Let's say I have 4 plants and I measure something under 2 conditions. For example:  The entries in the table show how many times I saw something under condition (C1 or C2) for plant (P1, P2, P3 or P4).         P1,  P2,  P3,  P4  C1    0   20    0   19  C2  100   80  180  150    Now I would like to answer the question "what is the probability that these 39 times of seeing something is unevenly distributed between these 4 plants"?   I am much interested in observation like this, rather than, say:        P1,  P2,  P3,  P4  C1   25   20   15   19  C2  100   80  180  150    Is it right to use Fisher's exact test for this? I just extended the question from a 2*2 table to 2*4.
122273
I am working on 4 different plants. I have the (RNA-Seq) data from sequencing. I look for two events E1 and E2, say, at certain positions in their genome. Let's say E2 is the common one and E1 is a special event. The positions I look for are identical across all 4 (in the genome). And let's say I see that the observation I have for 1 particular position is:      P1   P2  P3  P4 E1   0   20   0   17 E2 100   80 100  120    Here, P1 through P4 refers to plants and E1 and E2 refers to the events. E2 is more common. So, my objective is to actually check if E1 occurs more often in one or more plants than in the others. If they occur at the same proportion in all, of course it is not interesting to me.  I have 2 questions: (I have already asked  before but didn't get an answer)     Will a fisher test be right for this problem?    I hypothesize (Null) that the proportion of E1 is not different in occurrence between the 4 plants. Now, I set out to find if the proportion I have here is by any means significantly different. I use R, fisher.test() and I get p-value=2.5e-10. So, I reject my Null hypothesis for this case because I find strong evidence against it.  Sometimes, I have an observation like this,        P1   P2  P3  P4 E1   0   20   0  17 E2   0   80   0 120    then fisher.test() gives me a p-value of 0.147. So, I don't reject the Null   hypothesis. However, from a biological point of view, I would consider this significant. However fisher test answers the question I originally asked. I guess the proportion 0/0 for P1 and P3 are not useful (or not used).  So, my question is: Is it possible to modify the test such that it is sensitive even if E1 and E2 are 0 in 1 or more plants for a particular observation?     Having thought a bit to frame this post, I guess, in that case I have to ask a different question.
80432
A large amount of computing resources is required to compute exact probabilities for the Kruskal–Wallis test. Existing software only provides exact probabilities for sample sizes less than about 30 participants. These software programs rely on asymptotic approximation for larger sample sizes. Exact probability values for larger sample sizes are available. Spurrier (2003) published exact probability tables for samples as large as 45 participants.[7] Meyer and Seaman (2006) produced exact probability distributions for samples as large as 105 participants.[8]
44208
Suppose you have a series of n trials, where the probability of success  in each trial is p.  The distribution of the number of successful trials follows a Binomial distribution with parameters (n, p).  The mean is given by np whereas the variance is np(1-p).  So far so good: this is pretty mundane Stats 101 stuff.  But suppose now that I only knew about the successful trials, and had no knowledge of the total number n of trials, which is the variable I am interested in estimating.  For example, I knew I had 100 successful trials, where each trial had a 0.1 chance of success.  Is there a known probability distribution that describes the probable outcomes for n, the total number of trials?  Estimating the mean is easy: if m is the number of successes, then it's just m/p.  But what about variance and other measures?  What if each success had a different (but known) chance of success?  Suppose I had the following records:   success1 (with p=0.1) success2 (with p=0.1) success3 (with p=0.2)   Again, a good estimation of the total number of trials can be obtained by simply summing 1/p for each successful trial.  In this case that number  is 10+10+5=25.  But what about variance and other measures?
5733
I have data for three unequal groups: $N = 44$, $N = 354$ and $N = 347$. Is it possible to compare all three groups running a one-way ANOVA or is the first group too small?
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In the following example  &gt; m = matrix(c(3, 6, 5, 6), nrow=2) &gt; m      [,1] [,2] [1,]    3    5 [2,]    6    6 &gt; (OR = (3/6)/(5/6))    #1 [1] 0.6 &gt; fisher.test(m)        #2      Fisher's Exact Test for Count Data  data:  m  p-value = 0.6699 alternative hypothesis: true odds ratio is not equal to 1  95 percent confidence interval:  0.06390055 5.07793271  sample estimates: odds ratio   0.6155891    I calculated the odds ratio (#1) "manually", 0.600; then (#2) as one of the outputs of the Fisher's exact test, 0.616.  Why didn't I get the same value?  Why do several ways of computing the odds-ratio exist, and how to choose the most appropriate one?
25624
I have several hundred measurements. Now, I am considering utilizing some kind of software to correlate every measure with every measure. This means that there are thousands of correlations. Among these there should (statistically) be a high correlation, even if the data is completely random (each measure has only about 100 datapoints).  When I find a correlation, how do I include the information about how hard I looked for a correlation, into it?   I am not at a high level in statistics, so please bear with me.
37963
I'm new to stats and I need some help. Can anybody tell me, in the most "beginner friendly" way, how to perform hypothesis testing with a geometric distribution for 2 samples? please take into account that, until a month ago, Statistics for me was mean, mode and std dev...
26948
I've been reading up on $p$-values, type 1 error rates, significance levels, power calculations, effect sizes and the Fisher vs Neyman-Pearson debate. This has left me feeling a bit overwhelmed. I apologise for the wall of text, but I felt it was necessary to provide an overview of my current understanding of these concepts, before I moved on to my actual questions.    From what I've gathered, a $p$-value is simply a measure of surprise, the probability of obtaining a result at least as extreme, given that the null hypothesis is true. Fisher originally intended for it to be a continuous measure.  In the Neyman-Pearson framework, you select a significance level in advance and use this as an (arbitrary) cut-off point. The significance level is equal to the type 1 error rate. It is defined by the long run frequency, i.e. if you were to repeat an experiment 1000 times and the null hypothesis is true, about 50 of those experiments would result in a significant effect, due to the sampling variability. By choosing a significance level, we are guarding ourselves against these false positives with a certain probability. $P$-values traditionally do not appear in this framework.  If we find a $p$-value of 0.01 this does not mean that the type 1 error rate is 0.01, the type 1 error is stated a priori. I believe this is one of the major arguments in the Fisher vs N-P debate, because $p$-values are often reported as 0.05*, 0.01**, 0.001***. This could mislead people into saying that the effect is significant at a certain $p$-value, instead of at a certain significance value.  I also realise that the $p$-value is a function of the sample size. Therefore, it cannot be used as an absolute measurement. A small $p$-value could point to a small, non-relevant effect in a large sample experiment. To counter this, it is important to perform an power/effect size calculation when determining the sample size for your experiment. $P$-values tell us whether there is an effect, not how large it is. See .  My question: How can I reconcile the facts that the $p$-value is a measure of surprise (smaller = more convincing) while at the same time it cannot be viewed as an absolute measurement?  What I am confused about, is the following: can we be more confident in a small $p$-value than a large one? In the Fisherian sense, I would say yes, we are more surprised. In the N-P framework, choosing a smaller significance level would imply we are guarding ourselves more strongly against false positives.   But on the other hand, $p$-values are dependent on sample size. They are not an absolute measure. Thus we cannot simply say 0.001593 is more significant than 0.0439. Yet this what would be implied in Fisher's framework: we would be more surprised to such an extreme value. There's even discussion about the term highly significant being a misnomer:   I've heard that $p$-values in some fields of science are only considered important when they are smaller than 0.0001, whereas in other fields values around 0.01 are already considered highly significant.  Related questions:         (as provided by @amoeba)
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I don't have the minimum required data of 5 in each cell for a chi-squared test, but my contingency table is greater than 2x2, so I can't use a Fisher's exact. Would it help to use a chi-squared test set to either exact or Monte Carlo to prevent it from making the assumption of normal distribution?  I'm looking at trauma patterns created by five different tools; six categories of trauma have been defined. I would like to see whether the patterns of trauma (by occurrence of each type) differ significantly from one another. N=67, but not all tools have all types of trauma.
56145
So, for fun, I am taking some of the data of calls from the call center I work at and trying to do some hypothesis testing on them, specifically the number of calls received in a week, and using a Poisson distribution to fit it. Due to the subject matter of my job, there are two types of weeks, let's call one of them on-weeks where I hypothesize there are more calls, and off-weeks where I hypothesize there are fewer.  I have a theory that the $\lambda$ from on-weeks (let's call it $\lambda_1$) is larger than that of the one from off-weeks (let's call it $\lambda_2$)  So the hypothesis I want to test is $H_0: \lambda_1 &gt; \lambda_2, H_1: \lambda_1 \leq \lambda_2 $  I know how to test for one parameter (say  $H_0: \lambda_1 &gt; 1, H_1: \lambda_1 \leq 1 $) but not so sure how to go about doing 2 given a data set. Let's say I take two week's worth of data from each one $X_1 = 2$ and $X_2 = 3$ for the off-week and $Y_1 = 2$ and $Y_2=6$ for the on-week. Can someone help walk me though this simpler version such that I can apply it to a larger data set? Any help is appreciated, thank you.
67230
I have a pretty basic probability question, but I'm just having difficulties remembering what distribution this is.  A coin is tossed until a head appears two times in a row. Given that we are using a fair coin, what is the probability that we toss the coin exactly 4 times such that the two consecutive heads are the 3rd and 4th trials?  I know that this would be fairly easy to solve by brute force and listing out the different probabilities, but I'm a little confused as to how to use a "shortcut" such as identifying this as a binomial distribution. I also don't know how to account for the probability that we are using 4 tosses.  Any help is appreciated. Thanks!
23375
I am just learning probability in my Discrete Structures class and am very lost. This is the example given in the book and I have no idea how to solve this problem.   Problem: Suppose one in 1000 people have a certain disease. Suppose medical testing is not perfect (as is the case in real life) and consequently, only 99% of the people with the disease are tested positive. Suppose 2% of the people who don’t have the disease also test positive. What is the probability of actually having the disease, given someone tests positive?  Things I do know:   People with disease = 1/1000 Tested positive with disease = 99/100 People tested positive who don't have disease = 2/100   I'm not sure where to got from here with the information that I know. What are the next steps?
89690
I'm doing a textmining project about a videogame review dataset. I divided de reviews into a positive (reviewgrade > 8) and negative (reviewgrade &lt; 3) and want to draw conclusions based on the frequency of different grading factors mentioned in the text. I now have a dataframe with counts of certain categories mentioned per review.  0    13249 1     1565 2      292 3       65 4       19 5        6 6        4 7        3 8        2 9        1 Name: positive: gameplay, dtype: int64   0    5043 1     348 2      66 3      18 4       8 5       3 Name: negative: gameplay, dtype: int64   For example this are the distributions of the amount of reviews which have a certain amount of mentions of gameplay related words. There are for example 1565 reviews with precisely 1 mention of a word related to the category gameplay.  Now I want to use this data to determine if on average gameplay gets mentioned more in negative context than in positive or vice versa. Because the data is not normal distributed, I assumed a t-test is not appropriate, and found online that a Mann–Whitney U test might be suitable.  &gt; wilcox.test(positive$gameplay, negative$gameplay, alternative = "two.sided", conf.int = TRUE)      Wilcoxon rank sum test with continuity correction  data:  positive$gameplay and negative$gameplay W = 43702925, p-value &lt; 2.2e-16 alternative hypothesis: true location shift is not equal to 0 95 percent confidence interval:  2.963844e-05 4.797412e-05 sample estimates: difference in location            4.995671e-05    I do however get a very high W value, which doesn't seem to be correct. Is this not the appropriate test, or am I interpreting this wrong?
52652
I don’t know how to handle this 3 players case, may anyone give a hand? Thanks!     When playing card game, there are 3 players playing 32 cards, each   receive 10 cards, 2 remind on the table. Overall are 4 aces and 4   kings in the game. How likely is P (E | D)? D = "The table remains 2   aces" E = "I (at least) get one king".   I guess I should have steps as follows.   P(E) = P(1King)+P(2K)+P(3K)+P(4K) P(D) = (4/32) * (4/32) = 1/256 P (E | D) = P(E) + P(D)   Equations may be used:  Counting combinations      The number of combinations of n objects taken r at a time is     nCr = n(n - 1)(n - 2) . . . (n - r + 1)/r! = n! / r!(n - r)!                 Number of favorable outcomes P(I) =     Total number of possible outcome
53633
Question: whats the probability that at least 3 out of a group of n people have the same birthday.  I am confused as to where to start. I know that it would be complementary probability, but even then I dont know exactly.  Would it be;  P(at least 3 have the same bday) = 1 - (|all 3 have different| + (2 have the same|)? Any directions and suggestions?
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I had a question  that I got a bunch of great responses on.  I have, hopefully, a quicker question here.  There is a debate in the literature regarding reporting means vs medians in a Wilcoxon-Mann-Whitney test.  See  and also .  I would like to report means in my table, since I only have four possible values (0 through 3), rendering medians less effective as the differences are not pronounced.  If I do report means in the table, would I just put an asterisk saying that means are reported for the Mann-Whitney test because the medians don't show the differences effectively?  I feel like I need to explain why I used means and not medians to describe my ordinal data and show significance (even though a Mann-Whitney is comparing the distributions and not the medians, as some think).  Are there are any references out there that show this as a precedent?  As always, advice/help is greatly appreciated!
53967
I am struggling with using the correct test for count data in R. The dataset I have is the number of nymphs produced by three aphid species on wheat.  So this is count data with one response variable (number of nymphs) and one explanatory variable with three levels (i.e. three different species).  I want to test whether there are any differences between the three species with the number of nymphs they produce.  I think that I should not use an ANOVA with count data. I have tried a GLM with QuasiPoisson, but I am struggling to interpret the output and be sure that I have used the correct test. Essentially I want to equivalent for a one-way anova but for count data.