Interaction variable


Interaction variable

In statistics, an interaction variable is a variable often used in regression analysis. It is formed by the multiplication of two independent variables.

Example

There is a group of participants. Their postural control is being analysed and scored. Each participant performs 4 trials. These trials are based on two manipulated factors.

The two factors are stance (feet apart [S1] , feet together [S2] ) and vision (normal vision [V1] , blindfold [V2] ). So the four trials each participant completes are S1+V1, S1+V2, S2+V1, S2+V2.

Now with a repeated measures analysis of variance (ANOVA-RM), the data will be based on two within-subject factors (ie factors which the same subject can perform, as opposed to between subject factors such as gender, age group, intervention protocol, et cetera).

The ANOVA-RM will produce values indicating the probability that the difference is due to there being an actual difference (as opposed to the difference being the result of coincidence). Significance values will be obtained for each individual factor (ie main effects) as well as the significance of factor interrelationships (ie interaction effects). So an example of a main effect might be the ANOVA-RM returns a significance level of p=0.001 for the factor 'stance'. This means that there was a significant difference in performance, assuming p=0.001 (or a 0.1% probability that the result is due to chance and not an actual difference) is an acceptable level of significance. What this means is that 99.9% of the time, the difference between the feet apart and feet together conditions will be a result of there being an actual difference in performance associated with the stance (0.1% of the time it is due to coincidence).

With an interaction effect, a significant p-value is returned when multiple factors are considered, for example if stance*vision returns p=0.03. Whilst the significance of the interaction effect is less than that of the main effect, if the p=0.03 (97% of the time the result is due to the conditions, not coincidence) meets the pre-determined acceptable significance levels, interaction effects will take precedence over the main effects.

This means a main effect for stance or main effect for vision cannot be considered without acknowledging that an interaction effect was present.

What the interaction effect actually means in this example is that an interrelationship between the factors was found. So in this case, stance influences vision and/or vision influences stance (at least in some of the trials). Assuming the vision influencing stance is true, the postural control system will be more dependent upon vision when the stance condition is more difficult.

That is, in the feet together stance, there is a reduced base of support (so it is a more difficult stance to maintain). In this condition of a reduced base of support, the body might have to compensate by increasing the influence that visual feedback has on the balance control system.

Subsequently, even though the feet together trial might produce a reduced level of postural control compared to the feet apart trial (stance condition - main effect), the stance*vision interaction effect indicates that differences in performance associated with stance are influenced by visual feedback.

Where an interaction effect is present, it is necessary to run a post-hoc test (for example Scheffé test, Tukey test, Bonferroni test) to determine where abouts the interaction effect occurs. It may be found that there is only an interaction effect present between one or a few of the variables. In the case of a 2x2 design, there will be six possible interactions: V1S1-V1S2, V1S1-V2S1, V1S1-V2S2, V1S2-V2S1, V1S2-V2S2, V2S1-V2S2. For the present example it may be found that the post-hoc test identifies the significant values producing an interaction effect are V1S2-V2S2, V1S1-V1S2 and V2S1-V2S2. It is from here that conclusions can be drawn as to what has caused the interaction effect. It may be easier to identify an interaction effect where they are graphically represented.

This is demonstrated in the plot to the right (where PL/s or path length per second represents the velocity at which the centre of pressure is deviating in mm/s). It can be seen that the amount of change in score between vision and blindfolded conditions is not consistent between feet apart and feet together conditions.

References

*PDF| [http://pages.towson.edu/mchamber/chapter7eco306.pdf Using Indicator and Interaction Variables] |158 KiB

External links

* [http://foulger.info/davis/papers/statisticalInteraction1979.htm Credibility and the Statistical Interaction Variable: Speaking Up for Multiplication as a Source of Understanding]
* [http://www.ruf.rice.edu/~branton/interaction/faqfund.htm Fundamentals of Statistical Interactions: What is the difference between "main effects" and "interaction effects"? ]

Further reading

* James J. Jaccard, Robert Turrisi, "Interaction Effects in Multiple Regression", Sage Publications, 2003, ISBN 0-7619-2742-5

See also

*Dummy variable
*Interaction (statistics)


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Interaction (statistics) — In statistics, an interaction is a term in a statistical model added when the effect of two or more variables is not simply additive. Such a term reflects that the effect of one variable depends on the values of one or more other variables. Thus …   Wikipedia

  • Interaction information — The interaction information (McGill 1954) or co information (Bell 2003) is one of several generalizations of the mutual information, and expresses the amount information (redundancy or synergy) bound up in a set of variables, beyond that which is …   Wikipedia

  • Variable intensive et variable extensive — Extensivité intensivité Extensive et intensive sont des catégories de variables physiques. Prenons un exemple : si deux chevaux courent côte à côte et chacun à 60 km/h, à eux deux ils ne font pas un ensemble allant à 120 km/h, l ensemble va… …   Wikipédia en Français

  • Variable extensive — Extensivité intensivité Extensive et intensive sont des catégories de variables physiques. Prenons un exemple : si deux chevaux courent côte à côte et chacun à 60 km/h, à eux deux ils ne font pas un ensemble allant à 120 km/h, l ensemble va… …   Wikipédia en Français

  • Variable intensive — Extensivité intensivité Extensive et intensive sont des catégories de variables physiques. Prenons un exemple : si deux chevaux courent côte à côte et chacun à 60 km/h, à eux deux ils ne font pas un ensemble allant à 120 km/h, l ensemble va… …   Wikipédia en Français

  • Interaction électromagnétique — Électromagnétisme L électromagnétisme est la branche de la physique qui étudie le champ électromagnétique et son interaction avec les particules dotées d une charge électrique. Le concept de champ électromagnétique a été forgé au XIXe siècle pour …   Wikipédia en Français

  • Variable Specific Impulse Magnetoplasma Rocket — Artist s impression of several VASIMR engines propelling a craft through space The Variable Specific Impulse Magnetoplasma Rocket (VASIMR) is an electro magnetic thruster for spacecraft propulsion. It uses radio waves to ionize and heat a… …   Wikipedia

  • Variable cachée — En physique quantique, le terme de variable cachée désigne des paramètres physiques hypothétiques qui ne seraient pas pris en compte par les postulats de la mécanique quantique, soit dans la définition de l état quantique, ou dans l évolution… …   Wikipédia en Français

  • Variable Assembly Language — VAL is a computer based control system and language designed specifically for use with Unimation Inc. industrial robots.The VAL robot language is permanently stored as a part of the VAL system. This includes the programming language used to… …   Wikipedia

  • Dummy variable (statistics) — In statistics and econometrics, particularly in regression analysis, a dummy variable (also known as an indicator variable) is one that takes the values 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to …   Wikipedia