I did the Three-Way ANOVA test and A, B, C, AB, B*C, A*C, A*B*C are all significant. Now,   What can I tell based on this results? Is it valid to say for example A*B is significant? Or the fact that A*B*C is significant, makes it wrong to say A*B is significant?  Should/Can I do Two-way ANOVA even though I have 3 factors?
26100
I have a significant three-way interaction (with no significant two-way interactions and no significant main effects).  To begin with I have followed this up with two two-way ANOVAs (one at each level of the third variable). The first part of my question is whether this is an appropriate follow-up.  This showed no significant main effects or interactions at either level of the third variable...is this the end of the analysis?  If so, how would I interpret the three-way interaction?
41814
In my experiment, I asked 50 participants to rank on a 5 point scale which voice they preferred. I summed each particpants' rating for each voice: the total for voice 1 is 95, the total for voice 2 is 186.  Am I correct in doing this? Or should I analyse the raw data?  Which test should I use for this data? Would a t-test work here? Alternatively I thought I could use a chi-square test.   I am interested in seeing if the preference for voice 2 is significant.
8582
I have a question on how a statistician would normally interpret an anova output. Say I have anova output from R.  &gt; summary(fitted_data)  Call: lm(formula = V1 ~ V2)  Residuals:      Min       1Q   Median       3Q      Max  -2.74004 -0.33827  0.04062  0.44064  1.22737   Coefficients:             Estimate Std. Error t value Pr(&gt;|t|)     (Intercept)  2.11405    0.32089   6.588  1.3e-09 *** V2           0.03883    0.01277   3.040  0.00292 **  --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1   Residual standard error: 0.6231 on 118 degrees of freedom Multiple R-squared: 0.07262,    Adjusted R-squared: 0.06476  F-statistic:  9.24 on 1 and 118 DF,  p-value: 0.002917   &gt; anova(fit) Analysis of Variance Table  Response: V1            Df Sum Sq Mean Sq F value   Pr(&gt;F)    V2          1  3.588  3.5878  9.2402 0.002917 ** Residuals 118 45.818  0.3883                     --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1    From the above, I guess the most important value is Pr(>F), right? So this Pr, is less than 0.05 (95% level). How should my "explain" this? Do I explain it in "association", ie, V2 and V1 are associated (or not) ? or in terms of "significance"? I always felt that I couldn't understand when people say "This value is significant....". So what is "significant"? Is there a more intuitive form of explanation? like "I am 95% confident that ...." .   Also, is the Pr value the only important piece of information? or can i also look at residuals and the rest of the output to "explain" the result? thanks
82733
I recently conducted a online survey and are now having trouble deciding for the right analysis method. For example: I wanted to see if there is a correlation between Factor A and Factor B. However in my survey I did not ask the participants to directly rate Factor A and Factor B, but rather asked multiple subquestions for these two factors which were rated from 5(Strongly Agree) to 1 (Strongly Disagree). I created a sum score for item A and a sum score for item B by summing up the values of each subquestion and calculated the mean of the sumscores to measure them. So my question ist: Which method would be best to use here? I want to test if e.g. people with a higher score in Factor A would be more likely to decide for Factor B. I actually planned using Spearman or ANOVA depending on the number of independent variables, but I am not sure if that would really be the correct way to measure the correlation.
43570
I'm a little confused regarding the intraclass correlation coefficient and one-way ANOVA.  As I understand it, both tell you how similar observations within a group are, relative to observations in other groups.  Could someone explain this a little better, and perhaps explain the situation(s) in which each method is more advantageous?
100541
Recently I have been struggling with the following two questions regarding the chi-squared test of independence / association during reading an article.        Is the chi-squared test able to detect no association between two groups among three at two levels? That is in a 3X2 contingency table.   Does the chi-squared test change its behavior with a larger sample that was otherwise perfectly proportional to a smaller sample?     I prepared a sample data set in R to seek the answers of these two questions. Though my initial discomfort about the chi-squared test have been proven, but over-acceptance of this test statistic in the scientific community have forced me to re-think. May be I have been missing something here.    # Question 1 x1 = c(100, 450, 450) x2 = c(600, 450, 450) d1 = rbind(x1,x2) colnames(d1) = c("Type 1", "Type 2", "Type 3") rownames(d1) = c("No", "Yes") d1 chisq.test(d1) # Significantly associated (not independent), though "Type 2" &amp; "Type 3"  #  were not different at all!   # Question 2 d2 = d1/50 d2 chisq.test(d2) # Not significant!!!  d3 = d2*2 d3 chisq.test(d3) # Significant!!!
52413
I have some non-Gaussian distributed variable and I need to check if there are significant differences between the values of this variable in 5 different groups.  I have performed Kruskal-Wallis one-way analysis of variance (which came up significant) and after that I had to check which groups were significantly different. Since the groups are kind of sorted (the values of the variable in the first group are supposed to be lower than the values of the variable in the second group which are supposed to be lower than the values of the variable in the third group and so on) I only performed 4 tests:  Group 1 vs Group 2 Group 2 vs Group 3 Group 3 vs Group 4 Group 4 vs Group 5   I have performed this analysis with two different methods. I started by using Dunn's Multiple Comparison Test but nothing came up significant. On the other hand if I use Mann-Whitney test and correct for the number of tests (4) using Bonferroni, 3 tests come up significant.  What does it mean? Which results should I trust?
18795
This isn't a strictly stats question--I can read all the textbooks about ANOVA assumptions--I'm trying to figure out how actual working analysts handle data that doesn't quite meet the assumptions. I've gone through a lot of questions on this site looking for answers and I keep finding posts about when not to use ANOVA (in an abstract, idealized mathematical context) or how to do some of the things I describe below in R. I'm really trying to figure out what decisions people actually make and why.   I'm running analysis on grouped data from trees (actual trees, not statistical trees) in four groups. I've got data for about 35 attributes for each tree and I'm going through each attribute to determine if the groups differ significantly on that attribute. However, in a couple of cases, the ANOVA assumptions are slightly violated because the variances aren't equal (according to a Levene's test, using alpha=.05).   As I see it, my options are to: 1. Power transform the data and see if it changes the Levene p-val. 2. Use a non-parametric test like a Wilcoxon (if so, which one?). 3. Do some kind of correction to the ANOVA result, like a Bonferroni (I'm not actually sure if something like this exists?). I've tried the first two options and gotten slightly different results--in some cases one approach is significant and the other is not. I'm afraid of falling into the p-value fishing trap, and I'm looking for advice that will help me justify which approach to use.  I've also read some things that suggest that heteroscedasticity isn't really that big of a problem for ANOVA unless the means and variances are correlated (i.e. they both increase together), so perhaps I can just ignore the Levene's result unless I see a pattern like that? If so, is there a test for this?  Finally, I should add that I'm doing this analysis for publication in a peer-reviewed journal, so whatever approach I settle on has to pass muster with reviewers. So, if anyone can provide links to similar, published examples that would be fantastic.
73399
A woman I was working for asked me to do a one-way ANOVA on some data. I replied that the data were repeated measures (time series) data, and that I thought the assumption of independence was violated. She replied that I should not worry about the assumptions, just do the test and she would take into account that the assumptions might not have been met.  That did not seem right to me. I did some research, and found this wonderful blog post by David Robinson, , which exposed me to the No Free Lunch Theorem. I have looked at the original paper and some follow on stuff, and frankly the math is a bit over my head.  The gist of it -- according to David Robinson -- seems to be that the power of a statistical test comes from its assumptions. And he gives two great examples. As I wade through the other articles and blog posts about it, it seems to always be referenced in terms of either supervised learning or search.  So my question is, does this theorem apply to statistical tests in general? In other words, can one say that the power of a t-test or ANOVA comes from its adherence to the assumptions, and cite the No Free Lunch Theorem?   I owe my former boss a final document regarding the work I did, and I would like to know if I can reference the No Free Lunch Theorem in stating that you cannot just ignore the assumptions of a statistical test and say you'll take that into account when evaluating the results.
104861
I have an experiment where I measure the effect of a manipulation on two different groups of participants, and the variable that I manipulate also has two levels. Thus, I can essentially use a 2x2 ANOVA to analyze the results. But it is also possible for me to measure the effect of the different levels of the variable first on Group 1 and then on Group 2, by using paired-samples t-tests.   Is there a rule of thumb to decide what needs to be done in this case? I think one advantage of using an ANOVA could be the option to investigate the interaction between the different groups and the different levels of the variable. Perhaps one could also argue that an omnibus analysis is also a better choice from a stylistic point of view.   But is there a very compelling conceptual reason to prefer a 2x2 ANOVA over two separate pairwise comparisons in my case? And if so, what would it be?
48469
I am using a MANOVA test to compare nine different dependent variables (from neuropsychological and neuropsychiatric assessment) between three groups. The output shows a significant influence from GROUP on my variables ($p &lt; .001$).   Ofcourse, I am interested in how the three groups influence every dependent variable. I have studied Field's "Discovering Statistics Using IBM SPSS Statistics" chapter 16, and he states that the preferred post-hoc analysis is a discriminant analysis, because of the linear combination in which the dependent variables are related to group membership in a MANOVA. Discriminant analysis could account for this linear combination, so Field states.  Otherwise, I read some literature, on basic statistical sites, where is stated that I can use multiple univariate ANOVA's with Bonferroni correction, and use a post-hoc on these univariate ANOVA's when they are significant.   Which of these method's is better? That is, which will make my chance of a Type I or II error the least?
109655
So I have multiple questions about the different types of analyses that can be used on a 2x2 contingency table and when different analyses should be used.   To open, I'll note that this stems from my efforts to find the appropriate analyses to run for research using categorical data in a 2x2 contingency table. In my case I have two conditions: control and experimental and within the experimental group there are two items of interest (say, Item A and Item B). In all cases I'm investigating whether an outcome occurs or not: How many experimental participants show the outcome on Item A? How many experimental participants show the outcome on Item B? How many control participants show the outcome? So in addition to comparing Item A with the Control group (A vs. C) and Item B with the Control group (B vs. C), I also want to compare Item A with Item B (A vs. B).   My understanding is that for between-subjects comparisons (e.g., A vs. C   &amp;   B vs. C) a  is traditionally used and that for within-subjects comparisons (e.g., A vs. B) that  is a common choice.   Question 1: is this an accurate understanding of the common choices for statistical tests using 2x2 contingency tables?    My follow-up questions, and where most of my confusion lies, are related to what to do when multiple observed cell counts are low (less than 10). I've explored numerous threads here, the Wikipedia pages for different topics (Yates's correction, Fisher's exact, etc.), a few journal articles, and descriptions in R-packages, but I have found conflicting views.   Some sources indicate that you should use , others say it's out-dated because, in addition to being overly conservative, it was only preferred because the other options were computationally intense.   Others say that you should use , but I've seen additional information suggesting that Fisher's exact test is only appropriate if you know both the row and column totals and that other options (Boschloo, Barnard, etc.) are generally more powerful. However, which of those to use is also not clear.  Finally, even others suggest that the Pearson's $\chi^{2}$ test is appropriate as long as the expected cell counts are not low.   I've seen some indication that these arguments occur for McNemar's test as well (e.g., continuity correction &amp; McNemar's exact test).  Question 2: Is the assumption regarding cell counts about expected cell counts or observed cell counts? If the observed cell counts are low, does that matter to the type of test that should be used?  Question 3: What is an exact test and when should exact tests be used?    In addition to answers to these questions, I would also greatly appreciate any suggestions as to books or articles I can read to learn more about this. Part of my struggle with all of this has been just general difficult finding clear information about these topics and how they relate to one another.
58570
There is a significant 3-way interaction in a data-set I'm working with.  The interaction involves both categorical and quantitative variables.  I have been pointed towards simple slopes and this  but I find the explanations lacking. I only have a basic background in statistics, and Googling for other examples has not been very helpful.   Any insight as to how to begin to understand this interaction will be very welcome, especially using R rather than SPSS. Thank you very much in advance, from a lower-year college student who has suddenly found himself over his head!
35673
Many clinical studies are based on non-random samples. However, most standard tests (e.g. t-tests, ANOVA, linear regression, logistic regression) are based on the assumption that samples contain "random numbers". Are results valid if these non-random samples were analyzed by standard tests? Thank you.
114422
I am interested in whether or not a "correlation" of three variables is something, and if what, what would this be?  Pearson product moment correlation coefficient  $$\frac{\mathrm{E}\{(X-\mu_X)(Y-\mu_Y)\}}{\sqrt{\mathrm{Var}(X)\mathrm{Var}(Y)}}$$  Now the question for 3 variables: Is    $$\frac{\mathrm{E}\{(X-\mu_X)(Y-\mu_Y)(Z-\mu_Z)\}} {\sqrt{\mathrm{Var}(X)\mathrm{Var}(Y)\mathrm{Var}(Z)}}$$  anything?  In R it seems like something interpretable:  &gt; a &lt;- rnorm(100); b &lt;- rnorm(100); c &lt;- rnorm(100) &gt; mean((a-mean(a)) * (b-mean(b)) * (c-mean(c))) / (sd(a) * sd(b) * sd(c)) [1] -0.3476942   We normally look at the correlation between 2 variables given a fixed third variable's value. Could someone clarify?
101014
I did experiment on one group of rats, the group was tested during 8 days, this is the first stage. The same group was also tested again but this time the test phase was 7 days. I tried to do my analysis using ANOVA repeated measures but I had a problem with the days.. I want to know the difference in the 2 tests but the days are not the same number. I don't know how to handle it. If there is any way to do the analysis using repeated measures ANOVA.   I tried to use repeated measure anova within subjects effect. My first factor will be test with 2 levels (test 1 &amp; 2),second factor is day with the level of ?? Here is the problem! if I write 8 there will be extra day in test 2 and the analysis cant carry!!
824
I have multiple regression with, say 3 independent variables: $Y=B_0+B_1x_1+B_2x_2+B_3x_3$ I would like to test if $B_2+3B_3$ is significantly different from zero, i.e.  $$H_0: B_2+3B_3=0$$ $$H_1: B_2+3B_3\neq 0$$ Can you please help to find appropriate way to test for significance of linear functions of two coefficients as in above example.  Many thanks in advance.