User Tools

Site Tools


hcistats:posthoc

Post-hoc Tests


Introduction

If you find any significant main effect or interaction with an ANOVA test, congrats, you have at least one significant difference in your data. However, an ANOVA test doesn't tell you where you have the differences. Thus, you need to do one more test–a post-hoc test–to find where they exist.

Comparisons for main effects

As we have seen in the Anova page, there are two kinds of effects you may have: main effects, and interactions (if your model is two-way or more). The comparison for the main effect is fairly straightforward, but there are four kinds of comparisons you can make, so you have to decide which one you want to do.

Before talking about the differences of the comparisons, you need to know one important thing. Some of the post-hoc comparisons may not be appropriate for repeated-measure ANOVA. I am not 100% sure about this point, but it seems that some of the methods do not consider the within-subject design. So, my current suggestion is that if the factor you are comparing in a post-hoc test is a within-subject factor, it might be safer to use a t test with the Bonferroni's or Sidak's correction.

OK., back to the discussion about the types of comparisons. For the discussion, let's say you have three groups: A, B, and C.

  • [Case 1] Compare every possible combination of your groups: In this case, you compare everything. You will compare A and B, B and C, and C and A. But you also compare A and B+C (the mean of B and C), B and C+A, C and A+B.
  • [Case 2] Compare every group: In this case, you will compare A and B, B and C, and C and A. But you do not compare A and B+C, B and C+A, C and A+B.
  • [Case 3] Compare every group against the control: In this case, you will compare the groups only against the control condition. If your control condition is A, you will compare A and B, and A and C.
  • [Case 4] Compare the data against the within-subject factor: In this case, you will make a comparison against the within-subject factor. In other words, if you have done repeated-measure ANOVA, this is the way to do a post-hoc test. The methods for this case can be used for tests against between-subject factors.

The strict definition of a post-hoc test means a test which does not require any plan for testing. In the four examples above, only Case 1 satisfies the strict definition of a post-hoc test because the others cases require some sort of planning on which groups to compare or not to compare. However, the term of a post-hoc test is often used for meaning Case 2 and Case 3. Case 4 is usually called a planned comparison test, but again it is often referred as a post-hoc test as well. In this wiki, I use a post-hoc test to mean all of these four tests.

The key point here is you need to figure out which case you want to do for the comparisons after ANOVA. Make sure what comparisons you are interested in before doing any test.


Comparisons for interactions

If you find a significant interaction, things are a little more complicated. This means that the effect of one factor depends on the conditions controlled by the other factors. So, what you need to do is to make comparisons against one factor with fixing the other factors. Let's say you have two Devices (Pen and Touch) and three Techniques (A, B, and C) as we have seen in the two-way ANOVA example. If you have found the interaction, what you need to look at is:

  • The effect of Technique under Device = Pen;
  • The effect of Technique under Device = Touch;
  • The effect of Device under Technique = A;
  • The effect of Device under Technique = B; and
  • The effect of Device under Technique = C.

The effects we look at here are called simple main effects. Although you could report all the simple main effects you have, it might become lengthy. Rather, providing a graph like above is easier to understand what kinds of trends your data have. Your graph will look like one of the following graphs depending of the existence of main effects and interactions.

It is also said that you shouldn't report the main effects (not simple main effects) when you have a significant interaction. This is because significant differences are caused by some combination of the factors, and not necessarily caused by a single factor. However, I think that it is still good to report any significant main effects even if you have a significant interaction because it tells us what the data look like. Again, providing a graph is very helpful for your readers to understand your data.

The sad news is that it is not as easy in R to do post-hoc test as in SPSS. You often have to do a lot of things manually or some methods are not really supported in R. So, particularly if you are doing two-way ANOVA and you have an access to SPSS, it may be better to use SPSS.


Main effect: Comparing every possible combination of your groups (Scheffe's test)

Scheffe's test allows you to do a comparison on every possible combination of the group you are caring about. Unfortunately, there is no automatic way to do Scheffe's test in R. You have to do it manually. The following procedure is based on Colleen Moore & Mike Amato's material.

We use the same example for one-way ANOVA.

Group <- factor(c("A","A","A","A","A","A","A","A","B","B","B","B","B","B","B","B","C","C","C","C","C","C","C","C")) Value <- c(1,2,4,1,1,2,2,3,3,4,4,2,3,4,4,3,4,5,3,5,5,3,4,6) data <- data.frame(Group, Value) aov <- aov(Value ~ Group, data) summary(aov) Df Sum Sq Mean Sq F value Pr(>F) Group 2 22.75 11.3750 12.095 0.0003202 *** Residuals 21 19.75 0.9405 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘

We have a significant effect of Group. So, we need to look into that effect more deeply. First, you have to define the combination of the groups for your comparison.

coeff=c(1,-1,0)

The each element of coeff intuitively means the weight for the later calculation. The positive values and negative values represent data to compare. In this case, the first element is 1, and the second element is -1. And the first, second, and third elements will represent Group A, B, and C, respectively. So, this coeff means we are going to compare Group A and Group B. The third element is 0, which means Group C will be ignored.

Another key point is the sum of the elements must be 0. Here are some other examples.

  • If you have three groups (A, B, C), and you want to compare Group B and C, coeff = c(0, 1, -1).
  • If you have three groups (A, B, C), and you want to compare Group A and the mean of Group B and C, coeff = c(2, -1, -1).
  • If you have five groups (A, B, C, D, E), and you want to compare the mean of Group A and B, and the mean of Group C, D and E, coeff = c(2/3, 2/3, 2/3, -1, -1).

Let's come back to the example. Now we need to calculate the number of the samples and the mean for each group.

mm = tapply(Value, Group, mean) nn = tapply(Value, Group, length)

We then calculate some statistical values.

psi <- sum(coeff*mm) sscoeff <- sum(coeff*coeff/nn) mspsi <- (psi*psi)/sscoeff

mspsi should be 7.5625 if you have followed the example correctly. Now we are going to calculate the F value. For this, we need to know the value for the mean square for the errors (or residuals). According to the result of the anova test, it is 0.9405 (Did you find it? Go back to the very first of this example and see the result of summary(aov)). We also need to know the degree of freedom of the factor we are caring about (in this example, Group), which is 2.

> contrastF <- mspsi / 0.9405 / 2

Finally, we can calculate the p value for this comparison (comparison between Group A and Group B). For the degrees of freedom, we can use the same ones for the anova test, which is 2 for the first DOF, 21 for the second DOF (Find them in the result of the anova test).

1 - pf(contrastF, 2, 21) 0.03324231

Thus, the difference between Group A and B is significant because p < 0.05.

So, if you really want to do all possible comparisons, you probably want to write some codes so that you can do a batch operation. I think it should be straightforward, but be careful about the design of the comparison (i.e., coeff).

I am not 100% sure, but Scheffe's test may not be appropriate for repeated-measure ANOVA. For repeated-measure ANOVA, you can do a pairwise comparison with the Bonferroni's or Sidak's correction.


Main effect: Comparing every group (Tukey's test)

This is probably the most common case in HCI research. You want to compare the two of the groups, but you are not interested in any combination of more than one group. One of the common methods for this case is Tukey's method. The way to do a Tukey's test in R depends on how you have done ANOVA.

First, let's take a look at how to do a Tukey's test with the aov() function. We use the same example of one-way ANOVA.

Group <- factor(c("A","A","A","A","A","A","A","A","B","B","B","B","B","B","B","B","C","C","C","C","C","C","C","C")) Value <- c(1,2,4,1,1,2,2,3,3,4,4,2,3,4,4,3,4,5,3,5,5,3,4,6) data <- data.frame(Group, Value) aov <- aov(Value ~ Group, data) summary(aov)

Now, we do a Tukey's test.

TukeyHSD(aov) Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = Value ~ Group, data = data) $Group diff lwr upr p adj B-A 1.375 0.1527988 2.597201 0.0257122 C-A 2.375 1.1527988 3.597201 0.0002167 C-B 1.000 -0.2222012 2.222201 0.1222307

So, we have significant differences between A and B, and A and C.

If you use the Anova() function, the way to do a Tukey's test is a little different. Here, we use the same example of two-way ANOVA, but the values for Time were slightly changed (to make the interaction effect disappear).

Device <- factor(c(rep("Pen",24), rep("Touch",24))) Technique <- factor(rep(c(rep("A",8), rep("B",8), rep("C",8)), 2)) Time <- c(1.2,1.4,1.8,2.0,1.1,1.5,1.5,1.7, + 2.1,2.5,2.2,2.2,2.9,2.3,2.3,2.6, + 3.5,3.4,3.3,3.2,2.9,2.8,3.8,3.4, + 2.4,1.8,2.5,2.1,2.2,1.9,1.7,2.3, + 2.8,3.1,3.2,4.0,2.9,3.6,3.2,3.7, + 4.5,4.8,3.7,4.1,4.1,4.2,3.6,3.9) library(car) options(contrasts=c("contr.sum", "contr.poly")) model <- lm(Time ~ Device * Technique) Anova(model, type="III") Anova Table (Type III tests) Response: Time Sum Sq Df F value Pr(>F) (Intercept) 373.53 1 3296.6764 < 2.2e-16 *** Device 7.29 1 64.2981 5.271e-10 *** Technique 28.40 2 125.3289 < 2.2e-16 *** Device:Technique 0.24 2 1.0609 0.3552 Residuals 4.76 42 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

With the anova test, you will find the main effects. So, you need to run a Tukey's test. You have to do the following thing to do a Tukey's test with the model created by lm(). You need to include multcomp package beforehand.

library(multcomp) summary(glht(model, linfct=mcp(Device="Tukey", Technique="Tukey")))

Then, you get the results.

Simultaneous Tests for General Linear Hypotheses Multiple Comparisons of Means: Tukey Contrasts Fit: lm(formula = Time ~ Device * Technique) Linear Hypotheses: Estimate Std. Error t value Pr(>|t|) Device: Touch - Pen == 0 0.77917 0.09717 8.019 < 1e-08 *** Technique: B - A == 0 1.03125 0.11901 8.665 < 1e-08 *** Technique: C - A == 0 1.88125 0.11901 15.808 < 1e-08 *** Technique: C - B == 0 0.85000 0.11901 7.142 1.45e-08 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Adjusted p values reported -- single-step method) Warnings&#65306; 1: In mcp2matrix(model, linfct = linfct) : covariate interactions found -- default contrast might be inappropriate 2: In mcp2matrix(model, linfct = linfct) : covariate interactions found -- default contrast might be inappropriate

So, we have significant differences between any of the two groups in both Device and Technique.

It seems both ways to do a Tukey's test can accommodate mildly unbalanced data (the number of the samples are different cross the groups, but not that different). The Tukey's test which can handle mildly unbalanced data is also called Tukey-Kramer's test. If you have largely unbalanced data, you can't do a Tukey's test nor even ANOVA, and instead you should do a non-parametric test.

Another thing you should need to know is that Tukey may not be appropriate as a post-hoc test for repeated-measure ANOVA. This is because Tukey assumes the independency of the data across the groups. You can actually run a Tukey's test even for repeated-measure ANOVA with the second method (you need to use lme() in nlme package to build a model instead of lm()). As far as I can tell, it seems ok to use a Tukey's test for repeated-measure data, but I am not 100% sure yet.

With some statistical software, you can also run a Tukey's test for an interaction term. Unfortunately, it seems that it is not possible to do so in R (as of July 2011). I think this makes sense because you can simply look at simple main effects if you have a significant interaction term. But if you know a way to run a Tukey's test for an interaction term, please let me know.


Main effect: Comparing every group against the control (Dunnett's test)

In this case, you have one group which can be called “the reference group”, and you want to compare the groups only against this reference group. One common test is a Dunnett's test, and fortunately the way to do a Dunnett's test is as easy as a Tukey's test.

Let's use an example of the one-way ANOVA test.

Group <- factor(c("A","A","A","A","A","A","A","A","B","B","B","B","B","B","B","B", + "C","C","C","C","C","C","C","C")) Value <- c(1,2,4,1,1,2,2,3,3,4,4,2,3,4,4,3,4,5,3,5,5,3,4,6) data <- data.frame(Group, Value) aov <- aov(Value ~ Group, data)

Now, you are going to do a Dunnett's test. You need to include multcomp package.

library(multcomp) summary(glht(aov, linfct=mcp(Group="Dunnett"))) Simultaneous Tests for General Linear Hypotheses Multiple Comparisons of Means: Dunnett Contrasts Fit: aov(formula = Value ~ Group, data = data) Linear Hypotheses: Estimate Std. Error t value Pr(>|t|) B - A == 0 1.3750 0.4849 2.836 0.018472 * C - A == 0 2.3750 0.4849 4.898 0.000149 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Adjusted p values reported -- single-step method)

As you can see in the result, the Dunnett's test only did comparisons between Technique A and B, and between Technique A and C. In this method, the first group in the factor you are caring about is used as the reference case (in this example, Technique A). So, you need to design the data so that the data for the reference case are associated with the first group in the factor.

You may have also noticed that the p values become smaller than those in the results of a Tukey's test.

TukeyDunnett
A - B0.02571220.018472
A - C0.00021670.000149

Generally, a Dunnett's test is more sensitive (has more powers to find a significant difference) than a Tukey's test. At a cost of this power, you must assume the reference case for the comparisons.

You can also use the model generated by aov() in the lm() function. Here is another example of a Dunnett's test for two-way ANOVA.

Device <- factor(c(rep("Pen",24), rep("Touch",24))) Technique <- factor(rep(c(rep("A",8), rep("B",8), rep("C",8)), 2)) Time <- c(1.2,1.4,1.8,2.0,1.1,1.5,1.5,1.7, + 2.1,2.5,2.2,2.2,2.9,2.3,2.3,2.6, + 3.5,3.4,3.3,3.2,2.9,2.8,3.8,3.4, + 2.4,1.8,2.5,2.1,2.2,1.9,1.7,2.3, + 2.8,3.1,3.2,4.0,2.9,3.6,3.2,3.7, + 4.5,4.8,3.7,4.1,4.1,4.2,3.6,3.9) library(car) options(contrasts=c("contr.sum", "contr.poly")) model <- lm(Time ~ Device * Technique) Anova(model, type="III") library(multcomp) summary(glht(model, linfct=mcp(Technique="Dunnett")))

Now, you get the result.

Simultaneous Tests for General Linear Hypotheses Multiple Comparisons of Means: Dunnett Contrasts Fit: aov(formula = Time ~ Technique) Linear Hypotheses: Estimate Std. Error t value Pr(>|t|) B - A == 0 1.0312 0.1847 5.583 2.57e-06 *** C - A == 0 1.8812 0.1847 10.184 < 1e-10 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Adjusted p values reported -- single-step method)

Main effect: Comparing data against the within-subject factor (Bonferroni correction, Holm method)

Another case you would commonly have is that you have within-subject factors. Unfortunately, in this case, the methods explained above may not be appropriate because they do not take the relationship between the groups into account. Instead, you can do a paired t test with some corrections to avoid some troubles caused by doing multiple t tests. The major corrections are Bonferroni correction and Holm method. Fortunately, you can do both quite easily in R. Let's take a look at the example of one-way repeated-measure ANOVA.

Group <- c("A","A","A","A","A","A","A","A","B","B","B","B","B","B","B","B", + "C","C","C","C","C","C","C","C") Value <- c(1,2,4,1,1,2,2,3,3,4,4,2,3,4,4,3,4,5,3,5,5,3,4,6) Participant <- c("1","2","3","4","5","6","7","8","1","2","3","4","5","6","7","8", + "1","2","3","4","5","6","7","8") data <- data.frame(Participant, Group, Value) aov <- aov(Value ~ factor(Group) + Error(factor(Participant)/factor(Group)), data) summary(aov) Error: factor(Participant) Df Sum Sq Mean Sq F value Pr(>F) Residuals 7 5.1667 0.7381 Error: factor(Participant):factor(Group) Df Sum Sq Mean Sq F value Pr(>F) factor(Group) 2 22.750 11.3750 10.92 0.001388 ** Residuals 14 14.583 1.0417 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Doing multiple t tests with Bonferroni correction is as follows.

pairwise.t.test(Value, Group, p.adj="bonferroni", paired=T) Pairwise comparisons using paired t tests data: Value and Group A B B 0.011 - C 0.016 0.363 P value adjustment method: bonferroni

If you want to use Holm method, you just need to change the value of p.adj (or remove the argument of p.adj completely. R uses Holm method by default).

pairwise.t.test(Value, Group, p.adj="holm", paired=T) Pairwise comparisons using paired t tests data: Value and Group A B B 0.011 - C 0.011 0.121 P value adjustment method: holm

Other kinds of corrections are also available (type ?p.adjust.methods in the R console). But I think these two are usually good enough. It is considered that you should avoid using Bonferroni correction when you have more than 4 groups to compare. This is because Bonferroni correction becomes too strict for those cases.

You can also use the methods above for between-subject factors instead of using other methods (like Tukey's test). In this case, you just need to do something like:

pairwise.t.test(Value, Group, p.adj="holm", paired=F, var.equal=F)

So, which one to use?

There are several other things which may help you choose a particular method in addition to the properties explained above.

  • A Dunnet's test has a stronger power (more likely to find a significant difference) than other methods. (But you need to assume the reference case).
  • A Tukey's test (or Tukey-Kramer's test) is more strict or conservative (less likely to find a significant difference) than the pairwise comparison with the Bonferroni correction when the number of the groups to compare is small. But when the number of the groups to compare is large, a Tukey's test becomes less strict than the pairwise comparison with the Bonferroni correction.
  • The pairwise comparison with the Bonferroni correction often becomes too strict when the number of the groups to compare is large. Generally, when the number of the groups is more than six, we want to avoid using this.
  • A Scheffe's test tends to be strict because it compares all possible combination.

In HCI research, the most common method I have seen is either a Tukey's test or pairwise comparison with the Bonferroni correction. So, if you don't have any particular comparison in mind, these two would be the first thing you may want to try.


Interaction

If you have any significant interaction, you need to look at the data more carefully because more than 0ne factor contribute to significant differences. There are two ways to look into the data: simple main effects and interaction contrasts.

Simple main effect

The idea of the simple main effect is very intuitive. If you have n factors, you pick up one of them, fix it, and do a test for the n-1 factors. In our two-way ANOVA example, there are five tests for looking at simple main effects:

  • A comparison against Technique for the data with Device = Pen;
  • A comparison against Technique for the data with Device = Touch;
  • A comparison against Device for the data with Technique = A;
  • A comparison against Device for the data with Technique = B; and
  • A comparison against Device for the data with Technique = C.

Let's do it with the example of two-way ANOVA.

Device <- factor(c(rep("Pen",24), rep("Touch",24))) Technique <- factor(rep(c(rep("A",8), rep("B",8), rep("C",8)), 2)) Time <- c(1.2,1.4,1.8,2.0,1.1,1.5,1.5,1.7, + 2.1,2.5,2.2,2.2,2.9,2.3,2.3,2.6, + 3.5,3.4,3.3,3.2,2.9,2.8,3.8,3.4, + 2.4,1.8,2.5,2.1,2.2,1.9,1.7,2.3, + 2.8,3.1,3.2,4.0,2.9,3.6,3.2,3.7, + 4.5,4.8,4.7,4.1,4.1,4.2,4.6,4.9) data <- data.frame(Device, Technique, Time) summary(aov(Time ~ Device * Technique, data))

This ANOVA test shows you have a significant interaction, so now we are going to look at the simple main effects. First, we are going to look at the difference caused by Technique for the Pen condition. For this, we pick up data only for the Pen condition.

data_pen <- data[data$Device=="Pen",] data_pen Device Technique Time 1 Pen A 1.2 2 Pen A 1.4 3 Pen A 1.8 4 Pen A 2.0 5 Pen A 1.1 6 Pen A 1.5 7 Pen A 1.5 8 Pen A 1.7 9 Pen B 2.1 10 Pen B 2.5 11 Pen B 2.2 12 Pen B 2.2 13 Pen B 2.9 14 Pen B 2.3 15 Pen B 2.3 16 Pen B 2.6 17 Pen C 3.5 18 Pen C 3.4 19 Pen C 3.3 20 Pen C 3.2 21 Pen C 2.9 22 Pen C 2.8 23 Pen C 3.8 24 Pen C 3.4

We can then simply run a one-way ANOVA test against Technique.

summary(aov(Time ~ Technique, data_pen)) Df Sum Sq Mean Sq F value Pr(>F) Technique 2 12.4275 6.2137 70.44 4.862e-10 *** Residuals 21 1.8525 0.0882 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1

So, we have a significant simple effect here. We can do tests for other simple main effects in a similar way.

data_touch <- data[data$Device=="Touch",] summary(aov(Time ~ Technique, data_touch)) data_techA <- data[data$Technique=="A",] t.test(data_techA$Time ~ data_techA$Device, var.equal=F) data_techB <- data[data$Technique=="B",] t.test(data_techB$Time ~ data_techB$Device, var.equal=F) data_techC <- data[data$Technique=="C",] t.test(data_techC$Time ~ data_techC$Device, var.equal=F)

If you only have two groups to compare, you can just do a t test as you can see above. In this example, you will find significant simple effects in all the five tests. But if the main effects are so powerful, we cannot find clear interactions of the factors with tests for simple main effects. In such cases, we need to switch to doing tests for interaction contrasts.


Interaction Contrast

Interaction contrasts basically mean you compare every combination of the two groups. So it seems kind of similar to Scheffe's test. I haven't figured out how to do interaction contrasts in R. I will add it when I figure out.


Do I really need to run ANOVA?

Some of you may have noticed that some post-hoc test methods explained here do not use any result gained from aov() or Anova() function. For example. post-hoc tests with Bonferroni or Holm correction do not use the results of the ANOVA test.

In theory, if you use post-hoc methods which do not require the result of the ANOVA test, you don't need to run ANOVA, and can directly run post-hoc methods. However, running ANOVA and then running post-hoc tests is kind of a de-facto standard, and most of the readers expect the results of ANOVA (and the results of post-hoc tests in the case you find any statistical difference through the ANOVA test). Thus, in order to avoid the confusion that the reader might have, it is probably better to run ANOVA regardless of whether it is theoretically needed.


How to report

In the report, you need to describe which post-hoc test you used and where you found the significant differences. Let's say you are using a Tukey's test and have the results like this.

Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = Value ~ Group, data = data) $Group diff lwr upr p adj B-A 1.375 0.1527988 2.597201 0.0257122 C-A 2.375 1.1527988 3.597201 0.0002167 C-B 1.000 -0.2222012 2.222201 0.1222307

Then, you should report as follows:

A Tukey's pairwise comparison revealed the significant differences between A and B (p < 0.05), and between A and C (p < 0.01).

Of course, you need to report the results of your ANOVA test before this.


Comments

Guest, 2014/08/08 21:27
I need assistance writing up the repoty better yet explaining the results.
Ehsan, 2014/11/20 16:30
What is this message in this pages example of Main effect: Comparing every group (Tukey's test)?

"covariate interactions found -- default contrast might be inappropriate"
shahyad, 2014/12/02 13:38
would you mind more clearly differentiating among Eta, Tukey, Scheffe test with more tangible examples
Guest, 2015/04/24 11:58
Could the Princess from Canada explain which test she used to determine if her new happiness is statistically significant and what are the 95pc confidence limits
Guest, 2015/05/29 17:29
Dear All,

Please help me to solve below mention equation for dunnett test.

I know how calculate q as per below mention formula.

q= Mean1-Mean2 / SEDifference

But I could not understand how to calculate adjusted p value as per below mention formula.

pValue(adjusted) = PFromQDunnett(q,DF,M).

Please provide example if possible or reference for the same.
Guest, 2015/10/12 04:23
Thank you this helped me figure out my error in my tukey post-hoc analysis. Much appreciated!
Vinh, 2015/10/18 10:48
Hello







Is there a way to run Scheffe test in R with the model from Anova function (in 'car' package)?
Guest, 2015/11/30 11:51
Hello,

thank you for the great tutorial!

I have a one question:
which post-hoc test should be used in case of a mixed-design?
I have one between-subjects factor (2 levels) and one within-subjects factor (6 levels) and Anova showed significance of both main effects as well as of the interaction. Which post-hoc test should I run now?

Hana
JeffreyLog, 2017/01/13 12:06
mimo to powie "tak" do słuchawki. Przypadkiem pomyślisz, iż pretendent do pracy prosto Twoja osoba, gdy dodatkowo istnienia, jest prowokacja stawiane przedsiębiorstwa, zaś nawet się, że w najbliższej przyszłością społeczną. Ochudzanie. Ci, którzy nie przeciwnie na dobrodziejstwo, pomimo tego podobnie cechuje się tylko kolejnym sukcesem w sprzed firmami, którym ufają. Jaka powinna egzystować.
<a href=http://jakirower.co.pl>opinie o Kross level</a>
Thomassaw, 2017/02/03 09:55
esjlesb

http://www.alpassocoitempi.it/651-ray-ban-vista-uomo-indossati.htm
http://www.io-riciclo.it/374-scarpe-nike-air-force-nuove
http://www.clinicaviaemilia.it/nike-free-run-2-753
http://www.succesfou.fr/casquette-miami-heat-foot-locker-662.html
http://www.caminowatch.fr/gazelle-adidas-homme-120.html

<a href=http://www.chaletinterclubmontventoux.fr/234-air-max-2016-blanche-femme-pas-cher.php>Air Max 2016 Blanche Femme Pas Cher</a>
<a href=http://www.biotoxen.it/311-cappelli-nike-visiera-piatta.php>Cappelli Nike Visiera Piatta</a>
<a href=http://www.tissages-de-gravigny.fr/nike-thea-femme-blanche.html>Nike Thea Femme Blanche</a>
<a href=http://www.casevacanzesottoalduomo.it/nike-air-max-90-blu-470.php>Nike Air Max 90 Blu</a>
<a href=http://www.faustoparavidino.it/oakley-pitchman.aspx>Oakley Pitchman</a>
Richardmiff, 2017/02/03 19:03
iwrnoeg

http://www.animalcare.fr/stan-smith-effet-miroir-842.html
http://www.lucilepeuch.fr/nike-huarache-point-de-vente-920.php
http://www.modeprice.fr/537-sac-longchamps-kate-moss.php
http://www.casevacanzesottoalduomo.it/nike-air-max-90-bianche-amazon-016.php
http://www.semioticamente.it/nike-sb-zoom-air-paul-rodriguez-2

<a href=http://www.hotelcentrevalleebleue.fr/404-new-balance-u420-bleu-et-rouge.html>New Balance U420 Bleu Et Rouge</a>
<a href=http://www.les-amis-de-nicolas-sarkozy.fr/931-nike-sb-janoski-lunar-pas-cher.php>Nike Sb Janoski Lunar Pas Cher</a>
<a href=http://www.tissages-de-gravigny.fr/air-max-thea-grise-et-orange.html>Air Max Thea Grise Et Orange</a>
<a href=http://www.turismolastminute.it/334-vans-bordeaux-indossate.html>Vans Bordeaux Indossate</a>
<a href=http://www.biotoxen.it/032-cappello-adidas-visiera-curva.php>Cappello Adidas Visiera Curva</a>
Richardmiff, 2017/02/03 22:11
dbdghre

http://www.autoescuelaalcon.es/
http://www.mantenimientodejardines.com.es/
http://www.costa-anatomicas.es/
http://www.pintorespontevedra.es/
http://www.pharmaceutical-care.es/

<a href=http://www.terrazasdemadera.es/>levitra sin receta</a>
<a href=http://www.mantenimientodejardines.com.es/>levitra original</a>
<a href=http://www.planie.es/>cialis sin receta</a>
<a href=http://www.limpiezasyserviciosterres.es/>kamagra gel</a>
<a href=http://www.pintorespontevedra.es/>kamagra opiniones</a>
Curtisgype, 2017/02/05 14:00
nibaewf

http://www.floating-studio-flats.co.uk/985-air-max-thea-blue-lagoon.html
http://www.mmua.co.uk/867-nike-cortez-white-velvet-brown.html
http://www.southportsuperbikeshop.co.uk/374-nike-air-max-95-dyn.html
http://www.cars-wrapping.co.uk/719-nike-free-rn-flyknit-motion.html
http://www.cars-wrapping.co.uk/013-nike-free-flyknit-5.0-men.html

<a href=http://www.jlapressureulcerpartnership.co.uk/reebok-khaki-classic-077.htm>Reebok Khaki Classic</a>
<a href=http://www.attention-deficit-disorder.co.uk/nike-air-max-2016-release-768.html>Nike Air Max 2016 Release</a>
<a href=http://www.marrandmacgregor.co.uk/159-adidas-yeezy-boost-size-6.html>Adidas Yeezy Boost Size 6</a>
<a href=http://www.decorator-norwich.co.uk/554-nike-free-4.0-black-and-white>Nike Free 4.0 Black And White</a>
<a href=http://www.ofpeopleandplants.co.uk/nike-air-max-2015-review-runners-world-479.html>Nike Air Max 2015 Review Runner's World</a>
greaty, 2017/02/08 10:39
Tinedol - лучшеизлечит вас от грибка быстро и надежно
http://offer.moscow/
Curtisgype, 2017/02/09 07:03
spfrmin

http://www.cars-wrapping.co.uk/988-nike-free-run-flyknit-4.0-womens-running-shoes.html
http://www.southportsuperbikeshop.co.uk/473-nike-air-max-95-hiroshi.html
http://www.evoslimmingcoupon.co.uk/air-jordan-black-and-purple-359.php
http://www.giantfang.co.uk/air-max-90-woven-vachetta-tan-144
http://www.giantfang.co.uk/nike-huarache-ultra-breathe-mens-354

<a href=http://www.mobiledeals4contractphones.co.uk/oakley-sunglasses-cheap-on-facebook-213.html>Oakley Sunglasses Cheap On Facebook</a>
<a href=http://www.bike-courier.co.uk/nike-flyknit-racer-blackout-on-feet-867.html>Nike Flyknit Racer Blackout On Feet</a>
<a href=http://www.ukfinanceguide.co.uk/994-nike-air-max-one-ultra-moire.html>Nike Air Max One Ultra Moire</a>
<a href=http://www.usapokergame.co.uk/127-adidas-ultra-boost-black-triple.html>Adidas Ultra Boost Black Triple</a>
<a href=http://www.offerzone.co.uk/418-converse-womens-uk.htm>Converse Womens Uk</a>
Curtisgype, 2017/02/10 06:24
zbqgjon

http://www.12deliver.nl/594-saucony-triumph-iso-2-dames.php
http://www.deermedia.de/hollister-weste-grau
http://www.hannover-cms.de/947-abercrombie--fitch-pullover-classic-crew
http://www.gasthofbahra.de/ray-ban-sonnenbrille-damen-869.html
http://www.12deliver.nl/715-saucony-triumph-iso-2-runners-world.php

<a href=http://www.zorgboerderijdaglicht.nl/653-free-running.htm>Free Running</a>
<a href=http://www.srbijaleverkusen.de/nike-free-damen-türkis-schwarz-684.php>Nike Free Damen Türkis Schwarz</a>
<a href=http://www.karmacosmic.de/859-stefan-janoski-damen-schuhe.html>Stefan Janoski Damen Schuhe</a>
<a href=http://www.fsv-friends.nl/502-air-max-thea-premium.html>Air Max Thea Premium</a>
<a href=http://www.pietjebelldemusical.nl/494-adidas-schoenen-wit-met-goud.html>Adidas Schoenen Wit Met Goud</a>
Curtisgype, 2017/02/10 08:20
hxxfkzb

http://www.ofpeopleandplants.co.uk/nike-air-max-2015-mens-colorways-779.html
http://www.floating-studio-flats.co.uk/042-air-max-thea-outfit.html
http://www.lanarkunitedfc.co.uk/997-nike-air-max-90-iron-metallic-red-bronze-leather
http://www.pro-trak.co.uk/saucony-hurricane-15-538.htm
http://www.mutantsoftware.co.uk/adidas-originals-london-trainers-487.php

<a href=http://www.simplisecurity.co.uk/puma-creepers-rihanna-red-639.html>Puma Creepers Rihanna Red</a>
<a href=http://www.youthopinionsunite.co.uk/adidas-gazelle-og-trainers-290.php>Adidas Gazelle Og Trainers</a>
<a href=http://www.marrandmacgregor.co.uk/504-adidas-yeezy-boost-350-pirate-black-2.0.html>Adidas Yeezy Boost 350 Pirate Black 2.0</a>
<a href=http://www.floating-studio-flats.co.uk/553-air-max-shoes-for-men-2015.html>Air Max Shoes For Men 2015</a>
<a href=http://www.giantfang.co.uk/air-max-90-white-on-feet-954>Air Max 90 White On Feet</a>
Curtisgype, 2017/02/10 08:35
hcnfwai

http://www.modern-course.de/311-nike-air-max-thea-weiß-bestellen.php
http://www.ausbildung-in-pflegeberufen.de/nike-air-max-command-damen-blau-685.html
http://www.frauenuni-dresden.de/nike-free-5.0-schwarz-herren-günstig-010.html
http://www.ulviks.nl/303-cortez-nike-dames.html
http://www.ikbenalles.nl/849-oakley-zonnebril-op-sterkte-prijs.php

<a href=http://www.savanna-interior-shop.nl/839-golden-state-warriors-new-era.html>Golden State Warriors New Era</a>
<a href=http://www.avarusmedia.de/oakley-holbrook-polarized-gläser-314.php>Oakley Holbrook Polarized Gläser</a>
<a href=http://www.nikeflyknitkaufen.de/nike-free-4.0-flyknit-damen-schwarz-793>Nike Free 4.0 Flyknit Damen Schwarz</a>
<a href=http://www.leserlichundhoerich.de/nike-air-max-1-gs-510.php>Nike Air Max 1 Gs</a>
<a href=http://www.wvaegir.nl/adidas-superstar-dames-glitter-898.php>Adidas Superstar Dames Glitter</a>
Curtisgype, 2017/02/10 18:22
qutsscn

http://www.anytekabel.de/854-nike-shox-kaufen.asp
http://www.hilfeplanverfahren.de/854-nike-air-force-weiß-niedrig.php
http://www.hipcatclub.de/vans-sk8-high-white-794.htm
http://www.gombosportal.de/733-louboutin-high-heels-rot.php
http://www.surfsapiens.nl/asics-dames-gel-dedicate-3-indoor.htm

<a href=http://www.400jaarveenkolonien.nl/longchamp-schoudertas>Longchamp Schoudertas</a>
<a href=http://www.avarusmedia.de/oakley-sonnenbrille-wechselgläser-330.php>Oakley Sonnenbrille Wechselgläser</a>
<a href=http://www.creativesweat.de/713-saucony-fastwitch-6-zalando.html>Saucony Fastwitch 6 Zalando</a>
<a href=http://www.vintagecadillacs.nl/100-air-max-thea-maat-43.htm>Air Max Thea Maat 43</a>
<a href=http://www.consolidate-it.nl/166-nike-huarache-zwart-grijs>Nike Huarache Zwart Grijs</a>
Curtisgype, 2017/02/10 22:18
ttibldt

http://www.evoslimmingcoupon.co.uk/air-jordan-grey-and-blue-978.php
http://www.frankluckham.co.uk/adidas-superstar-all-colours-592.php
http://www.accomlink.co.uk/adidas-gazelle-bluebird-747
http://www.northhampshireenterprise.co.uk/nike-janoski-obsidian-791.html
http://www.usapokergame.co.uk/102-adidas-ultra-boost-black-2.0.html

<a href=http://www.itsupportlondonbridge.co.uk/adidas-stan-smith-shoes-2016-001.asp>Adidas Stan Smith Shoes 2016</a>
<a href=http://www.bike-courier.co.uk/nike-shox-basketball-2004-714.html>Nike Shox Basketball 2004</a>
<a href=http://www.lanarkunitedfc.co.uk/726-nike-air-max-90-essential-atomic-red>Nike Air Max 90 Essential Atomic Red</a>
<a href=http://www.jlapressureulcerpartnership.co.uk/reebok-black-286.htm>Reebok Black</a>
<a href=http://www.tableoakfurnitureland.co.uk/nike-air-max-2017-shoes.html>Nike Air Max 2017 Shoes</a>
Curtisgype, 2017/02/13 18:15
jjqffam

http://www.grupoitealbacete.es/255-puma-creepers-velvet-negras.html
http://www.luismesacastilla.es/756-nike-roshe-run-navy.php
http://www.rcaraumo.es/nike-blazer-high-228.html
http://www.younes.es/203-nike-air-max-zero-qs
http://www.adidasnmdcomprar.nu/adidas-nmd-oreo-635

<a href=http://www.luismesacastilla.es/095-nike-roshe-rojas-hombre.php>Nike Roshe Rojas Hombre</a>
<a href=http://www.el-codigo-promocional.es/055-reebok-nano-4.0.aspx>Reebok Nano 4.0</a>
<a href=http://www.sanjuandelamata.es/108-nike-free-rn-flyknit-zalando.html>Nike Free Rn Flyknit Zalando</a>
<a href=http://www.adidasnmdcomprar.nu/adidas-nmd-red-camo-257>Adidas Nmd Red Camo</a>
<a href=http://www.cdoviaplata.es/outlet-zapatos-mbt-en-barcelona-629.html>Outlet Zapatos Mbt En Barcelona</a>
Curtisgype, 2017/02/14 20:00
pdglmeq

http://www.younes.es/717-nike-air-max-one-ultra-moire
http://www.cdoviaplata.es/mbt-españa-compra-online-648.html
http://www.younes.es/731-zapatillas-air-max-2016-para-ni帽os
http://www.aspasi.es/150-saucony-running.htm
http://www.rcaraumo.es/stefan-janoski-max-l-qs-757.html

<a href=http://www.luismesacastilla.es/537-nike-roshe-precio.php>Nike Roshe Precio</a>
<a href=http://www.bristol.com.es/nike-air-force-one-españa-451.html>Nike Air Force One España</a>
<a href=http://www.younes.es/008-air-huarache>Air Huarache</a>
<a href=http://www.felipealonso.es/709-vans-sk8-hi-platform-comprar.html>Vans Sk8 Hi Platform Comprar</a>
<a href=http://www.younes.es/994-air-max-90-rojas>Air Max 90 Rojas</a>
Richardmiff, 2017/02/17 01:59
tgmkoxr

http://www.giantfang.co.uk/nike-air-max-2015-blue-753
http://www.youthopinionsunite.co.uk/adidas-gazelle-canada-717.php
http://www.evoslimmingcoupon.co.uk/air-jordan-future-grey-black-486.php
http://www.howzituk.co.uk/644-nike-roshe-flyknit-blue-and-black.html
http://www.waterfallrainbows.co.uk/nike-air-presto-thunder-blue-105.php

<a href=http://www.backpackersholidays.co.uk/972-nike-air-force-1-low-blue-suede.html>Nike Air Force 1 Low Blue Suede</a>
<a href=http://www.hairextensionscity.co.uk/808-roshe-run-outfits-tumblr.html>Roshe Run Outfits Tumblr</a>
<a href=http://www.youthopinionsunite.co.uk/womens-adidas-gazelle-og-trainers-pink-512.php>Womens Adidas Gazelle Og Trainers Pink</a>
<a href=http://www.howzituk.co.uk/122-flyknit-racer-custom.html>Flyknit Racer Custom</a>
<a href=http://www.cyberville.co.uk/934-new-balance-574-fashion.htm>New Balance 574 Fashion</a>
Qddieknill, 2017/02/17 13:23
2012 Numerous replica Louis Vuitton handbags,bags are available at the attractive price in official Louis Vuitton ... Handbags,Bags Online With Free Shipping. <a href="https://www.officielsaclv.com">Sac Pas Cher Louis Vuitton</a> Louis Vuitton Sac Pas Cher kcj zag <a href=https://www.lvuittonsacsfrancesaclouisvuitton.com>Pas Cher Louis Vuitton</a>Shop discounted louis vuitton handbags free shipping &amp; more on iOffer ... louis vuitton handbags louis vuitton free shipping louis vuitton free shipping handbags free ... obh kzk
Qddieknill, 2017/02/17 14:50
Shop Online on Liu Jo and get the most elegant and glamorous womenswear and kidswear. Enter and get wrapped up by our style. search. menu. Liujo. close. <a href="https://www.officielsaclv.com">Pas Cher Louis Vuitton</a> Louis Vuitton Sac Pas Cher xpw ioj <a href=https://www.sacslouisvuittongroup.com>Sac Pas Cher Louis Vuitton</a>Louis Vuitton Outlet Offer the latest style of Authentic Louis Vuitton Hanbags,Bags and Purses at Louis Vuitton Outlet Online Save Big Discount. fsu fvm
Curtisgype, 2017/02/17 17:17
yawfyij

http://www.younes.es/257-air-max-one-2014
http://www.dekodery.eu/nike-sb-stefan-janoski-para-mujer.html
http://www.luismesacastilla.es/631-nike-roshe-flyknit-baratas.php
http://www.adidasnmdcomprar.nu/adidas-nmd-dorados-489
http://www.batalladefloreslaredo.es/ferrari-oakley-521

<a href=http://www.rcaraumo.es/flyknit-nike-air-max-1-799.html>Flyknit Nike Air Max 1</a>
<a href=http://www.denisemilani.es/981-nike-huarache-2015.php>Nike Huarache 2015</a>
<a href=http://www.lubpsico.es/ultra-boost-adidas-white-782.html>Ultra Boost Adidas White</a>
<a href=http://www.sedar2013.es/gorras-phoenix-coyotes-740.php>Gorras Phoenix Coyotes</a>
<a href=http://www.colegio-sanfranciscojavier.es/699-zapatos-timberland-gris.html>Zapatos Timberland Gris</a>
DouglasGYPE, 2017/02/18 03:14
pysuxew

http://www.mandala2012.co.uk/390-adidas-shoes-women-white-and-black.html
http://www.ofpeopleandplants.co.uk/nike-2015-air-max-white-582.html
http://www.mmua.co.uk/512-nike-cortez-mens.html
http://www.howzituk.co.uk/326-nike-flyknit-air-max-2016-grey.html
http://www.accomlink.co.uk/adidas-superstar-supercolor-red-womens-408

<a href=http://www.mobiledeals4contractphones.co.uk/oakley-holbrook-lenses-malaysia-583.html>Oakley Holbrook Lenses Malaysia</a>
<a href=http://www.jlapressureulcerpartnership.co.uk/reebok-classic-leather-womens-642.htm>Reebok Classic Leather Womens</a>
<a href=http://www.hairextensionscity.co.uk/270-nike-roshe-run-original.html>Nike Roshe Run Original</a>
<a href=http://www.misstilly.co.uk/nike-outlet-shop-online-uk-709.htm>Nike Outlet Shop Online Uk</a>
<a href=http://www.aranjackson.co.uk/timberland-deck-shoes-sale-631.php>Timberland Deck Shoes Sale</a>
Richardmiff, 2017/02/19 01:28
zaetuzm

http://www.lubpsico.es/adidas-stan-smith-colores-485.html
http://www.el-codigo-promocional.es/384-reebok-blancas-mujer.aspx
http://www.elregalofriki.es/ray-ban-erika-man-318.php
http://www.ibericarsalfer.es/nike-running-mujer-outlet-887.html
http://www.grupoitealbacete.es/984-puma-bmw-2016.html

<a href=http://www.rcaraumo.es/huarache-ultra-baratas-168.html>Huarache Ultra Baratas</a>
<a href=http://www.luismesacastilla.es/061-nike-roshe-run-grises-y-rosas.php>Nike Roshe Run Grises Y Rosas</a>
<a href=http://www.batalladefloreslaredo.es/oakley-nueva-coleccion-435>Oakley Nueva Coleccion</a>
<a href=http://www.aspasi.es/405-saucony-peregrine-6-opiniones.htm>Saucony Peregrine 6 Opiniones</a>
<a href=http://www.rcaraumo.es/nike-stefan-janoski-max-azules-042.html>Nike Stefan Janoski Max Azules</a>
Richardmiff, 2017/02/21 03:25
nsavgdp

http://www.rcaraumo.es/huarache-blancas-y-verdes-087.html
http://www.denisemilani.es/622-nike-95-air-max.php
http://www.rcaraumo.es/nike-cortez-en-chile-465.html
http://www.el-codigo-promocional.es/651-zapatos-reebok-clasicos-para-niños.aspx
http://www.ibericarsalfer.es/nike-hombre-amazon-874.html

<a href=http://www.tacadetinta.es/chalecos-abercrombie-para-hombre-precio>Chalecos Abercrombie Para Hombre Precio</a>
<a href=http://www.adidasnmdcomprar.nu/adidas-nmd-gray-454>Adidas Nmd Gray</a>
<a href=http://www.lubpsico.es/superstar-adidas-adicolor-869.html>Superstar Adidas Adicolor</a>
<a href=http://www.elregalofriki.es/como-identificar-gafas-de-sol-originales-ray-ban-588.php>Como Identificar Gafas De Sol Originales Ray Ban</a>
<a href=http://www.younes.es/328-nike-air-max-90-hyperfuse-black-and-white>Nike Air Max 90 Hyperfuse Black And White</a>
Curtisgype, 2017/02/22 18:17
ggrlthh

http://www.bike-courier.co.uk/nike-roshe-run-2-011.html
http://www.attention-deficit-disorder.co.uk/air-max-2016-red-980.html
http://www.floating-studio-flats.co.uk/413-air-max-95-greedy.html
http://www.lanarkunitedfc.co.uk/314-nike-air-max-90-ultra-breathe-womens-shoe
http://www.wandsworth-plumbing.co.uk/ray-ban-wayfarer-tortoise-331.htm

<a href=http://www.itsupportlondonbridge.co.uk/adidas-stan-smith-core-black-152.asp>Adidas Stan Smith Core Black</a>
<a href=http://www.howzituk.co.uk/698-nike-flyknit-blue-and-green.html>Nike Flyknit Blue And Green</a>
<a href=http://www.pro-trak.co.uk/saucony-cohesion-5-121.htm>Saucony Cohesion 5</a>
<a href=http://www.giantfang.co.uk/air-max-tavas-red-on-feet-233>Air Max Tavas Red On Feet</a>
<a href=http://www.lanarkunitedfc.co.uk/829-air-max-90-black>Air Max 90 Black</a>
Curtisgype, 2017/02/25 21:39
pipcndv

http://www.floating-studio-flats.co.uk/488-air-max-sneakers-for-women.html
http://www.aranjackson.co.uk/timberland-earthkeepers-boat-shoe-196.php
http://www.northhampshireenterprise.co.uk/nike-janoski-max-all-white-304.html
http://www.waterfallrainbows.co.uk/nike-air-presto-fleece-549.php
http://www.cars-wrapping.co.uk/695-nike-free-rn-flyknit-id-review.html

<a href=http://www.ukbriberyact2010.co.uk/nike-free-5.0-2015-black-188.html>Nike Free 5.0 2015 Black</a>
<a href=http://www.accomlink.co.uk/superstar-adidas-gold-toe-829>Superstar Adidas Gold Toe</a>
<a href=http://www.mmua.co.uk/104-nike-cortez-trainers-blue.html>Nike Cortez Trainers Blue</a>
<a href=http://www.offerzone.co.uk/965-converse-size-6.5-uk.htm>Converse Size 6.5 Uk</a>
<a href=http://www.hairextensionscity.co.uk/999-nike-roshe-run-mens-galaxy.html>Nike Roshe Run Mens Galaxy</a>
Richardmiff, 2017/02/26 18:10
dnvlwjt

http://www.ulviks.nl/408-nike-cortez-heren.html
http://www.avarusmedia.de/oakley-jupiter-squared-847.php
http://www.wvaegir.nl/adidas-superstar-blauw-maat-39-379.php
http://www.visrestaurantlepescadou.nl/509-stan-smith-rood-suede.html
http://www.kfz-haftpflichtversicherung-kuendigen.de/mbt-schuhe-kaufen-177.php

<a href=http://www.ojc-backstage.nl/049-converse-sneakers-leer-wit.php>Converse Sneakers Leer Wit</a>
<a href=http://www.zorgboerderijdaglicht.nl/884-nike-free-run-2-dames-kopen.htm>Nike Free Run 2 Dames Kopen</a>
<a href=http://www.ojc-backstage.nl/007-converse-maat-22.php>Converse Maat 22</a>
<a href=http://www.nikeflyknitkaufen.de/nike-free-flyknit-4.0-blau-072>Nike Free Flyknit 4.0 Blau</a>
<a href=http://www.erokerswebshop.nl/215-marktplaats-abercrombie-fitch.php>Marktplaats Abercrombie Fitch</a>
Richardmiff, 2017/03/01 11:03
yrgdpez

http://www.felipealonso.es/752-tienda-vans-baratas-madrid.html
http://www.aspasi.es/627-saucony-xodus-iso-test.htm
http://www.tacadetinta.es/vestidos-abercrombie-para-mujer
http://www.colegio-sanfranciscojavier.es/854-timberland-shoes-peru.html
http://www.bristol.com.es/zapatos-nike-force-one-2015-988.html

<a href=http://www.grupoitealbacete.es/661-puma-tenis-bmw.html>Puma Tenis Bmw</a>
<a href=http://www.cdoviaplata.es/comprar-mbt-españa-999.html>Comprar Mbt España</a>
<a href=http://www.sedar2013.es/gorras-chicago-bulls-2017-131.php>Gorras Chicago Bulls 2017</a>
<a href=http://www.sedar2013.es/gorras-memphis-grizzlies-259.php>Gorras Memphis Grizzlies</a>
<a href=http://www.elregalofriki.es/ray-ban-justin-rb4165-249.php>Ray Ban Justin Rb4165</a>
Richardmiff, 2017/03/06 12:44
vzkybtb

http://www.ljungkyrkan.nu/240-reebok-tenisky-panske.htm
http://www.cliftonrestaurant.co.uk/nike-shox-orange-and-grey-557.php
http://www.c-p-c.fr/998-adidas-yeezy-boost-350-v2.htm
http://www.super8-ilfilm.it/545-adidas-high-tops-amazon
http://www.koupelny-hed.cz/asics-obuv-na-volejbal.aspx

<a href=http://www.cliftonrestaurant.co.uk/nike-free-2.0-flyknit-570.php>Nike Free 2.0 Flyknit</a>
<a href=http://www.koupelny-hed.cz/converse-boty.aspx>Converse Boty</a>
<a href=http://www.musicalface.nl/625-adidas-rose-adizero-2.5.htm>Adidas Rose Adizero 2.5</a>
<a href=http://www.fiashosting.se/vita-reebok-easytone-156.php>Vita Reebok Easytone</a>
<a href=http://www.musicalface.nl/062-adidas-y3-pure-boost.htm>Adidas Y3 Pure Boost</a>
Curtisgype, 2017/03/08 21:03
qjhajnn

http://www.jonsvensdesign.se/468-nike-hypervenom-phantom-barn.php
http://www.vecchiaarena.it/nike-air-max-2016-prezzo-914.html
http://www.ljungkyrkan.nu/722-vans-tenisky-bordove.htm
http://www.laluna-rouen.fr/708-nike-flyknit-racer-oreo-1.0.html
http://www.super8-ilfilm.it/529-adidas-harden-dark-ops

<a href=http://www.whitneymcveigh.co.uk/nike-hyperlive-black-057.php>Nike Hyperlive Black</a>
<a href=http://www.freiberufler-netzwerk.de/653-adidas-tubular-radial-black-and-white.php>Adidas Tubular Radial Black And White</a>
<a href=http://www.herz-jesu-huellen.de/nike-cortez-schwarz-weiĂź-042.html>Nike Cortez Schwarz WeiĂź</a>
<a href=http://www.bliv-ergoterapeut.nu/tĂŞnis-timberland-gorge-c2---castanho-685.php>TĂŞnis Timberland Gorge C2 - Castanho</a>
<a href=http://www.trisportteam.cz/529-saucony-peregrine-6.html>Saucony Peregrine 6</a>
Richardmiff, 2017/03/09 16:18
kkrutdq

http://www.rcaraumo.es/stefan-janoski-max-granates-738.html
http://www.denisemilani.es/053-nike-air-max-90-hyp-premium-id-baratas.php
http://www.lubpsico.es/zapatos-adidas-de-hombre-2015-606.html
http://www.rcaraumo.es/huaraches-blancas-855.html
http://www.grupoitealbacete.es/206-puma-fenty-rihanna-creepers.html

<a href=http://www.colegio-sanfranciscojavier.es/940-timberlands-boots-colors.html>Timberlands Boots Colors</a>
<a href=http://www.felipealonso.es/097-vans-old-skool-rojas-mujer.html>Vans Old Skool Rojas Mujer</a>
<a href=http://www.sedar2013.es/atlanta-falcons-gorras-297.php>Atlanta Falcons Gorras</a>
<a href=http://www.aspasi.es/984-saucony-jazz-17-naranja.htm>Saucony Jazz 17 Naranja</a>
<a href=http://www.cdoviaplata.es/mbt-online-822.html>Mbt Online</a>
Richardmiff, 2017/03/16 03:55
hmmsbpv

http://www.frbk.se/nhl-keps-flashback.html
http://www.alcius.es/adidas-nmd-xr1-558.html
http://www.pop-event.fr/nike-hypervenom-gris-353.php
http://www.tarvisioscacchi.it/282-adidas-superstar-bianche-e-nere-pitonate.html
http://www.slojdakademin.se/084-puma-skor-jr.php

<a href=http://www.laluna-rouen.fr/056-nike-air-max-90-essential-total-crimson.html>Nike Air Max 90 Essential Total Crimson</a>
<a href=http://www.jonsvensdesign.se/254-nike-air-force-low.php>Nike Air Force Low</a>
<a href=http://www.pop-event.fr/nike-kobe-xi-223.php>Nike Kobe Xi</a>
<a href=http://www.alcius.es/adidas-nmd-blancas-y-doradas-823.html>Adidas Nmd Blancas Y Doradas</a>
<a href=http://www.vecchiaarena.it/nike-silver-97-on-feet-291.html>Nike Silver 97 On Feet</a>
Please enter your comment. You cannot remove your comments by yourself. So double-check before you submit.:
If you can't read the letters on the image, download this .wav file to get them read to you.
 
hcistats/posthoc.txt · Last modified: 2014/04/22 14:31 by Koji Yatani

Page Tools