# Tagged Questions

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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Are my p-values really this small or is my R code wrong?

Here is my R code: ...