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| In [[statistics]], an '''interaction'''<ref name=Dodge>{{cite book | last=Dodge | first=Y. | year=2003 | title=''The Oxford Dictionary of Statistical Terms'' | publisher=Oxford University Press | isbn=0-19-920613-9}}</ref><ref>{{cite journal | doi=10.2307/1403235 | last=Cox | first=D.R. | year=1984 | title=Interaction | journal=International Statistical Review | volume=52 | pages=1–25 | jstor=1403235 | issue=1 | publisher=International Statistical Review / Revue Internationale de Statistique}}</ref> may arise when considering the relationship among three or more variables, and describes a situation in which the simultaneous influence of two variables on a third is not [[additive function|additive]]. Most commonly, interactions are considered in the context of [[regression analysis|regression analyses]]. | | In case you adored this post as well as you would like to obtain more info with regards to [http://circuspartypanama.com gem Hack clash of Clans] kindly visit the website. Hold a [http://photo.net/gallery/tag-search/search?query_string=video+game video game] contest. These can be a lot amongst fun for you and then your gaming friends. You may do this online, at your home or at a pals place. Serve amazing snacks and get several people as you could possibly involved. This is a great way to enjoy your amazing game playing with buddies.<br><br>Home business inside your games when you find yourself ready playing them. A variety of retailers provide discount percentage rates or credit score to help your next buy when ever you business your clash of clans sur pc tlcharger for. You can find the next online video you would like relating to the affordable price immediately after you try this. All things considered, clients don't need the graphics games as soon since you defeat them.<br><br>Equipment games offer entertaining to everybody, and they could be surely more complicated as compared to Frogger was! As a way to get all you also can out of game titles, use the advice put down out here. An individual going to find one exciting new world inside of gaming, and you undoubtedly wonder how you previously got by without individuals!<br><br>Ideal some online games provde the comfort of setting up a true-entire world time accessible in the video clip clip game itself. This particular really is usually a downside in full-monitor game titles. You don't want the parties using up even more of your time and after that energy than within your budget place a season clock of your particular to your display movie screen to be able to help you monitor just how you've been enjoying.<br><br>Conserve some money on some games, think about following into a assistance that you can rent payments console games from. The worth of these lease commitments for the year is now normally under the cost of two video game. You can preserve the online titles until you do more than them and simply pass out them back remember and purchase another one in particular.<br><br>At master game play throughout the shooter video games, pro your weapons. Have an understanding of everything there is learn about each and every weapon style in recreation. Each weapon excels when certain ways, but lies short in others. When you know i would say the pluses and minuses at each weapon, you can use them to king advantage. |
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| The presence of interactions can have important implications for the interpretation of statistical models. If two variables of interest interact, the relationship between each of the interacting variables and a third "dependent variable" depends on the value of the other interacting variable. In practice, this makes it more difficult to predict the consequences of changing the value of a variable, particularly if the variables it interacts with are hard to measure or difficult to control.
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| The notion of "interaction" is closely related to that of "[[Moderation (statistics)|moderation]]" that is common in social and health science research: the interaction between an explanatory variable and an environmental variable suggests that the effect of the explanatory variable has been moderated or modified by the environmental variable.<ref name=Dodge />
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| ==Introduction==
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| An "interaction variable" is a variable constructed from an original set of variables to try to represent either all of the interaction present or some part of it. In exploratory statistical analyses it is common to use products of original variables as the basis of testing whether interaction is present with the possibility of substituting other more realistic interaction variables at a later stage. 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.
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| [[Image:Quantitative interaction.svg|right|thumb|250px|The binary factor ''A'' and the quantitative variable ''X'' interact (are non-additive) when analyzed with respect to the outcome variable ''Y''.]] | |
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| Thus, for a response ''Y'' and two variables ''x''<sub>1</sub> and ''x''<sub>2</sub> an ''additive'' model would be:
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| :<math>Y = c + ax_1 + bx_2 + \text{error}\,</math>
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| In contrast to this,
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| :<math>Y = c + ax_1 + bx_2 + d(x_1\times x_2) + \text{error} \,</math>
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| is an example of a model with an ''interaction'' between variables ''x''<sub>1</sub> and ''x''<sub>2</sub> ("error" refers to the [[random variable]] whose value is that by which ''Y'' differs from the [[expected value]] of ''Y''; see [[errors and residuals in statistics]]).
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| ==Interaction variables in modeling==
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| ===Interactions in ANOVA===
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| A simple setting in which interactions can arise is a [[factorial experiment|two-factor experiment]] analyzed using [[Analysis of Variance]] (ANOVA). Suppose we have two binary factors ''A'' and ''B''. For example, these factors might indicate whether either of two treatments were administered to a patient, with the treatments applied either singly, or in combination. We can then consider the average treatment response (e.g. the symptom levels following treatment) for each patient, as a function of the treatment combination that was administered. The following table shows one possible situation:
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| {| cellpadding="5" cellspacing="0" align="center"
| |
| |-
| |
| !
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| ! style="background:#ffdead;border-left:1px solid black;border-top:1px solid black;" | ''B'' = 0
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| ! style="background:#ffdead;border-top:1px solid black;border-right:1px solid black;" | ''B'' = 1
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| |-
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| ! style="background:#ffdead;border-left:1px solid black;border-top:1px solid black;" | ''A'' = 0
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| ! style="border-left:1px solid black;" | 6
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| ! style="border-right:1px solid black;" | 7
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| |-
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| ! style="background:#ffdead;border-bottom:1px solid black;border-left:1px solid black;" | ''A'' = 1
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| ! style="border-bottom:1px solid black;border-left:1px solid black;" | 4
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| ! style="border-bottom:1px solid black;border-right:1px solid black;" | 5
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| |}
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| In this example, there is no interaction between the two treatments — their effects are additive. The reason for this is that the difference in mean response between those subjects receiving treatment ''A'' and those not receiving treatment ''A'' is −2 regardless of whether treatment ''B'' is administered (−2 = 4 − 6) or not (−2 = 5 − 7). Note that it automatically follows that the difference in mean response between those subjects receiving treatment ''B'' and those not receiving treatment ''B'' is the same regardless of whether treatment ''A'' is administered (7 − 6 = 5 − 4).
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| In contrast, if the following average responses are observed
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| {| cellpadding="5" cellspacing="0" align="center"
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| |-
| |
| !
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| ! style="background:#ffdead;border-left:1px solid black;border-top:1px solid black;" | ''B'' = 0
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| ! style="background:#ffdead;border-top:1px solid black;border-right:1px solid black;" | ''B'' = 1
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| |-
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| ! style="background:#ffdead;border-left:1px solid black;border-top:1px solid black;" | ''A'' = 0
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| ! style="border-left:1px solid black;" | 1
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| ! style="border-right:1px solid black;" | 4
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| |-
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| ! style="background:#ffdead;border-bottom:1px solid black;border-left:1px solid black;" | ''A'' = 1
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| ! style="border-bottom:1px solid black;border-left:1px solid black;" | 7
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| ! style="border-bottom:1px solid black;border-right:1px solid black;" | 6
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| |}
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| then there is an interaction between the treatments — their effects are not additive. Supposing that greater numbers correspond to a better response, in this situation treatment ''B'' is helpful on average if the subject is not also receiving treatment ''A'', but is more helpful on average if given in combination with treatment ''A''. Treatment ''A'' is helpful on average regardless of whether treatment ''B'' is also administered, but it is more helpful in both absolute and relative terms if given alone, rather than in combination with treatment ''B''.
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| ===Qualitative and quantitative interactions===
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| In many applications it is useful to distinguish between qualitative and quantitative interactions.<ref>{{cite book | last=Peto | first=DP | year=1982 | title=Statistical aspects of cancer trials (first ed.) | publisher=Chapman and Hall, London}}</ref> A quantitative interaction between ''A'' and ''B'' refers to a situation where the magnitude of the effect of ''B'' depends on the value of ''A'', but the direction of the effect of ''B'' is constant for all ''A''. A qualitative interaction between ''A'' and ''B'' refers to a situation where both the magnitude and direction of each variable's effect can depend on the value of the other variable.
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| The table of means on the left, below, shows a quantitative interaction — treatment ''A'' is beneficial both when ''B'' is given, and when ''B'' is not given, but the benefit is greater when ''B'' is not given (i.e. when ''A'' is given alone). The table of means on the right shows a qualitative interaction. ''A'' is harmful when ''B'' is given, but it is beneficial when ''B'' is not given. Note that the same interpretation would hold if we consider the benefit of ''B'' based on whether ''A'' is given.
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| {| cellpadding="5" cellspacing="0" align="center"
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| |-
| |
| !
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| ! style="background:#ffdead;border-left:1px solid black;border-top:1px solid black;" | ''B'' = 0
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| ! style="background:#ffdead;border-top:1px solid black;border-right:1px solid black;" | ''B'' = 1
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| !
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| !
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| !
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| !
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| !
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| !
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| ! style="background:#ffdead;border-left:1px solid black;border-top:1px solid black;" | ''B'' = 0
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| ! style="background:#ffdead;border-top:1px solid black;border-right:1px solid black;" | ''B'' = 1
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| |-
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| ! style="background:#ffdead;border-left:1px solid black;border-top:1px solid black;" | ''A'' = 0
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| ! style="border-left:1px solid black;" | 2
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| ! style="border-right:1px solid black;" | 1
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| !
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| !
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| !
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| !
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| !
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| ! style="background:#ffdead;border-left:1px solid black;border-top:1px solid black;" | ''A'' = 0
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| ! style="border-left:1px solid black;" | 2
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| ! style="border-right:1px solid black;" | 6
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| |-
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| ! style="background:#ffdead;border-bottom:1px solid black;border-left:1px solid black;" | ''A'' = 1
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| ! style="border-bottom:1px solid black;border-left:1px solid black;" | 5
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| ! style="border-bottom:1px solid black;border-right:1px solid black;" | 3
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| !
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| !
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| !
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| !
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| !
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| ! style="background:#ffdead;border-left:1px solid black;border-bottom:1px solid black;" | ''A'' = 1
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| ! style="border-left:1px solid black;border-bottom:1px solid black;" | 5
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| ! style="border-right:1px solid black;border-bottom:1px solid black;" | 3
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| |}
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| The distinction between qualitative and quantitative interactions depends on the order in which the variables are considered (in contrast, the property of additivity is invariant to the order of the variables). In the following table, if we focus on the effect of treatment ''A'', there is a quantitative interaction — giving treatment ''A'' will improve the outcome on average regardless of whether treatment ''B'' is or is not already being given (although the benefit is greater if treatment ''A'' is given alone). However if we focus on the effect of treatment ''B'', there is a qualitative interaction — giving treatment ''B'' to a subject who is already receiving treatment ''A'' will (on average) make things worse, whereas giving treatment ''B'' to a subject who is not receiving treatment ''A'' will improve the outcome on average.
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| {| cellpadding="5" cellspacing="0" align="center"
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| |-
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| !
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| ! style="background:#ffdead;border-left:1px solid black;border-top:1px solid black;" | ''B'' = 0
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| ! style="background:#ffdead;border-top:1px solid black;border-right:1px solid black;" | ''B'' = 1
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| |-
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| ! style="background:#ffdead;border-left:1px solid black;border-top:1px solid black;" | ''A'' = 0
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| ! style="border-left:1px solid black;" | 1
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| ! style="border-right:1px solid black;" | 4
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| |-
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| ! style="background:#ffdead;border-bottom:1px solid black;border-left:1px solid black;" | ''A'' = 1
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| ! style="border-bottom:1px solid black;border-left:1px solid black;" | 7
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| ! style="border-bottom:1px solid black;border-right:1px solid black;" | 6
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| |}
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| ===Unit treatment additivity===
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| In its simplest form, the assumption of treatment unit additivity states that the observed response ''y''<sub>''ij''</sub> from experimental unit ''i'' when receiving treatment ''j'' can be written as the sum ''y''<sub>''ij''</sub> = ''y''<sub>''i''</sub> + ''t''<sub>''j''</sub>.<ref>Kempthorne (1979)</ref><ref name=Cox1958_2>Cox (1958), Chapter 2</ref><ref>Hinkelmann & Kempthorne (2008), Chapters 5-6</ref> The assumption of unit treatment additivity implies that every treatment has exactly the same additive effect on each experimental unit. Since any given experimental unit can only undergo one of the treatments, the assumption of unit treatment additivity is a hypothesis that is not directly falsifiable, according to Cox{{Citation needed|date=April 2010}} and Kempthorne.{{Citation needed|date=April 2010}}
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| However, many consequences of treatment-unit additivity can be falsified.{{Citation needed|date=April 2010}} For a randomized experiment, the assumption of treatment additivity implies that the variance is constant for all treatments. Therefore, by contraposition, a necessary condition for unit treatment additivity is that the variance is constant.{{Citation needed|date=April 2010}}
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| The property of unit treatment additivity is not invariant under a change of scale,{{Citation needed|date=April 2010}} so statisticians often use transformations to achieve unit treatment additivity. If the response variable is expected to follow a parametric family of probability distributions, then the statistician may specify (in the protocol for the experiment or observational study) that the responses be transformed to stabilize the variance.<ref>Hinkelmann and Kempthorne (2008), Chapters 7-8</ref> In many cases, a statistician may specify that logarithmic transforms be applied to the responses, which are believed to follow a multiplicative model.<ref name=Cox1958_2/><ref>Bailey on eelworms.</ref>
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| The assumption of unit treatment additivity was enunciated in experimental design by Kempthorne{{Citation needed|date=April 2010}} and Cox{{Citation needed|date=April 2010}}. Kempthorne's use of unit treatment additivity and randomization is similar to the design-based analysis of finite population survey sampling.
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| In recent years, it has become common{{Citation needed|date=April 2010}} to use the terminology of Donald Rubin, which uses counterfactuals. Suppose we are comparing two groups of people with respect to some attribute ''y''. For example, the first group might consist of people who are given a standard treatment for a medical condition, with the second group consisting of people who receive a new treatment with unknown effect. Taking a "counterfactual" perspective, we can consider an individual whose attribute has value ''y'' if that individual belongs to the first group, and whose attribute has value ''τ''(''y'') if the individual belongs to the second group. The assumption of "unit treatment additivity" is that ''τ''(''y'') = ''τ'', that is, the "treatment effect" does not depend on ''y''. Since we cannot observe both ''y'' and τ(''y'') for a given individual, this is not testable at the individual level. However, unit treatment additivity imples that the [[cumulative distribution function]]s ''F''<sub>1</sub> and ''F''<sub>2</sub> for the two groups satisfy
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| ''F''<sub>2</sub>(''y'') = ''F''<sub>1</sub>(''y − τ''), as long as the assignment of individuals to groups 1 and 2 is independent of all other factors influencing ''y'' (i.e. there are no [[confounding variable|confounders]]). Lack of unit treatment additivity can be viewed as a form of interaction between the treatment assignment (e.g. to groups 1 or 2), and the baseline, or untreated value of ''y''.
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| ===Categorical variables===
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| Sometimes the interacting variables are categorical variables rather than real numbers and the study might then be dealt with as an [[analysis of variance]] problem. For example, members of a population may be classified by religion and by occupation. If one wishes to predict a person's height based only on the person's religion and occupation, a simple ''additive'' model, i.e., a model without interaction, would add to an overall average height an adjustment for a particular religion and another for a particular occupation. A model with interaction, unlike an additive model, could add a further adjustment for the "interaction" between that religion and that occupation. This example may cause one to suspect that the word ''interaction'' is something of a misnomer.
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| Statistically, the presence of an interaction between categorical variables is generally tested using a form of [[analysis of variance]] (ANOVA). If one or more of the variables is continuous in nature, however, it would typically be tested using moderated multiple regression.<ref name=Overton2001>{{Cite journal
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| | author = Overton, R. C.
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| | year = 2001
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| | title = Moderated multiple regression for interactions involving categorical variables: a statistical control for heterogeneous variance across two groups
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| | journal = Psychol Methods
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| | volume = 6
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| | issue = 3
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| | pages = 218–33
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| | doi = 10.1037/1082-989X.6.3.218
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| | pmid = 11570229
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| | postscript = <!--None-->
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| }}</ref> This is so-called because a moderator is a variable that affects the strength of a relationship between two other variables.
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| ===Designed experiments===
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| [Genichi Taguchi]] contended{{Citation needed|date=April 2010}} that interactions could be eliminated from a [[system]] by appropriate choice of response variable and transformation. However [[George Box]] and others have argued that this is not the case in general.<ref>{{Cite journal
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| | author = [[George E. P. Box]]
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| | year = 1990
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| | title = Do interactions matter?
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| | journal = Quality Engineering
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| | volume = 2
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| | pages = 365–369
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| | url = http://cqpi.engr.wisc.edu/system/files/r046.pdf
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| | postscript = <!--None-->
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| }}</ref>
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| ===Model size===
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| Given ''n'' predictors, the number of terms in a linear model that includes a constant, every predictor, and every possible interaction is <math>\tbinom{n}{0} + \tbinom{n}{1} + \tbinom{n}{2} + \cdots + \tbinom{n}{n} = 2^n</math>. Since this quantity grows exponentially, it readily becomes impractically large. One method to limit the size of the model is to limit the order of interactions. For example, if only two-way interactions are allowed, the number of terms becomes <math>\tbinom{n}{0} + \tbinom{n}{1} + \tbinom{n}{2} = 1 + \tfrac{1}{2}n + \tfrac{1}{2}n^2</math>. The below table shows the number of terms for each number of predictors and maximum order of interaction.
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| {| class="wikitable" style="text-align: right;"
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| |+ Number of terms
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| ! rowspan="2" | Predictors
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| ! colspan="5" | Including up to ''m''-way interactions
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| |-
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| ! 2 !! 3 !! 4 !! 5 !! ∞
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| |-
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| ! scope="row" | 1
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| | 2 || 2 || 2 || 2 || 2
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| |-
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| ! scope="row" | 2
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| | 4 || 4 || 4 || 4 || 4
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| |-
| |
| ! scope="row" | 3
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| | 7 || 8 || 8 || 8 || 8
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| |-
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| ! scope="row" | 4
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| | 11 || 15 || 16 || 16 || 16
| |
| |-
| |
| ! scope="row" | 5
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| | 16 || 26 || 31 || 32 || 32
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| |-
| |
| ! scope="row" | 6
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| | 22 || 42 || 57 || 63 || 64
| |
| |-
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| ! scope="row" | 7
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| | 29 || 64 || 99 || 120 || 128
| |
| |-
| |
| ! scope="row" | 8
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| | 37 || 93 || 163 || 219 || 256
| |
| |-
| |
| ! scope="row" | 9
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| | 46 || 130 || 256 || 382 || 512
| |
| |-
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| ! scope="row" | 10
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| | 56 || 176 || 386 || 638 || 1,024
| |
| |-
| |
| ! scope="row" | 11
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| | 67 || 232 || 562 || 1,024 || 2,048
| |
| |-
| |
| ! scope="row" | 12
| |
| | 79 || 299 || 794 || 1,586 || 4,096
| |
| |-
| |
| ! scope="row" | 13
| |
| | 92 || 378 || 1,093 || 2,380 || 8,192
| |
| |-
| |
| ! scope="row" | 14
| |
| | 106 || 470 || 1,471 || 3,473 || 16,384
| |
| |-
| |
| ! scope="row" | 15
| |
| | 121 || 576 || 1,941 || 4,944 || 32,768
| |
| |-
| |
| ! scope="row" | 20
| |
| | 211 || 1,351 || 6,196 || 21,700 || 1,048,576
| |
| |-
| |
| ! scope="row" | 25
| |
| | 326 || 2,626 || 15,276 || 68,406 || 33,554,432
| |
| |-
| |
| ! scope="row" | 50
| |
| | 1,276 || 20,876 || 251,176 || 2,369,936 || 10<sup>15</sup>
| |
| |-
| |
| ! scope="row" | 100
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| | 5,051 || 166,751 || 4,087,976 || 79,375,496 || 10<sup>30</sup>
| |
| |-
| |
| ! scope="row" | 1,000
| |
| | 500,501 || 166,667,501 || 10<sup>10</sup> || 10<sup>12</sup> || 10<sup>300</sup>
| |
| |}
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| ==Examples==
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| Real-world examples of interaction include:
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| *''Interaction'' between adding sugar to coffee and stirring the coffee. Neither of the two individual variables has much effect on sweetness but a combination of the two does.
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| *''Interaction'' between adding [[carbon]] to [[steel]] and [[quenching]]. Neither of the two individually has much effect on [[tensile strength|strength]] but a combination of the two has a dramatic effect.
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| *''Interaction'' between smoking and inhaling [[asbestos]] fibres: Both raise lung carcinoma risk, but exposure to asbestos ''multiplies'' the cancer risk in smokers and non-smokers. Here, the ''joint effect'' of inhaling asbestos and smoking is higher than the sum of both effects.<ref>{{Cite journal
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| | author = Lee, P. N.
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| | year = 2001
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| | title = Relation between exposure to asbestos and smoking jointly and the risk of lung cancer
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| | journal = Occupational and Environmental Medicine
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| | volume = 58
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| | issue = 3
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| | pages = 145–53
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| | doi = 10.1136/oem.58.3.145
| |
| | pmid = 11171926
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| | pmc = 1740104
| |
| | postscript = <!--None-->
| |
| }}</ref>
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| *''Interaction'' between genetic risk factors for [[Diabetes mellitus type 2|type 2 diabetes]] and diet (specifically, a "western" dietary pattern). The western dietary pattern was shown to increase diabetes risk for subjects with a high "genetic risk score", but not for other subjects.<ref>{{Cite journal | author = Lu, Q. | year = 2009 | title = Genetic predisposition, Western dietary pattern, and the risk of type 2 diabetes in men | journal = Am J Clin Nutr | volume = 89 | pages = 1453–1458 | doi = 10.3945/ajcn.2008.27249 | display-authors = 1 | issue = 5 | author2 = <Please add first missing authors to populate metadata.>}}</ref>
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| == See also ==
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| * [[Analysis of variance]]
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| * [[Factorial experiment]]
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| * [[Generalized randomized block design]]
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| * [[Linear model]]
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| * [[Main effect]]
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| * [[Interaction]]
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| * [[Tukey's test of additivity]]
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| ==Notes==
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| {{Reflist}}
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| ==References==
| |
| * {{cite book |author=Bailey, R. A.|title=Design of Comparative Experiments|url=http://www.maths.qmul.ac.uk/~rab/DOEbook/|publisher=[http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521683579 Cambridge University Press]|year=2008 |isbn=978-0-521-68357-9}} Pre-publication chapters are available on-line.
| |
| *[[David R. Cox|Cox, David R.]] (1958) ''Planning of experiments'' ISBN 0-471-57429-5
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| *[[David R. Cox|Cox, David R.]] and Reid, Nancy M. (2000) ''The theory of design of experiments'', Chapman & Hall/CRC. ISBN 1-58488-195-X
| |
| *{{cite book
| |
| |author=Hinkelmann, Klaus and [[Oscar Kempthorne|Kempthorne, Oscar]]
| |
| |year=2008
| |
| |title=Design and Analysis of Experiments, Volume I: Introduction to Experimental Design
| |
| |edition=Second
| |
| |publisher=Wiley
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| |isbn=978-0-471-72756-9
| |
| }}
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| *{{cite book
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| |author=[[Oscar Kempthorne|Kempthorne, Oscar]]
| |
| |year=1979
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| |title=The Design and Analysis of Experiments
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| |edition=Corrected reprint of (1952) Wiley
| |
| |publisher=Robert E. Krieger
| |
| |isbn=0-88275-105-0
| |
| }}
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| ==Further reading==
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| *{{Cite journal | doi = 10.1086/226678 | last1 = Southwood | first1 = K.E. | year = 1978 | title = Substantive Theory and Statistical Interaction: Five Models | url = | journal = [[The American Journal of Sociology]] | volume = 83 | issue = 5| pages = 1154–1203 }}
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| *{{Cite journal | doi = 10.3758/BRM.41.3.924 | last1 = Hayes | first1 = A. F. | last2 = Matthes | first2 = J. | year = 2009 | title = Computational procedures for probing interactions in OLS and logistic regression: SPSS and SAS implementations | url = | journal = Behavior Research Methods | volume = 41 | issue = 3| pages = 924–936 | pmid = 19587209 }}
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| *{{Cite journal | doi = 10.1007/s00181-012-0604-2 | last1 = Balli| first1 = H. O. | last2 = Sørensen| first2 = B. E. | year = 2012 | title = Interaction effects in econometrics | url = | journal = Empirical Economics | volume = 43 | issue = x | pages = 1–21 }}
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| ==External links==
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| *{{PDF|[http://pages.towson.edu/mchamber/chapter7eco306.pdf Using Indicator and Interaction Variables]|158 [[Kibibyte|KiB]]<!-- application/pdf, 162090 bytes -->}}
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| *[http://davis.foulger.info/papers/statisticalInteraction1979.htm Credibility and the Statistical Interaction Variable: Speaking Up for Multiplication as a Source of Understanding]
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| *[http://www.ruf.rice.edu/~branton/interaction/faqfund.htm Fundamentals of Statistical Interactions: What is the difference between "main effects" and "interaction effects"? ]
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| {{Statistics}}
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| {{Experimental design}}
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| {{DEFAULTSORT:Interaction (Statistics)}}
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| [[Category:Analysis of variance]]
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| [[Category:Regression analysis]]
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| [[Category:Design of experiments]]
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