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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130 votes
7 answers
103k 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 ...
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85 votes
9 answers
75k 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 ...
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  • 1,469
24 votes
3 answers
21k 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 ...
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  • 585
92 votes
10 answers
386k 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 ...
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16 votes
3 answers
8k 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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60 votes
2 answers
99k 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 ...
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30 votes
6 answers
11k 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 ...
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110 votes
7 answers
175k 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 ...
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  • 2,197
41 votes
3 answers
42k 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 $p$-...
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  • 2,504
28 votes
4 answers
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 ...
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  • 423
41 votes
8 answers
23k 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 ...
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62 votes
4 answers
38k 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?
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25 votes
1 answer
34k 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 ...
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  • 3,046
32 votes
4 answers
14k 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 ...
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22 votes
1 answer
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 ...
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62 votes
6 answers
51k 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. (...
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25 votes
5 answers
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 ...
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22 votes
2 answers
18k 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 ...
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23 votes
6 answers
27k 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: ...
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53 votes
7 answers
35k 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 ...
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23 votes
3 answers
52k views

Test model coefficient (regression slope) against some value

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

Significance test for two groups with dichotomous variable

I have a 2x2 table with two independent groups of people that replied Yes or No in the survey: Yes No Group A 350 1250 Group B 1700 3800 Could you help to find a test that can be run on these ...
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  • 253
13 votes
2 answers
14k views

Why use a z test rather than a t test with proportional data?

When testing the difference between 2 proportions why do we use a z-test rather than a t-test? Further, is there a simple way to conduct an omnibus test for significant differences between more ...
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  • 225
26 votes
2 answers
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 ...
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12 votes
3 answers
53k views

Prove F test is equal to T test squared

I need to show that F test is equal to T test squared, when the T test is for 2 independent groups and assuming variances are equal. I know that $F=\frac{MSB}{MSW}=\frac{SSB/k-1}{SSW/N-K}$ and I know ...
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  • 511
12 votes
1 answer
126k views

"Accept null hypothesis" or "fail to reject the null hypothesis"? [duplicate]

I'm trying to conduct a Student's t-test for a table of values while trying to follow the explanation and details found on this website. I understand that if the p-value is <.01 then it's really ...
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  • 223
11 votes
4 answers
66k views

How to visualize independent two sample t-test?

What are the most accepted ways to visualize the results of an independent two sample t-test? Is a numeric table more often used or some sort of plot? The goal is for a casual observer to look at the ...
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  • 111
22 votes
5 answers
25k 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 ...
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7 votes
4 answers
8k views

Should I use t-test on highly skewed and discrete data?

I have samples from a highly skewed dataset about users' participation (e.g.: number of posts), that have different sizes (but not less than 200) and I want to compare their mean. For that, I'm using ...
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35 votes
2 answers
31k 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 ...
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24 votes
2 answers
46k 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 ...
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22 votes
2 answers
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 ...
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  • 2,416
27 votes
3 answers
19k 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 ...
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  • 543
16 votes
8 answers
72k views

Minimum sample size for unpaired t-test

Is there a "rule" to determine the minimum sample size required for a t-test to be valid? For example, a comparison needs to be performed between the means of 2 populations. There are 7 data points ...
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3 votes
2 answers
13k views

Significant difference between time series - Can I do this?

I'd like to know whether the solution proposed below is valid/acceptable and any justification available. We have two biological conditions, and for each condition we measured 3 time series, so at ...
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18 votes
1 answer
3k views

$t$-tests vs $z$-tests?

I'm trying to figure out exactly what the difference is between $t$-tests and $z$-tests. As far as I can tell, for both classes of tests one uses the same test statistic, something of the form $$\...
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9 votes
2 answers
3k views

Equivalent to Welch's t-test in GLS framework

How can Welch's t-test be expressed as a generalized least squares model? A standard independent samples t-test (where it is assumed that the samples being compared are drawn from populations with ...
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9 votes
2 answers
10k views

Normality of residuals vs sample data; what about t-tests?

An addition to the common confusion about normality testing in inferential statistics for general linear models: I understand the assumption of normality refers to the residuals in ANOVA and ...
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  • 871
5 votes
2 answers
1k views

Analysing pre-and-post intervention study with anonymous responses

The study I am analysing is a pre-and-post intervention questionnaire of students' views before and after studying a module. The questionnaire was distributed in three different geographical ...
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26 votes
3 answers
26k 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 ...
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  • 405
12 votes
2 answers
90k views

Minimum number of observations for multiple linear regression

I am doing multiple linear regression. I have 21 observations and 5 variables. My aim is just finding the relation between variables Is my data set enough to do multiple regression? The t-test result ...
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  • 493
25 votes
4 answers
25k 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 ...
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  • 1,630
16 votes
2 answers
7k views

Independent samples t-test: Do data really need to be normally distributed for large sample sizes?

Let's say I want to test if two independent samples have different means. I know the underlying distribution is not normal. If I understand correctly, my test statistic is the mean, and for large ...
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  • 557
15 votes
1 answer
25k views

How to perform a bootstrap test to compare the means of two samples?

I have two heavily skewed samples and am trying to use bootstrapping to compare their means using t-statistic. What is the correct procedure to do it? The process I am using I am concerned about ...
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10 votes
2 answers
4k views

Power of a Mann Whitney test compared to a t test

So a Mann Whitney U test is supposedly about 95% as powerful as a t-test when t-test assumptions of normality and homogeneous variance are satisfied. I also know that a Mann Whitney U test is more ...
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  • 1,053
5 votes
1 answer
470 views

Why bother looking at an omnibus ANOVA when I have a priori hypotheses about group differences?

I am examining three independent groups that were measured on a continuous outcome variable. I have a priori belief that the result should be Group 1 < Group 2 < Group 3. I've been told to do an ...
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43 votes
5 answers
81k 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 ...
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  • 2,133
21 votes
1 answer
36k 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 ...
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18 votes
5 answers
10k 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 ...
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  • 10.4k
8 votes
2 answers
21k views

Power of the t-test under unequal sample sizes

I heard that the power of a t-test used with unequal samples is limited by the size of the smaller sample. Can I take this to mean that the power of a t-test with unequal sample sizes is equal to the ...
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