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As you may guess, there are long discussions about which type should be used, and each type has pros and cons. Well, this sounds complicated, right?

But here is a good news. If your data are balanced the same sample size for each group to compare , all of those SSs will be the same.

So, if this is the case, you don't have to worry about it much. Here we have two independent variables, Device and Technique. Anova in car library requires us to explicitly build a linear model.

We can use lm for this. I won't explain what this magic code means for now. We have significant main effects of Device and Technique, and we also have a significant interaction of Device and Technique.

For example, the partial eta-squared for Technique is If you have to report the confidence interval of the effect size, you have to calculate the eta squared.

For example, the eta-squared for Technique is First, we reform the data. Each row represents each participant, and each column represents a different condition.

We now make the variables for representing these conditions. The rows of factor should correspond to the column of data2.

Make sure to run a magic code using options function I won't explain what this magic code means for now. In this example, each participant experienced all Devices and Techniques, so we include both D and T.

Now you have the results. Mauchly Tests do not show any significant effect, so we don't need any correction. For instance, the partial eta squared of Technique is Similarly the partial eta squared of Device is 9.

You don't have to do any adjustment on the sum of square even if you have to do Greenhouse-Geisser or Huynh-Feldt correction. Calculating the eta squared is a bit trickier.

So in this example, the effect size of Technique is You can find how to calculate the confidence interval for the eta squared in the example code for one-way ANOVA.

You may also have noticed that there is no correction for Device. This is because the degree of freedom of Device is 1 there are only two options for Device.

This is kind of similar to a paired t test. If you do a paired t test, the test looks at the difference between the two groups rather than separate distributions of two groups.

Thus, the equality of variances of the two groups doesn't matter. The same thing is happening here. Because Device is a within-subject factor, our interest is the distribution after we take the difference between the two groups, and thus we only have one distribution to test.

But for Technique, we still have more than one distribution even after we take the differences because we had three techniques , and Technique may need a correction.

Although this function uses Anova function internally, it is easier to use, so you may prefer this method. In this example, Participant represent eight different cases.

If you have a between-subject factor, you can also use the between option. You have to specify the factors and variables like.

Although the format is different, this shows the same information as the results of Anova function. In some cases, the two methods explained above won't work.

With Anova function, you may have an error like this. This means that the degree of freedom for one the factors you have becomes larger than the number of different cases in terms of the within-subject factors i.

In this case, Anova function cannot calculate a matrix necessary for the test. In this case, we have to do a test in a more manual manner as follows.

The first part of th procedure is pretty much the same as the way with car package. I don't explain details of what each command means in this procedure for now.

I may add them later, but if you are interested, please look at the manual by executing? Then, we use anova function. Please note that the function name is anova with all small letters.

With anova function, you have to execute the command with the models for each factor. D where T is Technique, and D is Device.

For instance, the degree of freedom of Technique is 2. But you don't need to run Mauchly's test for Device.

Because the degree of freedom of Device is 2, you can automatically assume the sphericity. So, how about an interaction term?

In this case, you have to change the command a bit. Please note that the changes on the options for M and X.

If the degree of freedom of a factor is larger than the number of the subjects repeatedly measured e. This means it cannot run the test because you need more subjects repeatedly measured participants.

In SPSS, the results for this factor become just blank instead of having any error message. This NaN can happen when you test an interaction term.

Suppose you test five different techniques and four different devices with ten participants. I haven't figured out whether we should make any correction when Mauchly's test is impossible to run.

I will post once I figure it out. My current guess is that we just cannot do any kind of correction. You just need to explain the results of each factor and the interaction terms:.

You may also want to report the results of the test for homogeneity of variances or sphericty before this. And remember that you have to run a post-hoc test if you find a significant difference.

Mixed-design means that you have both within-subject and between-subject factors. Let's say you recruited different people for the devices: But within each device, every participant was exposed to the three techniques.

In this case, Device is a between-subject factor, and Technique is a within-subject factor. There are some other examples which usually are considered as between-subject factors: Gender male or female , age group younger or older group , handedness right-handed or left-handed , and country US, Canada, Japan,….

Before conducting a test, you have to be clear on which variable is within- or between-subject. As you can see, we have different participants for Pen and Touch.

And you get the results. You will notice that some values are different e. These differences are caused by the experimental design. We have seen examples with balanced data, but what should we do if you have unbalanced data?

Although ANOVA can accommodate mildly unbalanced data and you can use the same codes presented in this page, you have to be more careful than when you have balanced data.

The main reason is that the results may become different depending on the types of sum of squares. If you do one-way ANOVA, it does not really matter whether the data are balanced or unbalanced unless the sample size for each group is extremely different.

But if you do two-way or mixed-design ANOVA, you need to be careful about which type of sum of squares your test is using. But please double-check with stats experts or other references.

Yes, we can do that mathematically. The problem is that the analysis becomes really hard. For instance, if you do a three-way ANOVA test, you have the three main effects, three interactions of two factors, and one interaction of three factors.

And let's say if you have a significant effect of some of them and have to do a post-hoc test? Your post-hoc test would have a huge list of comparisons.

So, I recommend you to design your experiment so that you don't have to use a more complicated test than two-way ANOVA. If you have found any significant effect, you are not done yet.

You may want to know exactly where you have differences. For this purpose, you need to run a post-hoc test, which is also a long topic.

For more details, please jump to the post-hoc test page. User Tools Log In. Sphericity test with the car package. Sphericity test with the ez package.

How to interpret the results of a sphericity test. Another way to do a Mauchly's test. The distributions of the populations you take samples from are normal.

The basic idea of this requirement is that the variance in each group should be similar enough although there is an additional thing for the sphericity, I didn't discuss it in this wiki page.

The dependent variable must be interval or ratio e. Value by Group Fligner-Killeen: First, prepare the data to analyze.

You are almost there. You need to include car package. But it is not impossible. The error SSP matrix is apparently of deficient rank We can calculate eta squared as follows: Bartlett test of homogeneity of variances data: In the example above, you can report something like: Make sure you have to do a test for sphericity: If you need to report the confidence interval of the effect size, you can do something like this: SSs are calculated by the model specified.

This means that the order of the factors in the model matters unless A and B are completely orthogonal. SSs are calculated in a similar way to the case of Type I SS, but the SS for each factor is calculated given all other factors in the model except higher order factors which contain that factor.

The SS for each factor is calculated with considering the effects from all the other factors. Here, we use Levene's test. And factor should look like this.

When you execute this command, you get the following result. Device 2 14 0. So we don't need any correction. You just need to explain the results of each factor and the interaction terms: Technique 2 28 0.

You can also use aov function, but remember that aov function uses Type I SSs. If you have difficulty sleeping, it may be a symptom of sleep apnea.

Lots of people deal with this condition every day, and it is often a problem that is quite unpleasant to manage. But the good news is that there are effective treatments out there.

Read this article to learn some basic information about recognizing and treating sleep apnea. Strengthen your throat and jaw with some basic exercises.

Developing these muscles should reduce the symptoms of sleep apnea. You can exercise your throat and jaw by simply pulling your tongue or practicing some very simple breathing exercises.

The goal is to train you to breathe differently and hopefully make your sleep apnea disappear. If you are over weight, going on a diet can reduce your sleep apnea, or in rare cases, eliminate it completely.

Maintaining a healthy weight can help you breathe easier, so losing weight and maintaining a healthy weight when you have trouble breathing is an obvious step in treating your sleep apnea.

Do not take sleeping pills if you suffer from sleep apnea. These pills are not recommended if you suffer from this condition because they relax the muscles of your throat.

Skipping them can actually help you get a better night of sleep because your apnea symptoms are not aggravated. Sleeping at a high altitude can worsen your sleep apnea because of the lower levels of oxygen.

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Keep your bedroom in prime shape for sleeping. Insomnia and sleep apnea are often connected. This makes keeping an environment in which you sleep at the right temperature, lightness level and sound level important for helping you get a good night of rest.

The right environment also means leaving your stresses outside the bedroom to ensure you are relaxed enough to fall asleep. Weight loss can be a big help for those that suffer from sleep apnea.

The condition is common in overweight patients that have larger neck circumferences. Losing weight can significantly reduce the pressure on your airway and improve the flow of air as you breathe at night.

If you use a continuous positive airway pressure, or CPAP machine to treat your sleep apnea, sleep with it every night. When you take the mask off at night, your symptoms will return.

Sometimes they might disappear for one or two nights, but then return. Wearing the mask every night prevents episodes of sleep apnea from occurring.

If you are a trucker who has sleep apnea, take precautions to stay safe on the road. First of all, get yourself properly diagnosed and treated. If your doctor prescribes a CPAP, use it.

They are small and easily portable and can run on battery power if necessary. Try to stay fit and get regular sleep to keep your condition under control.

By reading through the great sleep apnea tips found in this article, you are ready to face your problem head on.

While you may not be able to rid yourself of the problem completely, you will feel more confident and start working towards that all-important goal, a good night's sleep.

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Your independent variable is Group, and dependent variable is Value. Because the F value for Group is large enough, the p value is below 0.

Thus, you have found a significant effect of Group in the means of Value. For the effect size, both eta squared and partial eta squared become the same in this case.

If you need to calculate the confidence interval of the effect size, it is safer to use the eta squared at least there is an easy way to calculate its confidence interval in R.

Then, you just need to call the ci. You need the F value, first and second degree of freedom, and sample size. This procedure assumes the sphericity implicitly.

I recommend you to do a test for the sphericity before doing repeated-measure ANOVA, and the procedure for that is available in the Sphericity section.

The results of the sphericity test for the data we use here is also available there as an example of the test. In R, you can do so in Error.

As you can see here, R considers Participants as one random factor or an error term , and it is used as the repeated-measure factor. By comparing the results of one-way ANOVA the data are the same , you notice some differences in the results.

This is why your experimental design is important. It does affect your analysis. You may have noticed the total of the sum of square for Participants 5.

What repeated-measure ANOVA does is to separate the effect caused by the participants or individual differences from the errors whose causes we really don't know.

Thus, if you calculate the partial eta squared, it becomes larger However, if you calculate the eta squared, it is This is because the eta squared considers all the mean squares.

In the example above, you can report something like:. Make sure you have to do a test for sphericity:. If you have done any correction on the degrees of freedom, you need to explain those details e.

It revealed a significant effect of Group on Value F 1. If you need to report the confidence interval of the effect size, you can do something like this:.

Note that we use the eta squared, not the partial eta squared. It is often common that the results of a homogeneity or sphericity test are omitted.

Follow what your research community does. Remember that you have to run a post-hoc test if you find a significant difference. But it is not quite true, and there are some complicated stuff.

One of these stuff is the type of the sum of squares. The sum of squares, more precisely the sum of the squared deviations, is one of the key metrics in ANOVA.

It is kind of similar to variance, and represents how spread the data are from the mean. This is kind of a rough explanation, but I think it is easy to understand.

Unfortunately, this is not the end of the story. First, there may be some effects caused by having both two independent variables.

This is called an interaction whereas the effect caused by one factor is called a main effect. Another bad news is that this model causes another problem on how to calculate the sum of squares.

There are three kinds of types of sum of squares commonly used: We really don't want to have effects caused by the model in most cases, so want to avoid using Type I.

If you have unbalanced data the sample sizes are fairly different across your groups , it is recommended to use Type II SSs. As you may guess, there are long discussions about which type should be used, and each type has pros and cons.

Well, this sounds complicated, right? But here is a good news. If your data are balanced the same sample size for each group to compare , all of those SSs will be the same.

So, if this is the case, you don't have to worry about it much. Here we have two independent variables, Device and Technique.

Anova in car library requires us to explicitly build a linear model. We can use lm for this. I won't explain what this magic code means for now.

We have significant main effects of Device and Technique, and we also have a significant interaction of Device and Technique.

For example, the partial eta-squared for Technique is If you have to report the confidence interval of the effect size, you have to calculate the eta squared.

For example, the eta-squared for Technique is First, we reform the data. Each row represents each participant, and each column represents a different condition.

We now make the variables for representing these conditions. The rows of factor should correspond to the column of data2.

Make sure to run a magic code using options function I won't explain what this magic code means for now.

In this example, each participant experienced all Devices and Techniques, so we include both D and T. Now you have the results.

Mauchly Tests do not show any significant effect, so we don't need any correction. For instance, the partial eta squared of Technique is Similarly the partial eta squared of Device is 9.

You don't have to do any adjustment on the sum of square even if you have to do Greenhouse-Geisser or Huynh-Feldt correction.

Calculating the eta squared is a bit trickier. So in this example, the effect size of Technique is You can find how to calculate the confidence interval for the eta squared in the example code for one-way ANOVA.

You may also have noticed that there is no correction for Device. This is because the degree of freedom of Device is 1 there are only two options for Device.

This is kind of similar to a paired t test. If you do a paired t test, the test looks at the difference between the two groups rather than separate distributions of two groups.

Thus, the equality of variances of the two groups doesn't matter. The same thing is happening here. Because Device is a within-subject factor, our interest is the distribution after we take the difference between the two groups, and thus we only have one distribution to test.

But for Technique, we still have more than one distribution even after we take the differences because we had three techniques , and Technique may need a correction.

Although this function uses Anova function internally, it is easier to use, so you may prefer this method. In this example, Participant represent eight different cases.

If you have a between-subject factor, you can also use the between option. You have to specify the factors and variables like. Although the format is different, this shows the same information as the results of Anova function.

In some cases, the two methods explained above won't work. With Anova function, you may have an error like this.

This means that the degree of freedom for one the factors you have becomes larger than the number of different cases in terms of the within-subject factors i.

In this case, Anova function cannot calculate a matrix necessary for the test. In this case, we have to do a test in a more manual manner as follows.

The first part of th procedure is pretty much the same as the way with car package. I don't explain details of what each command means in this procedure for now.

I may add them later, but if you are interested, please look at the manual by executing? Then, we use anova function. Please note that the function name is anova with all small letters.

With anova function, you have to execute the command with the models for each factor. D where T is Technique, and D is Device.

For instance, the degree of freedom of Technique is 2. But you don't need to run Mauchly's test for Device. Because the degree of freedom of Device is 2, you can automatically assume the sphericity.

So, how about an interaction term? In this case, you have to change the command a bit. Please note that the changes on the options for M and X.

If the degree of freedom of a factor is larger than the number of the subjects repeatedly measured e. This means it cannot run the test because you need more subjects repeatedly measured participants.

In SPSS, the results for this factor become just blank instead of having any error message. This NaN can happen when you test an interaction term.

Suppose you test five different techniques and four different devices with ten participants. I haven't figured out whether we should make any correction when Mauchly's test is impossible to run.

I will post once I figure it out. My current guess is that we just cannot do any kind of correction. You just need to explain the results of each factor and the interaction terms:.

You may also want to report the results of the test for homogeneity of variances or sphericty before this.

And remember that you have to run a post-hoc test if you find a significant difference. Mixed-design means that you have both within-subject and between-subject factors.

Let's say you recruited different people for the devices: But within each device, every participant was exposed to the three techniques. In this case, Device is a between-subject factor, and Technique is a within-subject factor.

There are some other examples which usually are considered as between-subject factors: Gender male or female , age group younger or older group , handedness right-handed or left-handed , and country US, Canada, Japan,….

Before conducting a test, you have to be clear on which variable is within- or between-subject. As you can see, we have different participants for Pen and Touch.

And you get the results. You will notice that some values are different e. These differences are caused by the experimental design.

We have seen examples with balanced data, but what should we do if you have unbalanced data? Although ANOVA can accommodate mildly unbalanced data and you can use the same codes presented in this page, you have to be more careful than when you have balanced data.

The main reason is that the results may become different depending on the types of sum of squares.

If you do one-way ANOVA, it does not really matter whether the data are balanced or unbalanced unless the sample size for each group is extremely different.

But if you do two-way or mixed-design ANOVA, you need to be careful about which type of sum of squares your test is using. But please double-check with stats experts or other references.

Yes, we can do that mathematically. The problem is that the analysis becomes really hard. For instance, if you do a three-way ANOVA test, you have the three main effects, three interactions of two factors, and one interaction of three factors.

And let's say if you have a significant effect of some of them and have to do a post-hoc test? Your post-hoc test would have a huge list of comparisons.

So, I recommend you to design your experiment so that you don't have to use a more complicated test than two-way ANOVA. If you have found any significant effect, you are not done yet.

You may want to know exactly where you have differences. For this purpose, you need to run a post-hoc test, which is also a long topic.

For more details, please jump to the post-hoc test page. User Tools Log In. Sphericity test with the car package. Sphericity test with the ez package.

How to interpret the results of a sphericity test. Another way to do a Mauchly's test. The distributions of the populations you take samples from are normal.

The basic idea of this requirement is that the variance in each group should be similar enough although there is an additional thing for the sphericity, I didn't discuss it in this wiki page.

The dependent variable must be interval or ratio e. Value by Group Fligner-Killeen: First, prepare the data to analyze.

You are almost there. You need to include car package. But it is not impossible. The error SSP matrix is apparently of deficient rank We can calculate eta squared as follows: Bartlett test of homogeneity of variances data: In the example above, you can report something like: Make sure you have to do a test for sphericity: If you need to report the confidence interval of the effect size, you can do something like this: SSs are calculated by the model specified.

This means that the order of the factors in the model matters unless A and B are completely orthogonal. SSs are calculated in a similar way to the case of Type I SS, but the SS for each factor is calculated given all other factors in the model except higher order factors which contain that factor.

The SS for each factor is calculated with considering the effects from all the other factors. Here, we use Levene's test. And factor should look like this.

When you execute this command, you get the following result. Device 2 14 0. So we don't need any correction.

You just need to explain the results of each factor and the interaction terms: Technique 2 28 0. You can also use aov function, but remember that aov function uses Type I SSs.

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The experiment consisted of a survey designed to form two age cohorts of game players subdivided into two categories flash game players and console players.

Both cohorts consisted of two focussed groups, one relating to players of flash communities and the other to those who identified as being console players.

A causal experiment was then designed to determine the responsiveness of the gaming groups in terms of 'time to response'. Experimental observations were conducted for the two age cohorts alongside extensive metrics between players of the two groups.

The objective was not determining the accuracy of the answer but 'time to response' fairly accurate. Interestingly both groups of the respective cohorts patterned different distributions for parametric testing.

Logical reasoning and analysis, and basic math were also structured and administered into the causal analysis to further strengthen the evidence.

The metrics were standardised to nullify intelligence factors and the 'time to response' argument established.

The implications of this are significant effecting both developer and player. Although the flash player spends the same amount of time playing, as a console player, the very fact that a flash game is structured to be a mini game and made available in abundance, motivates the player to experiment with different games thereby reducing the time spent on a single game perse.

The domino effect is interpreted in terms of a larger experience of the 'spectrum of creativity', benefiting a larger community of game developers.

This is in stark contrast to the console player whose brand and thematic loyalty is imbibed with inertia acting as a barrier to change. It is during a transition of themes that the console player exhibits thematic lethargy.

Secondly a lognormal probability distribution characterises a thinning long tail, if this is indicative of gaming addiction, then we may surmise that flash games are less addictive compared to their console counterparts.

In a nut shell it appears fair to conclude that flash games players just might be more alert and this may be attributed to the conditioning of 'time to response' in an environment which is not thematically stuck nor addictive.

For that addict that has chose to confront his or her habit, the ongoing method associated with recovery is normally fulfilled along with difficulties, challenges, setbacks, and ultimately, achievement.

In addition, numerous junkies must deal with other fundamental circumstances or even concerns that is included with the habit.

For these people, the twin diagnosis alcohol and drugs detox may well end up being particularly helpful and it is frequently an ideal system whenever all things are regarded as.

It can be typically discovered that conditions such as depression and anxiousness, for example, may well have been around in a provided individual before the actual start of chemical addiction.

These types of conditions may well possess, the fact is, contributed to the addicting conduct in the first location.

In certain instances, on the other hand, these types of conditions occur consequently from the addiction.

Regardless of that arrived very first, the clinical condition or the substance abuse, more as well as more specialist physicians tend to be obtaining it essential and crucial to deal with both concurrently.

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