order effect

Examples of order effect in the following topics:

• Tests Supplementing ANOVA

  • As will be seen, significant main effects in multi-factor designs can be followed up in the same way as significant effects in one-way designs.
  • Since an interaction means that the simple effects are different, the main effect as the mean of the simple effects does not tell the whole story.
  • It is not necessary to know whether the simple effects differ from zero in order to understand an interaction because the question of whether simple effects differ from zero has nothing to do with interaction except that if they are both zero there is no interaction.
  • It is not uncommon to see research articles in which the authors report that they analyzed simple effects in order to explain the interaction.
  • Since an interaction indicates that simple effects differ, it means that the main effects are not general.

• Further Discussion of ANOVA

  • Power analysis is often applied in the context of ANOVA in order to assess the probability of successfully rejecting the null hypothesis if we assume a certain ANOVA design, effect size in the population, sample size and significance level.
  • Jacob Cohen, an American statistician and psychologist, suggested effect sizes for various indexes, including $f$ (where $0.1$ is a small effect, $0.25$ is a medium effect and $0.4$ is a large effect).
  • He also offers a conversion table for eta-squared ($\eta^2$) where $0.0099$ constitutes a small effect, $0.0588$ a medium effect and $0.1379$ a large effect.
  • This can be performed in order to assess which groups are different from which other groups, or to test various other focused hypotheses.
  • Comparisons can also look at tests of trend, such as linear and quadratic relationships, when the independent variable involves ordered levels.

• Unequal Sample Sizes

  • The order in which the confounded sums of squares are apportioned is determined by the order in which the effects are listed.
  • The first effect gets any sums of squares confounded between it and any of the other effects.
  • The second gets the sums of squares confounded between it and subsequent effects, but not confounded with the first effect, etc.
  • Type I sums of squares allow the variance confounded between two main effects to be apportioned to one of the main effects.
  • As Tukey (1991) and others have argued, it is doubtful that any effect, whether a main effect or an interaction, is exactly 0 in the population.

• Statistical Power

  • Statistical power helps us answer the question of how much data to collect in order to find reliable results.
  • In statistical practice, it is possible to miss a real effect simply by not taking enough data.
  • For instance, we might miss a viable medicine or fail to notice an important side-effect.
  • The Magnitude of the Effect of Interest in the Population: The magnitude of the effect of interest in the population can be quantified in terms of an effect size, where there is greater power to detect larger effects.
  • Other things being equal, effects are harder to detect in smaller samples.

• Randomized Design: Single-Factor

  • Completely randomized designs study the effects of one primary factor without the need to take other nuisance variables into account.
  • In the design of experiments, completely randomized designs are for studying the effects of one primary factor without the need to take into account other nuisance variables.
  • denotes factorial) possible run sequences (or ways to order the experimental trials).
  • Because of the replication, the number of unique orderings is 90 (since $90=\frac{6!}
  • Discover how randomized experimental design allows researchers to study the effects of a single factor without taking into account other nuisance variables.

• ANOVA Design

  • ANOVA generalizes to the study of the effects of multiple factors.
  • Fortunately, experience says that high order interactions are rare.
  • Random effects models are used when the treatments are not fixed.
  • The fixed-effects model would compare a list of candidate texts.
  • Differentiate one-way, factorial, repeated measures, and multivariate ANOVA experimental designs; single and multiple factor ANOVA tests; fixed-effect, random-effect and mixed-effect models

• Interaction Models

  • An interaction variable is a variable constructed from an original set of variables in order to represent either all of the interaction present or some part of it.
  • When there are more than two explanatory variables, several interaction variables are constructed, with pairwise-products representing pairwise-interactions and higher order products representing higher order interactions.
  • In this example, there is no interaction between the two treatments — their effects are additive.
  • A table showing no interaction between the two treatments — their effects are additive.
  • A table showing an interaction between the treatments — their effects are not additive.

• Two-Way ANOVA

  • The two-way ANOVA can not only determine the main effect of contributions of each IV but also identifies if there is a significant interaction effect between the IVs.
  • In a factorial design multiple independent effects are tested simultaneously.
  • The combined effect is investigated by assessing whether there is a significant interaction between the factors.
  • The use of ANOVA to study the effects of multiple factors has a complication.
  • Fortunately, experience says that high order interactions are rare, and the ability to detect interactions is a major advantage of multiple factor ANOVA.

• Multi-Factor Between-Subjects Designs

  • The first two effects (Weight and Relationship) are both main effects.
  • A main effect of an independent variable is the effect of the variable averaging over the levels of the other variable(s).
  • In contrast to a main effect, which is the effect of a variable averaged across levels of another variable, the simple effect of a variable is the effect of the variable at a single level of another variable.
  • Always keep in mind that the lack of evidence for an effect does not justify the conclusion that there is no effect.
  • If you have three or more levels on the X-axis, you should not use lines unless there is some numeric ordering to the levels.

• Comparing Two Sample Averages

  • Student's t-test is used in order to compare two independent sample means.
  • In order to account for the variation, we take the difference of the sample means,
  • and divide by the standard error in order to standardize the difference.
  • For example, suppose we are evaluating the effects of a medical treatment.
  • By comparing the same patient's numbers before and after treatment, we are effectively using each patient as their own control.