Questions tagged [t-test]

A test for comparing the means of two samples, or the mean of one sample (or even parameter estimates) with a specified value; also known as the "Student t-test" after the pseudonym of its inventor.

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119
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7answers
95k views

How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples

Certain hypotheses can be tested using Student's t-test (maybe using Welch's correction for unequal variances in the two-sample case), or by a non-parametric test like the Wilcoxon paired signed rank ...
106
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7answers
156k views

T-test for non normal when N>50?

Long ago I learnt that normal distribution was necessary to use a two sample T-test. Today a colleague told me that she learnt that for N>50 normal distribution was not necessary. Is that true? If ...
87
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10answers
368k views

Is there a minimum sample size required for the t-test to be valid?

I'm currently working on a quasi-experimental research paper. I only have a sample size of 15 due to low population within the chosen area and that only 15 fit my criteria. Is 15 the minimum sample ...
83
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9answers
68k views

Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?

In a multiple linear regression, why is it possible to have a highly significant F statistic (p<.001) but have very high p-values on all the regressor's t tests? In my model, there are 10 ...
60
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6answers
48k views

Which permutation test implementation in R to use instead of t-tests (paired and non-paired)?

I have data from an experiment that I analyzed using t-tests. The dependent variable is interval scaled and the data are either unpaired (i.e., 2 groups) or paired (i.e., within-subjects). E.g. (...
58
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2answers
95k views

How should one interpret the comparison of means from different sample sizes?

Take the case of book ratings on a website. Book A is rated by 10,000 people with an average rating of 4.25 and the variance $\sigma = 0.5$. Similarly Book B is rated by 100 people and has a rating of ...
57
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4answers
142k views

Manually Calculating P value from t-value in t-test

I have a sample dataset with 31 values. I ran a two-tailed t-test using R to test if the true mean is equal to 10: t.test(x=data, mu=10, conf.level=0.95) Output: ...
56
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4answers
37k views

How are regression, the t-test, and the ANOVA all versions of the general linear model?

How are they all versions of the same basic statistical method?
50
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4answers
62k views

If the t-test and the ANOVA for two groups are equivalent, why aren't their assumptions equivalent?

I'm sure I've got this completely wrapped round my head, but I just can't figure it out. The t-test compares two normal distributions using the Z distribution. That's why there's an assumption of ...
50
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7answers
34k views

When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df?

It seems like when the assumption of homogeneity of variance is met that the results from a Welch adjusted t-test and a standard t-test are approximately the same. Why not simply always use the Welch ...
47
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4answers
21k views

Bayesian equivalent of two sample t-test?

I'm not looking for a plug and play method like BEST in R but rather a mathematical explanation of what are some Bayesian methods I can use to test the difference between the mean of two samples.
41
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8answers
22k views

How to test hypothesis of no group differences?

Imagine you have a study with two groups (e.g., males and females) looking at a numeric dependent variable (e.g., intelligence test scores) and you have the hypothesis that there are no group ...
40
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5answers
76k views

How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data?

Let's say we have the statistics given below gender mean sd n f 1.666667 0.5773503 3 m 4.500000 0.5773503 4 How do you perform a two-sample t-test (to see if ...
39
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3answers
40k views

Significance contradiction in linear regression: significant t-test for a coefficient vs non-significant overall F-statistic

I'm fitting a multiple linear regression model between 4 categorical variables (with 4 levels each) and a numerical output. My dataset has 43 observations. Regression gives me the following $p$-...
34
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2answers
30k views

How to statistically compare the performance of machine learning classifiers?

Based on estimated classification accuracy, I want to test whether one classifier is statistically better on a base set than another classifier . For each classifier, I select a training and testing ...
32
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3answers
13k views

Can ANOVA be significant when none of the pairwise t-tests is?

Is it possible for one-way (with $N>2$ groups, or "levels") ANOVA to report a significant difference when none of the $N(N-1)/2$ pairwise t-tests does? In this answer @whuber wrote: It is ...
30
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6answers
10k views

t-test for partially paired and partially unpaired data

An investigator wishes to produce a combined analysis of several datasets. In some datasets there are paired observations for treatment A and B. In others there are unpaired A and/or B data. I am ...
30
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5answers
7k views

Distinguishing between two groups in statistics and machine learning: hypothesis test vs. classification vs. clustering

Assume I have two data groups, labeled A and B (each containing e.g. 200 samples and 1 feature), and I want to know if they are different. I could: a) perform a statistical test (e.g. t-test) to see ...
28
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4answers
15k views

How to perform Student's t-test having only sample size, sample average and population average are known?

Student's $t$-test requires the sample standard deviation $s$. However, how do I compute for $s$ when only the sample size and sample average are known? For example, if sample size is $49$ and sample ...
26
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2answers
35k views

When to use the Wilcoxon rank-sum test instead of the unpaired t-test?

This is a followup question to what Frank Harrell wrote here: In my experience the required sample size for the t distribution to be accurate is often larger than the sample size at hand. The ...
26
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1answer
1k views

Have the reports of the death of the t-test been greatly exaggerated?

Reading through CV all-time classics I came across a statement that I would like to clarify. This is the post and my question refers to the closing remarks: "I have to note that all of the knowledge I ...
26
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1answer
2k views

Common statistical tests as linear models

(UPDATE: I dived deeper into this and and posted the results here) The list of named statistical tests is huge. Many of the common tests rely on inference from simple linear models, e.g. a one-sample ...
25
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3answers
16k views

Logistic regression or T test?

A group of persons answers one question. The answer can be "yes" or "no". The researcher wants to know whether age is associated with the type of answer. The association was assessed by doing a ...
25
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1answer
33k views

Why Levene test of equality of variances rather than F ratio?

SPSS uses the Levene test to evaluate homogeneity of variances in the independent group t-test procedure. Why is the Levene test better than a simple F ratio of the ratio of the variances of the ...
25
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1answer
14k views

Kolmogorov–Smirnov test vs. t-test

I'm having some difficulty in understanding the interpretation of the 2 sample KS test, and how it is different from a regular t test between 2 groups. Lets say I have males and females doing some ...
25
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1answer
37k views

Is a log transformation a valid technique for t-testing non-normal data?

In reviewing a paper, the authors state, "Continuous outcome variables exhibiting a skewed distribution were transformed, using the natural logarithms, before t tests were conducted to satisfy the ...
24
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3answers
62k views

Understanding t-test for linear regression

I'm trying to work out how to perform some hypothesis testing on a linear regression (null hypothesis being no correlation). Every guide and page on the subject I run into seems to be using a t-test. ...
24
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3answers
20k views

t-test on highly skewed data

I have a data set with tens of thousands of observations of medical cost data. This data is highly skewed to the right and has a lot of zeros. It looks like this for two sets of people (in this case ...
24
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5answers
19k views

How robust is the independent samples t-test when the distributions of the samples are non-normal?

I've read that the t-test is "reasonably robust" when the distributions of the samples depart from normality. Of course, it's the sampling distribution of the differences that are important. I have ...
24
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2answers
18k views

Is Student's t test a Wald test?

Is Student's t test a Wald test? I've read the description of Wald tests from Wasserman's All of Statistics. It seems to me that the Wald test includes t-tests. Is that correct? If not, what makes a ...
23
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2answers
44k views

How to test for differences between two group means when the data is not normally distributed?

I'll eliminate all the biological details and experiments and quote just the problem at hand and what I have done statistically. I would like to know if its right, and if not, how to proceed. If the ...
23
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6answers
26k views

Group differences on a five point Likert item

Following on from this question: Imagine that you want to test for differences in central tendency between two groups (e.g., males and females) on a 5-point Likert item (e.g., satisfaction with life: ...
23
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3answers
24k views

Comparing two classifier accuracy results for statistical significance with t-test

I want to compare the accuracy of two classifiers for statistical significance. Both classifiers are run on the same data set. This leads me to believe I should be using a one sample t-test from what ...
23
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4answers
23k views

What sense does it make to compare p-values to each other?

I have two populations (men and women), each containing $1000$ samples. For each sample I have two properties A & B (first year grade point average, and SAT score). I have used a t-test separately ...
22
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5answers
24k views

Paired versus unpaired t-test

Suppose I have 20 mice. I pair the mice in some way, so that I get 10 pairs. For the purpose of this question, it could be a random pairing, OR it could be a sensible pairing, like trying to pair mice ...
22
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2answers
17k views

Choosing between $z$-test and $t$-test

Background: I'm giving a presentation to colleagues at work on hypothesis testing, and understand most of it fine but there's one aspect that I'm tying myself up in knots trying to understand as well ...
22
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3answers
50k views

Test model coefficient (regression slope) against some value

In R, when I have a (generalized) linear model (lm, glm, gls, ...
22
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2answers
15k views

Paired t-test as a special case of linear mixed-effect modeling

We know that a paired t-test is just a special case of one-way repeated-measures (or within-subject) ANOVA as well as linear mixed-effect model, which can be demonstrated with lme() function the nlme ...
21
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1answer
3k views

Is there a statistical test to compare two samples of size 1 and 3?

For an ecology project, my lab group added vinegar to 4 tanks containing equal volumes of pond water, 1 control with no elodea (an aquatic plant) and 3 treatments with the same amount of elodea in ...
20
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1answer
33k views

Should I use t-test on highly skewed data ? Scientific proof, please?

I have samples from a highly skewed (looking like an exponential distribution) dataset about users' participation (e.g.: number of posts), that have different sizes (but not less than 200) and I want ...
20
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3answers
1k views

How to simulate data to be statistically significant?

I am in 10th grade and I am looking to simulate data for a machine learning science fair project. The final model will be used on patient data and will predict the correlation between certain times of ...
19
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1answer
4k views

Why do t-test and ANOVA give different p-values for two-group comparison?

In the Wikipedia article on ANOVA, it says In its simplest form, ANOVA provides a statistical test of whether or not the means of several groups are equal, and therefore generalizes the t-test to ...
19
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2answers
4k views

How does the power of a logistic regression and a t-test compare?

Is the power of a logistic regression and a t-test equivalent? If so, they should be "data density equivalent" by which I mean that the same number of underlying observations yields the same power ...
18
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3answers
7k views

Is "test statistic" a value or a random variable?

I am a student taking my first Statistics course now. I am confused by the term "test statistic". In the following (I saw this in some textbooks), $t$ seems to be a specific value calculated from a ...
17
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6answers
5k views

Can I trust a significant result of a t-test if the sample size is small?

If my one sided t-test result is significant but the sample size is small (e.g. below 20 or so), can I still trust this result? If not, how should I deal and/or interpret this result?
17
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2answers
14k views

Explanation for non-integer degrees of freedom in t test with unequal variances

The SPSS t-Test procedure reports 2 analyses when comparing 2 independent means, one analysis with equal variances assumed and one with equal variances not assumed. The degrees of freedom (df) when ...
17
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3answers
40k views

When doing a t-test for the significance of a regression coefficient, why is the number of degrees of freedom $n-p-1$?

I read here that $n-p-1$ was the number of degrees of freedom I should use when doing a t-test for the significance of a regression coefficient, but I don't understand why. My understanding was that t-...
17
votes
5answers
9k views

Robust t-test for mean

I am trying to test the null $E[X] = 0$, against the local alternative $E[X] > 0$, for a random variable $X$, subject to mild to medium skew and kurtosis of the random variable. Following ...
17
votes
1answer
20k views

Is there any difference between the terms "paired t-test" and "pairwise t-test"?

What is paired t-test, and under which circumstances should I use paired t-test? Is there any difference between paired t-test and pairwise t-test?
16
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3answers
6k views

What follows if we fail to reject the null hypothesis? [duplicate]

What conclusions can we draw if $p>\alpha$? Does not rejecting the $H_0$ mean anything?

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