for selecting the number of experimental units include graphical methods based on limiting the probability of imitation negative errors, graphical methods based on an expected variation increment (in a higher place the residuals ) and methods based on achieving a desired conviction interval.

Power Analysis

Ability analysis is ofttimes practical in the context of ANOVA in society to assess the probability of successfully rejecting the nothing hypothesis if we assume a sure ANOVA design, effect size in the population, sample size and significance level. Power analysis can assist in written report design by determining what sample size would be required in social club to take a reasonable chance of rejecting the null hypothesis when the culling hypothesis is truthful.

Effect Size

Upshot size estimates facilitate the comparison of findings in studies and across disciplines. Therefore, several standardized measures of result guess the forcefulness of the association between a predictor (or set of predictors) and the dependent variable.

Eta-squared ([latex]\eta^two[/latex]) describes the ratio of variance explained in the dependent variable by a predictor, while decision-making for other predictors. Eta-squared is a biased estimator of the variance explained past the model in the population (it estimates but the effect size in the sample). On average, it overestimates the variance explained in the population. As the sample size gets larger the amount of bias gets smaller:

[latex]\eta^2 = \dfrac{\text{SS}_{\text{treatment}}}{\text{SS}_{\text{total}}}[/latex]

Jacob Cohen, an American statistician and psychologist, suggested effect sizes for various indexes, including [latex]\text{f}[/latex] (where [latex]0.1[/latex] is a pocket-size effect, [latex]0.25[/latex] is a medium effect and [latex]0.4[/latex] is a big effect). He also offers a conversion table for eta-squared ([latex]\eta^two[/latex]) where [latex]0.0099[/latex] constitutes a small effect, [latex]0.0588[/latex] a medium effect and [latex]0.1379[/latex] a big effect.

Follow-Up Analysis

Model Confirmation

Information technology is prudent to verify that the assumptions of ANOVA have been met. Residuals are examined or analyzed to confirm homoscedasticity and gross normality. Residuals should have the appearance of (zero hateful normal distribution) racket when plotted every bit a role of annihilation including time and modeled information values. Trends hint at interactions among factors or amongst observations. One rule of thumb is: if the largest standard deviation is less than twice the smallest standard deviation, nosotros can apply methods based on the assumption of equal standard deviations, and our results will however be approximately right.

Follow-Upwardly Tests

A statistically significant effect in ANOVA is oftentimes followed up with i or more different follow-upwards tests. This can be performed in lodge to assess which groups are dissimilar from which other groups, or to test various other focused hypotheses. Follow-upward tests are frequently distinguished in terms of whether they are planned (a priori) or post hoc. Planned tests are determined before looking at the data, and mail hoc tests are performed later looking at the information.

Post hoc tests, such as Tukey'due south range test, most commonly compare every grouping mean with every other grouping mean and typically comprise some method of decision-making for type I errors. Comparisons, which are most commonly planned, can be either elementary or chemical compound. Simple comparisons compare one group hateful with one other grouping hateful. Compound comparisons typically compare two sets of groups means where one gear up has ii or more than groups (east.yard., compare average grouping ways of groups [latex]\text{A}[/latex], [latex]\text{B}[/latex], and [latex]\text{C}[/latex] with that of group [latex]\text{D}[/latex]). Comparisons can also look at tests of tendency, such as linear and quadratic relationships, when the independent variable involves ordered levels.

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Source: https://courses.lumenlearning.com/boundless-statistics/chapter/repeated-measures-anova/

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