A test (typically of distribution, independence, or goodness of fit) or a family of distributions related to such a test.

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How to assess similarity of two plots?

I want to compare two plots and see how similar they are in shape. The question is similar to this one where comparison between two histograms are discussed. However the main difference is the length ...
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3answers
67 views

How is the $\chi^2_1$-distribution not a Gaussian?

The $\chi ^2_n$-distro is the distribution of the sum $Z_1 ^2+Z_2 ^2+...$ where the $Z_i$ are drown from a standard normal distribution. However, the standard normal distribution is a Gaussian bell ...
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7 views

Determining degrees of freedom for deviance-based hypothesis tests

I am following the section in Chapter 4 of Singer and Willett's Applied Longitudinal Data Analysis about deviance-based hypothesis tests, trying to apply it to my own design. I am attempting to test ...
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14 views

adjusted residual is above 1.96, but the confidence interval goes through 1?

I am analysing whether patients ethnicity affects uptake of the influenza vaccination. I have undertaken chi square test on a 6x2 table (6 categories of ethnicity against accepted/declined vaccination)...
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1answer
17 views

What does it mean in real-world terms that the Chi-Squared distribution is a special case of the Gamma distribution?

Among other applications, a gamma distribution answers the question: "If the average time (or other quantity) between events is β, what is the probability that x time will elapse before α events occur?...
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14 views

SPSS Chi Square goodness-of-fit expected frequencies distribution check

My question is about the Chi Square goodness-of-fit test. Not to be mistaken with the test for association or the test for correlation (both called Chi Square). Let's say I have following variable '...
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32 views

SPSS Chi square test proportions (less than 5 expected)

Let's say I have a (fictive) sample: White: 25 Foreign: 1 General population: White: 30 Foreign: 9 Now I want to compare if my frequencies do not differ from the population. Normally I could use a ...
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1answer
31 views

In medical statistics, when to use $\chi^2$ and when to use Kruskal-Wallis H?

I am conducting a retrospective analysis on the effect of three different treatment option (intervention treatment) on a special type of cancer, so I have three groups: 1, 2, and 3. In the baseline ...
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14 views

A/B Testing - Risk of excluding guests

I have a sample of 1.6 million users who were split 80/20. 80% of the guests were treated with a message and 20% were shown nothing. ~5% of the guests converted in BOTH populations... but the ...
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8 views

Goodness of fit when all your variables have errors?

I have $N$ measurements of type $(X_i,Y_i,Z_i)$ where each measurement has uncertainty $({\sigma_X}_i,{\sigma_Y}_i,{\sigma_Z}_i)$. I am trying to fit these measurements to a plane: $Z = \alpha X + \...
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1answer
28 views

I do not understand the chisq.test output

I have three variables: str(vw) num[1:2500] 56 74 98 23 ... str(autos) num[1:2500] 29 34 57 21 ... str(ask) num[1:2500] 41 118 70 79 ... The summary functions ...
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1answer
21 views

when dependent variable is categorical with only 2 levels: t-test or chi-square goodness of fit?

Let's say I'm trying to compare if two groups of people are significantly different from each other in terms of their access to the internet. One could code each person's internet access ...
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11 views

Why should we normalize Bag of Features histograms?

I was reading these slides about Bag of Features (BoF). At slide 23 you can read: each image is represented by a vector, typically 1000-4000 dimension, normalization with L1/L2 norm Why we ...
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0answers
10 views

Is chi square test appropriate for testing frequencies of modifications?

I have a lot of sequence reads from next generation sequencing that I'm converting to a sequence of number of Stops, sorted by position on a specific gene. Such a sequence can look like: 0 0 0 0 1 0 ...
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35 views

Applying the $\chi^2$ test of independence: why $(observed - expected)^2 \over expected$?

In the $\chi^2$ test of independence, the test statistic is defined over the contingency table as such: $\chi^2 = \sum_{cells} \frac{(observed - expected)^2}{expected}$ Why is it defined like that? ...
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2answers
121 views

Chi-squared test: Investigating fruit flies attraction to different colours

I have a few questions about the Chi-squared test. First of all, this is what I was investigating: H0: Fruit flies show no difference in attraction to light of different colours Protocol: 20 fruit ...
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8 views

Fit indices of CFA are good looking, but chi square is significant in a medium-to-small sample

I am working with a data set which I did not collect, but a (recently death) college. The idea was to examine validity and confidence of a questionnaire. However, the sample he got is only N = 122. ...
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15 views

Chi-square, Kruskal Wallis or something else?

I am working on a project where I am attempting to compare a series of health indicators from several populations and need to know which statistical test would be the most appropriate. To clarify, I ...
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31 views

When I compare two samples with a chi squared, should I compare one sample against a combination of the two?

I have a categorical variable for measured for two samples and I want to see if this variable differs significantly between the samples. I want to do a chi-squared test, with the samples as the ...
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0answers
7 views

What is the appropriate test of association with one nominal variable and one (ordinal) Likert scale variable?

I have one nominal variable and one (ordinal) Likert scale variable. I've read that in this situation the most appropriate test is the mantel-haenszel linear-by-linear test. However, I've found may ...
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1answer
21 views

What is the right usage in Fisher test in R

So I have data in form (in real data I have more rows, of course so this is just a sample) ...
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65 views

How is the $ \chi^2 $ distribution defined at 0 for various degrees of freedom?

I'm trying to understand the $\chi^2$-distribution. Wikipedia has the following graph for the probability density function: This graph shows that for $ k = 1$, the PDF will be... infinite? The mode ...
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14 views

Why does increasing lambda for a poisson distribution decrease the p-value obtained from a chi-square test?

I generated some random numbers that is suppose to follow the Poisson distribution, where n =200 and lambda =20. ...
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2answers
137 views

Expectation of $\frac{X_1^4}{(X_1^2 + \cdots + X_d^2)^2}$

Let $X_1$, $X_2$, $\cdots$, $X_d \sim \mathcal{N}(0, 1)$ and be independent. What is the expectation of $\frac{X_1^4}{(X_1^2 + \cdots + X_d^2)^2}$? It is easy to find $\mathbb{E}(\frac{X_1^2}{X_1^2 +...
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12 views

An appropriate alternative to chi2 for paired, categorical data (tables larger than 2X2)

I am analysing a data set consisting mostly of categorical data. This has resulted in a number of contingency tables (mostly, but not always larger than 2X2) that need statistical testing. Now, I ...
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14 views

Chi square kernel function: which version?

I'm not a machine learning expert, so sorry if this is a stupid question. I was reading this paper about Kernenlized locality-sensitive hashing (LSH) and in section 6.4 the chi-square-kernel function ...
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1answer
18 views

multiple testing with BH correction

I want to do genome wide association study. I have about 1,500,000 SNPs, and 36 samples with 18 from tumor cells and 18 from normal lood cells. We make fisher test or chi square test(we admit fisher ...
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28 views

significant chi-squared test but confidence interval for odds ratio does include 1

I have the contingency table: A B a 28 0 b 35 9 I applied the chi-squared test with Yates's correction, with p-values: ...
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1answer
16 views

How to test if two conditions in of a 2AFC (Two-alternative forced choice) task is different or not?

My situation is as follows: My 2AFC (Two-alternative forced choice) task yields data in the following form: 1. number of true positives 2. number of true negatives 3. number of false positives 4. ...
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1answer
16 views

Analysing mesh hole sizes

I have generated some data in an image analysis programme for some woven wire mesh. I have sampled 5 random holes (could easily sample more/less if that helps) and the software has given me a ...
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1answer
12 views

Compare the proportions of different groups for a sample with that of the population

I got a population which could be categorized into 4 groups. The population contains 169996 unit. The 4 groups contains 109881, 11318, 32242 and 16555 units respectively. And I also got a sample of ...
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25 views

Goodness of fit test for categorical data with non-negative real numbers

An experiment that I conduct has 5 outcomes: A, B, C and D. I conduct 12 trials for this experiment. I observe, for example: Outcome Frequency A            &...
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78 views

Generate $r_i$ following condition $\sum_{i=1}^n \left|\frac{r_i}{\sigma_i}\right|^2\leq\chi^2_{n,\alpha}$

How can I generate $r_i$ for $1 \leq i \leq n$, such that $\sum_{i=1}^n \left|\frac{r_i}{\sigma_i}\right|^2\leq\chi^2_{n,\alpha}$, where $\sigma_i^2$ is the variance of $r_i$ and $\chi^2_{n,\alpha}$ ...
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35 views

How to prove significantly high or low values?

I have the counts of genes in particular pathways from three organisms. How to statistically prove that few counts are significantly high or low as compared to another organism. My data looks like ...
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18 views

Goodness of fit tests in R

I have a population of 663 random balls drawn. The interval of this population's values is [1,27]. I want to do a Goodness of fit test to proof if it has a gamma ...
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22 views

Robust one sample tests of variance or scale

A common one sample test for variance is the chi-square test, e.g., http://www.itl.nist.gov/div898/handbook/eda/section3/eda358.htm. What are some robust testing alternatives for variance when the ...
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1answer
41 views

McNemar's test vs chi-squared test for before & after data with different people from the same population

I have 2 proportions I want to compare. They are from the same population but at different time periods, in between which there was an intervention. H0: Proportion in Period#1 = Proportion in Period#...
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35 views

Can I compare chi-square values for goodness of fit tests to see which observed distribution deviated most from its null distribution?

I have a series of goodness-of-fit tests using chi-square a few of which are below, $$ \begin{array}{r|r|c} \text{df} & \chi^2 & \text{Reject } H_0 \\ \hline 49 & 1744.68 & \text{Yes}...
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1answer
61 views

Why is the mean of a Chi Square distribution equal to the degree of freedom?

Is this part of the definition of a Chi Square distribution? Or is it deduced from another property? In which case, what is the proof?
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1answer
27 views

Performing a chi-squared test with overlapping observations

I have a process that can be modeled by looking at the occurrence of particular patterns in a 12 digit binary string to determine if those patterns occur more or less often than they would randomly. ...
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0answers
34 views

R squared and higher order polynomial regression

The plot below shows the saturation of a road against the impact on journey time (normalized to free flow journey time). The blue (BPR function) curve presents a standardized model used in the field ...
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2answers
109 views

Estimate of parameter of exponential distribution with binned data

I have the following data, which can be modeled by exponential distribution ...
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1answer
36 views

why are the degrees of freedom for a chi-square test on a 2x2 contigency table always 1?

I know the "formula" is (# rows - 1) * (# columns -1). However, shouldn't the design of the experiment or observational study being conducted make a difference? The only experimental design I can ...
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1answer
37 views

Determining an effect of a seatbelt enforcement and a public outreach program in a town

We conducted a seat belt use observation study in two similar sociodemographic towns with different media markets. We sampled two towns and measured outcomes in a pre and post format. One town was a ...
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24 views

mle for the binomial distributed data

For example i have folowing dataset of number of boys in families that have 5 kids: 0 boy - 34(number of such families) 1 boy - 128 families 2 boys - 233 families 3 boys - 267 families 4 boys - 144 ...
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1answer
61 views

Why Yates correction in McNemar's Test subtract 1?

McNemar's test statistic is given by: Yates's correction defines something like this: However, the correction for the McNemar's test statistic requires 1 (not ...
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13 views

Which test is appropriate when comparing proportions of a sample to a subgroup of that same sample?

I have sample of patients and their demographic information. A subset of this sample is identified as having a particular genetic marker. I'd like to know if the subset with this genetic marker have ...
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1answer
105 views
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1answer
33 views

How to relate 2 sets of classifications (types of runners & motivations)

I am currently writing a proposal and am confused regarding which statistical method I should use. I aim to examine the motivation of runners in participating a charity marathon. It will use runners ...
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27 views

Comparing and ranking differentiating attributes across groups

I'm looking for some help on how to approach this problem. Say I have two or more groups of people. Each group has characteristics and attributes. For example, say we have the following two groups: ...