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18 votes
Accepted

ANOVA vs pairwise t-tests with multiple test correction

The difference becomes clear if you understand the null/alternative hypothesis of each test. ANOVA's null hypothesis is that the group means are the same, while the alternative is that at least one ...
Demetri Pananos's user avatar
14 votes
Accepted

If the difference of scores is normally distributed, the sample distributions don't matter in a paired t-test, right?

You are correct. A paired t-test is conducted on the differences of the paired scores. It doesn't look at the individual scores in any way. A paired t-test is precisely the same as a one-sample t-test ...
Sal Mangiafico's user avatar
13 votes
Accepted

Can a paired (or two group) t-test test if the difference between two means is less than a specific value?

Sure, you can do that. You don't have to test against a null hypothesis of $0$ (sometimes called a "nil null"); you can test against any value. You also don't have to do a two-tailed test; you can ...
gung - Reinstate Monica's user avatar
13 votes
Accepted

Paired t-test with multiple observations per pair

Averaging the data will result in a loss information and statistical power, so it is best avoided. Since you have repeated measures for websites, you can account the differences between websites (or ...
Robert Long's user avatar
  • 61.9k
13 votes
Accepted

Why doesn't R output for a paired t-test match the formula for a confidence interval in the t-distribution?

0.5547 is not the $t$ you are looking for. The $t$ you want to use in the equation is the critical value for the $t$-distribution with 8 degrees of freedom (n - 1). ...
kmm's user avatar
  • 557
10 votes

Paired data comparison: regression or paired t-test?

The way you set up the regression in a "correlation style" does answer a different question (which is explained nicely by @olooney). However, you can use regressions to test for mean differences. In ...
statmerkur's user avatar
  • 6,120
9 votes

what is the difference between a two-sample t-test and a paired t-test

When you use a paired T-test, you are essentially doing a one-sample test, where your one sample consists of the paired differences between outcomes in two groups. If you create a new sample of these ...
Ben's user avatar
  • 127k
8 votes
Accepted

Can I use a paired t-test on data that are averages?

It's probably not a problem at all, provided the sample sizes are similar to each other. There could be complications with small sample sizes, though. Intuitively, an average of a small sample is ...
whuber's user avatar
  • 326k
8 votes
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How to interpret pairs plot in R?

If you have a number of different measurements in your data.frame, then pairs will show scatterplots of between all pairs of these measures. Example data: ...
Bernhard's user avatar
  • 8,467
8 votes
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Distribution of the pooled variance in paired samples

I'm not sure about a reference for this result, but it is possible to derive it relatively easily, so I hope that suffices. One way to approach this problem is to look at it as a problem involving a ...
Ben's user avatar
  • 127k
8 votes

equal *population* variances in paired t test

Any assumptions you make in a paired test would have to do with the paired differences. After all, a paired test is a one-sample test in disguise. Therefore, NO, you do not need to assume equal ...
Dave's user avatar
  • 63.7k
8 votes

Can Wilcoxon be used in large sample with non-normal distribution?

I would not call n=37 large (!). Yes, you can use a Wilcoxon signed rank test, but there are some substantial caveats. It's not suitable for all situations. Then again, the t-test might not be either. ...
Glen_b's user avatar
  • 284k
7 votes
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t-test for partially paired and partially unpaired data

Guo and Yuan suggest an alternative method called the optimal pooled t-test stemming from Samawi and Vogel's pooled t-test. Reference: Guo B, Yuan Y. A comparative review of methods for comparing ...
yani_t's user avatar
  • 116
7 votes

Testing whether two data sets are statistically different

It depends on the type of statistical diffrences you are looking. It also depends upon the data distribution. A great small table summarizing the statistical test are here with the use cases : https:...
Rituraj Singh's user avatar
7 votes
Accepted

Can matched samples be analysed using regression?

See my answer here for a discussion of two approaches to standard error estimation for matched samples. For a discussion on standard error and effect estimation when using matching with replacement, ...
Noah's user avatar
  • 34.2k
7 votes
Accepted

what is the difference between a two-sample t-test and a paired t-test

In a two-sample test, you have two independent samples. Of course, by independence, we expect the two sets of measurements will not be correlated. Sample sizes for the two samples need not be equal. (...
BruceET's user avatar
  • 56.6k
7 votes

Paired, discrete hypothesis testing

Lazy version: permutation testing. The null hypothesis is that their interests would be unchanged. Operationally, that means that for each student, you might as well flip a coin to pick their "...
kqr's user avatar
  • 814
6 votes
Accepted

normality for extremely small sample N=5

You can't make much of a distributional assessment at n=5 -- you can (sometimes) see non-normality at n=5 -- but at such small sample sizes the non-normality has to be quite strong to have a good ...
Glen_b's user avatar
  • 284k
6 votes

How to deal with ties when conducting Wilcoxon signed rank test?

There are two obstacles to doing a Wilcoxon signed-rank test: (a) You have only 13 non-zero differences among 21. The 0 differences provide no evidence that Q1 and Q2 differ. You may hate to 'discard' ...
BruceET's user avatar
  • 56.6k
6 votes

Comparing two sensors timeseries that measure the same variable

Some ideas: The plot shows that the agreement is fairly good, and with your amount of data maybe you want to study the agreement with more details, not only reduce it to one summary statistic. For ...
kjetil b halvorsen's user avatar
6 votes
Accepted

Paired and repeated measures! Now what? ANOVA or mixed model?

This is basically an analysis of change model. 2 measurements on each subject were taken at baseline, and 2 more at follow-up. I will refrain from calling this "control" and "...
Robert Long's user avatar
  • 61.9k
6 votes

Paired vs unpaired samples t-test in crossover study

The Deutsches Ärzteblatt article recommends a two-stage analysis of cross-over trials: Run a preliminary test for carry-over effect between periods 1 and 2. Let's call this test SEQ. Conditional on ...
dipetkov's user avatar
  • 10.2k
6 votes

Determination of sample size vs. repeated measurements in experimental design

Repeated testing of one widget will allow you to determine the magnitude of measurement variation (noise) and, maybe, if there are time or test-dependent changes in the performance. Those things are ...
Michael Lew's user avatar
  • 15.8k
5 votes
Accepted

Weighted, Paired-Sample T-test? in R

A paired $t$-test is a one-sample $t$-test on differences. If you have two variables, such as before and after or ...
gung - Reinstate Monica's user avatar
5 votes

Effect size for Wilcoxon signed rank test that incorporates the possible range of the attribute

The effect size statistic Z/sqrt(N) --- sometimes called r --- in the paired observations case, is related to the probability that one group is larger than the other, or if you'd rather, that the ...
Sal Mangiafico's user avatar
5 votes

Paired t-test following main effect of mixed model with missing data

With regard to the missing data, the mixed model will give you correct inferences under the more plausible missing at random assumption whereas the t-test only under the more stringent missing ...
Dimitris Rizopoulos's user avatar
5 votes
Accepted

Sensibility and specificity with inconclusive cases (non binary problem)

The clearest answer I know of comes from "Diagnostic accuracy studies: how to report and analyse inconclusive test results" by Shinkins et al., which the STARD 2015 (Standards for Reporting ...
Gabriel's user avatar
  • 743
5 votes

Is a statistically significant difference within analytical uncertainty still valid?

Suppose you are trying to weigh a package on a scale that gives unbiased readings but is subject to variations from one weighing to the next. If the true weight of the box is 960g and we have the ...
BruceET's user avatar
  • 56.6k
5 votes
Accepted

Paired t test: check normality with residuals or paired differences (or both)?

The paired differences. A paired t-test is the same as a one-sample t-test on the differences, so the assumption is that the differences are normally distributed. The residuals are simply the ...
Eoin's user avatar
  • 9,197
5 votes
Accepted

Ratio between two values with confidence intervals

I do not think that equidistant sampling of values from the confidence intervals produces representative samples, because the probability distribution inside the intervals is not taken into account. ...
cdalitz's user avatar
  • 5,232

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