Is there any biological basis for excluding outliers in a dataset of blood cytokine levels (e.g. values outside 3 standard deviations from the mean for each cytokine) as measured by multiplex technology? How may I distinguish values reflecting the potential heterogeneity of my sample cohort from real outliers (e.g. measurement or coding errors)?
108775
Following my question , I am wondering if there are strong views for or against the use of standard deviation to detect outliers (e.g. any datapoint that is more than 2 standard deviation is an outlier).  I know this is dependent on the context of the study, for instance a data point, 48kg, will certainly be an outlier in a study of babies' weight but not in a study of adults' weight.  Outliers are the result of a number of factors such as data entry mistakes. In my case, these processes are robust.   I guess the question I am asking is: Is using standard deviation a sound method for detecting outliers?
7003
I am observing strange patterns in residuals for my data:   [EDIT] Here are the partial regression plots for the two variables:      [EDIT2] Added the PP Plot   The distribution  seems to be doing fine (see below) but I have no clue where this straight line might be coming from. Any ideas?   [UPDATE 31.07]  It turns out you were absolutely right, I had cases where the retweet count was indeed 0 and these ~ 15 cases resulted in those strange residual patterns.   The residuals look much better now:   I've also included the partial regressions with a loess line.
95815
a very naive question for some of you. I have a population of 80000 data points. Some points in the population are many SD away from the rest of the population and they could be easily identified and visualized assigning them a p-value. I know that excluding those values, the population follow a nice normal distribution. What I ask you today is whether you can suggest me an approach to assigning a pvalue to each data point in the population where the null hypothesis is that the data contribute to the normality.
87477
Is it possible for one-way (with $N&gt;2$ groups, or "levels") ANOVA to report a significant difference when none of the $N(N-1)/2$ pairwise t-tests does?   In  @whuber wrote:      It is well known that a global ANOVA F test can detect a difference of means even in cases where no individual [unadjusted pairwise] t-test of any of the pairs of means will yield a significant result.   so apparently it is possible, but I do not understand how. When does it happen and what the intuition behind such a case would be? Maybe somebody can provide a simple toy example of such a situation?  Some further remarks:   The opposite is clearly possible: overall ANOVA can be non-significant while some of the pairwise t-tests erroneously report significant differences (i.e. those would be false positives). My question is about standard, non-adjusted for multiple comparisons t-tests. If adjusted tests are used (like e.g. Tukey's HSD procedure), then it is possible that none of them turns out to be significant even though the overall ANOVA is. This is covered here in several questions, e.g.  and . Update. My question originally referred to the usual two-sample pairwise t-tests. However, as @whuber pointed out in the comments, in the ANOVA context, t-tests are usually understood as post hoc contrasts using the ANOVA estimate of the within-group variance, pooled across all groups (which is not what happens in a two-sample t-test). So there are actually two different versions of my question, and the answer to both of them turns out to be positive. See below.
113630
We have a series of observations of different properties (such as heart rate or blood sugar level and others as well) across different days from different people from different geographical regions. The number of days on which the observations are made is the same for all regions; but there could be different number of participants in each region. The result of the data collection will be as follows: DATA We have a matrix, $M_{i,j}$, for each region $i$ and property $j$, with $T$ observations across time (rows) and $N_{i,j}$ (columns) for number of participants from region $i$ and property $j$. Here, we consider all properties together as representing a region. OBJECTIVE The goal is to identify people from which regions have a more similar constitution. QUESTION How can we compute the Bhattacharya Distance across the various matrices $M_{i,j}$ for all the properties combined for a region (corresponding to Case 2 of the data collection)? Dimension of Matrix: $Dim(M_{i,j})=(T,N_{i,j})$ There are two cases here. 1) $N_{i,j}=N_{i,k}$ $,\forall j,k$ That is the number of participants in a region are the same for all properties being measured. 2) $N_{i,j} \neq N_{i,k}$ $,\forall j,k$ That is the number of participants in a region could be different for some of the properties being measured. But if helpful we can assume the simple case 1) $N_{i,j}=N_{i,k}$. Please let me know if anything is not clear and if you need any further information. Related Case When we have a matrix, $M_i$, for each region $i$, with $T$ observations across time (rows) and $N_i$ (columns) for number of participants from that region. Here, we consider each property separately. How can we compute the Bhattacharya Distance across the various matrices $M_i$ (in pairs or combined, whichever is simpler) separately for each property (corresponding to Case 1 of the data collection)? Answer:
51630
I am trying to find out how inflammatory markers change in response to a mechanical device change. I have daily readings for the 5 days before the event and for the 5 days after the event. I am expecting a rise in inflammatory markers in the pre readings followed by a fall after the device change. I also need to find out how the change differs in two subgroups (sample sizes of the subgroups are n=21 and n=88). The aim is to find out if the change is significant, to consider these markers as predictors of the device failing and hence needing to be changed.    I would like to know what test would be appropriate to analyse this. I need to keep things simple as I and the people reading the results are non-statisticians.
57410
I was working on historical data looking for anomalous patterns that we would not expect to occur at random. I'd like to create a scheme to analyze data and markets to test for statistical significance and consistency over time.  Question : Are there some tools we could use to evaluate the nonrandomness of a database? What do we use usually to say that something is random or not (statistically)? Figure we work with change in some value over time.
16999
Hi I am trying to find the non-parametric equivalent of a two-way ANOVA (3x4 design) which is capable of including interactions. From my reading in Zar 1984 "Biostatistical analysis" this is possible using a method put forth in Scheirer, Ray, and Hare (1976), however, according to other posts online it was inferred that this method is no longer appropriate (if it ever was).  Does anyone know what method would be appropriate for doing so, and if so the corresponding functions in R or Stata?
47837
I have an existing data set that comes from the same group of people before and after they received a treatment.  The data set comes from when participants tested their blood sugar values over a 30 day period before receiving an insulin pump and a 30 day period after receiving an insulin pump. This data was obtained from user logs (archival data) and was not controlled to ensure that they were tested at fixed intervals. Participants tested themselves when they needed to test throughout the day for a period of 30 days.  My goal is to determine whether the average blood sugar across 30 days was different for the before vs after group.   Normally this would be a paired samples t-test but unfortunately the before and after group have an unequal number of data points with the after group having significantly more. People are testing more often after receiving an insulin pump.  What is the correct way to handle this?  I can collapse the data to find a mean for each participant before treatment and after treatment (across all participants) so that the data matches up and then run a paired samples t-test on this data but I think this is not the ideal solution.   Would a one way within subjects ANOVA be the appropriate test to run in this case?
54299
Regarding s, I am wondering why $1$% and $5$% seem to be the gold standard for "statistical significance". Why not other values, like $6$% or $10$%?  Is there a fundamental mathematical reason for this, or is this just a widely held convention?
99785
I'm fairly new to Machine Learning/Modelling and I'd like some background to this problem. I have a dataset where the number of observations is $n&lt;200$ however the number of variables is $p\sim 8000$. Firstly does it even make sense to consider building a model on a dataset like this or should one consider a variable selection technique to start with such as ridge regression or Lasso? I've read that this situation can lead to over-fitting. Is that the case for all ML techniques or do some techniques handle this better than others? Without too much maths a simple explanation on why the maths start to breakdown for $p&gt;n$ would be appreciated.
32732
A published article () contains these 2 sentences:     Moreover, misreporting may be caused by the application of incorrect rules or by a lack of knowledge of the statistical test. For example, the total df in an ANOVA may be taken to be the error df in the reporting of an $F$ test, or the researcher may divide the reported p value of a $\chi^2$ or $F$ test by two, in order to obtain a one-sided $p$ value, whereas the $p$ value of a $\chi^2$ or $F$ test is already a one-sided test.    Why might they have said that?  The chi-squared test is a two-sided test.  (I have asked one of the authors, but gotten no response.)  Am I overlooking something?
111247
1) I had a dataset with missing data for baseline variables and outcome variables. Through multiple imputation in SPSS (10 imputations, 50 iterations, PMM for scale variables) I imputed the missing data for the baseline variables. When I analyse the data (i.e. only the 10 imputation data sets) and use the independent sample t-test for a continuous variable results are pooled. This includes mean and p-value, but not standard deviation. Is it correct that I can take the average of the 10 standard deviations calculated for the imputed data sets to calculate the pooled standard deviation?  2) The pooled p-value from the independent t-test on 10 imputation data sets in SPSS is not the average of the 10 p-values that are calculated: am I correct? As I believe a correction is made for the fact that the p-value is based on imputed data?  3) I want to impute the missing data for the outcome variables as well. I did not include those variables in the first imputation process since one of the outcome variables is affected by the value of one of the baseline variables for which data was missing. So I figured that I would first impute the baseline variable, create a 'complete' data set for it and than impute the outcome variables using that data and the other baseline variables. Is it actually possible to impute a second time? And how would I do that? Now (after the first imputation process) I have a dataset which is 11 times as large as originally (original data set + 10 x imputed data set). Do I use all 10 imputation data sets to run the imputation process again which would result in another tenfold of that data set (so 100 fold of my original data set size)? And is it true this would lead to a larger standard deviation for scale variables?
83320
I am calculating the Intraclass Correlation coefficient (ICC) as per the method of Shrout-Fleiss (1979), using the (3, 1) model in which the judges are fixed as are the targets.  Some of my ICC values are negative.  Is this to be expected?  How to interpret this?  I understand that the maximum ICC is 1.0, but is there a minimum value?  How are negative values interpreted?
43620
There are there groups (colA, colB, colC) representing three different measurement methods. The question is whether there is a difference between the three methods. To decide the question we perform experiments and measure the same thing with each method. The output of each method is a label not a value on a numeric scale. In addition, we do not have a control group so we do not know which method's output is the right one in the experiment. I solved the question in the way below  but I became uncertain whether it is a correct solution. I might have oversimplified the problem. Consequently, the chi-square approach used tests something else not what we want.  Data:             colA,    colB,    colC experiment1 label1,  label1,  label2 experiment2 label3,  label1,  label3 experiment3 label4,  label4,  label2 experiment4 label5,  label4,  label5 ...    My first approach, probably oversimplified:   As we do not know which label is correct and which not, we regard at first all the outputs of method A correct and compare them to the other two columns and count the same labels in the same experiments in the other columns, then we regard all the outputs of method B correct and then method C. So we get the label count below:   I. colA regarded as correct colA(4) colB(2) colC(2)  II. colB regarded as correct colA(2), colB(4), colC(0)  III. colC regarded as correct colA(2), colB(0), colC(4)   Then we compute a chi-square test for each, here II. and III. are the same. (There are more than 5 expected values in each column it is just the example to highlight the problem.) This way we get three p values for each test, from which we select the highest one to be on the safe side and decide whether the deviations between columns are likely to be caused by chance only.    My second approach would probably be:   The data same data transformed in a different format:                          label1, label2, label3, label4, label5 methodA (earlier colA)       1,      0,      1,      1,      1, methodB (earlier colB)       2,      0,      0,      2,      0, methodC (earlier colC)       0,      2,      1,      0,      1,   Here the expected values for each label would be greater than 5 with the real data. However, we do not want to test whether the distribution among the labels are caused by chance only but whether there is a difference between the methodA, methodB and methodC. Can Chi-Square be used here? What other tests would you propose to use to see whether there is a difference between the three methods?  What would be your solution?
84118
I have following problem:   Within an independent groups 1-factor design I have two independent groups, with a sample size of 20 each. The data of the treatment group is not normally distributed, whereas the data for the control group is (checked with Shapiro-Wilk Normality Test). Now I want to check if the differences of the means of both groups are significant.  What is the appropriate test for this? I think it should be the Wilcoxon Rank Sum and Signed Rank Test, but I am not sure...  Could please anybody help me?
17171
I've been asked to review the literature for all studies that estimate the mean and median Blood Lead Level (BLL) in a certain country, and then perform a meta-analysis to come up with one overall value for the mean and median level.   Is such a thing typically done? I'm not interested in any "effect size," just a univariate measure.   I'd like to create a forest plot and do some of the standard tests of heterogeneity across studies. Is there a package and function in R that will allow me to do a meta-analysis of mean and median BLLs?  Just to clarify, this would be a separate meta-analysis for means, and a separate meta-analysis for medians.