![Subject 13 1.0 Subject 13 1.0](/uploads/1/3/3/8/133890979/308864250.jpg)
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Reaction times in video games
Learning goals:
* model a numerical outcome in terms of multiple categoricalpredictors
* understand the appropriate use and interpretation of dummy variablesand interaction terms
* model a numerical outcome in terms of multiple categoricalpredictors
* understand the appropriate use and interpretation of dummy variablesand interaction terms
Data files:
* rxntime.csv:data on a neuroscience experiment measuring people's reaction time tovisual stimuli
* rxntime.csv:data on a neuroscience experiment measuring people's reaction time tovisual stimuli
More than one categorical predictor
The reaction-time data set comes from an experiment run by a Britishvideo-game manufacturer in an attempt to calibrate the level ofdifficulty of certain tasks in the video game. Subjects in thisexperiment were presented with a simple 'Where's Waldo?'-style visualscene. Fl studio 12 download mac crack. The subjects had to find a number (1 or 2) floating somewhere inthe scene, to identify the number, and to press the corresponding buttonas quickly as possible. The response variable is their reaction time.The predictors are different characteristics of the visual scene.
You'll need the mosaic library, so make sure to load it first.
The variables of interest for us are:
* PictureTarget.RT: the subject's reaction time in milliseconds.
* Subject: a numerical identifier for the subject undergoing thetest.
* FarAway: a dummy variable. Was the number to be identified far away(1) or near (0) in the visual scene?
* Littered: the British way of saying whether the scene was cluttered(1) or mostly free of clutter (0).
* PictureTarget.RT: the subject's reaction time in milliseconds.
* Subject: a numerical identifier for the subject undergoing thetest.
* FarAway: a dummy variable. Was the number to be identified far away(1) or near (0) in the visual scene?
* Littered: the British way of saying whether the scene was cluttered(1) or mostly free of clutter (0).
https://ballintensive.weebly.com/blog/internet-download-manager-lifetime-crack-download. First let's look at some plots to show between-group and within-groupvariation for the three predictors:
Main effects
Our first model will use whether the scene was littered as a predictor:
Remember baseline/offset form: the coefficients of this model are simplya different way of expressing the group means for the littered andunlittered scenes:
Now we will add a second dummy variable for whether the number to beidentified was near or far away:
This model says that the predicted 'baseline' reaction time (forunlittered scenes with a nearby target) is 481.6 ms. For scenes thatwere littered, we'd predict a reaction time 87.5 ms longer than thebaseline. For scenes with a far-away target, we'd predict a reactiontime 50.1 ms longer than baseline. For scenes that are both litteredand far away, the model tells us to simply add the sum of the twoindividual effects:
So according to the model, we'd predict these scenes to be 137.6 mslonger than baseline.
For reasons that will become clear in a moment, we refer to the Litteredand FarAway coefficients as the 'main effects' of the model.
![Subject Subject](/uploads/1/3/3/8/133890979/713995524.jpg)
Interactions
The model we just fit assumed that the Littered and FarAway variableshad individual additive effects on the response. However, what if scenesthat are both Littered and FarAway are even harder than we'd expectbased on the individual Littered and FarAway effects? If we think thismay be the case, we should consider adding an interaction term to themodel:
As before, the first two terms are called 'main effects.' The last termin the model is an interaction variable, with an estimated coefficientof 39.1. It allows the joint effect of the two predictors to bedifferent than the sum of the individual (main) effects.
To understand the output, let's work our way through the predictions ofthe above model based on the fitted coefficients:
* Baseline scenes: (Littered=0, FarAway=0): baseline only (491.4 ms)
* Littered=1, FarAway=0 scenes: add the baseline and the Littered maineffect (491.4 + 67.9 = 559.3 ms)
* FarAway=1, Littered=0 scenes: add the baseline and the FarAway maineffect (491.4 + 30.6 = 522 ms)
* Littered=1, FarAway=1 scenes: add the baseline, both main effects,and the interaction term (491.4 + 67.9 + 30.6 + 39.1 = 629 ms)
* Baseline scenes: (Littered=0, FarAway=0): baseline only (491.4 ms)
* Littered=1, FarAway=0 scenes: add the baseline and the Littered maineffect (491.4 + 67.9 = 559.3 ms)
* FarAway=1, Littered=0 scenes: add the baseline and the FarAway maineffect (491.4 + 30.6 = 522 ms)
* Littered=1, FarAway=1 scenes: add the baseline, both main effects,and the interaction term (491.4 + 67.9 + 30.6 + 39.1 = 629 ms)
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Notice that to get the prediction for scenes that are both littered andfar away, we add the baseline, both main effects, and the interactionterm. The resulting predictions match up exactly with the group means wecalculate if we stratify the scenes into all four possible combinationsof Littered and FarAway:
A reasonable question is: why bother with the extra complexity of maineffects and interactions if all we're doing is computing the group-wisemeans for all four combinations of the two variables?
https://listingburn.weebly.com/home/macro-key-manager-download-mac. In fact, if we have only these two variables, there isn't really acompelling reason to do so. However, let's suppose we wanted to add athird variable: Nelonen pro.
Now we've added subject-level dummy variables to account forbetween-subject variability, and R-squared has jumped from 13% to 23%.But we're still assuming that the effect of the Littered and FarAwayvariables is the same for every subject. Thus we have 15 parameters toestimate: an intercept/baseline, two main effects for Littered andFarAway, one interaction term, and 11 subject-level dummy variables.Suppose that instead we were to look at all possible combinations ofsubject, Littered, and FarAway variables, and compute the groupwisemeans:
Now we've got 48 parameters to estimate: the group mean for eachcombination of 12 subjects and 4 experimental conditions. Moreover,we're now implicitly assuming that the Littered and FarAway variablesaffect each person in a different way, rather than all people in thesame way. There's no way to reproduce the output of the model we justfit (
lm4
) by computing group-wise means.Subject 13 1.0 Free
This should convey the power of using dummies and interactions toexpress how a response variable changes as a function of severalgrouping variables. It allows us to be selective: some variables mayinteract with each other, while other variables have only a 'maineffect' that holds across the entire data set, regardless of what valuesthe other predictors take.
The choice of which variables fall in which category can be guided bothby the data itself and by knowledge of the problem at hand. This is animportant modeling decision---one which we'll study carefully.
Analysis of variance
Bigasoft total video converter 5.4.0 crack. Finally, what if we wanted to quantify how much each predictor wascontributing to the overall explanatory power of the model? A naturalway to do so is to compute the amount by which the addition of eachpredictor reduces the unpredictable (residual) variation, compared to amodel without that predictor. R's `anova' function computes this forus:
The 'Sum Sq' (for sums of squares) column in the one that interests us.This column is computed by adding the predictors sequentially andasking: by how much did the residual sum of squares drop when thispredictor was added to the previous model? (Remember the variancedecomposition here.) The larger the entry in the 'Sum Sq' column, themore that variable improved the predictive ability of the model. Thefinal entry (Residuals) tells you the residual sums of squares after allvariables were added. This serves as a useful basis for comparison whentrying to interpret the magnitude of the other entries in this column.
This breakdown of the sums of squares into its constituent parts iscalled the 'analysis of variance' for the model, or 'ANOVA' for short.
A modified ANOVA table
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However, I've always found R's basic
anova
table to be kind of hard toread. After all, how is a normal human being supposed to interpret sumsof squares? The number are on a completely non-intuitive scale.Subject 13 1.0 Vs
Aimbooster pro 1 5 10. So I coded up a different version of an ANOVA table, called
simple_anova
, which you can find on my website. The following codesnippet shows you how to source this function directly into R; this iskind of like loading a library, except less official :-)Free google home mini code spotify. Now you can call the
simple_anova
function in the same way you callthe anova
one:As before, each row involves adding a variable to the model. But theoutput is a little different. There are six columns:
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- Df: how many degrees of freedom (i.e. parameters added to the model)did this variable use?
- R2: what was the R-squared of the model?
- R2_improve: how much did R-squared improve (go up), compared to theprevious model, when we added this variable?
- sd: what was the residual standard deviation of the model?
- sd_improve: how much did the residual standard deviation improve (godown), compared to the previous model, when we added this variable?
- pval: don't worry about this for now, but this corresponds to ahypothesis test (specifically, an F test) about whether the variableappears to have a statistically significant partial relationship withthe response.
For me, at least, these quantities convey a lot more useful informationthan the basic
anova
table. Just remember that if you want to use thesimple_anova
command in the future, you'll always have to preface itby sourcing the function using the command we saw above: