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what would be a correct t-test to use if i have two sample set data with equal number of samples but variance of the sample set is different e.g

group1,group2
26.1,14.8
27.9,14.7
29.5,15.6
19.7,14.9
21.1,14.7
18.3,15.2
21.3,16.4
20.1,17.1
20.9,14.6
19.2,14.6

i referred to some sites and their flow looks like picture attached which suggest to use equal variance independent t-test enter image description here

sherpaurgen
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  • It looks like the chart is telling you to use the unequal variance t-test. My stance (and R defaults to this) is to use the unequal variance t-test unless there is pairing in the data, pretty much never using the equal variance t-test. (When do you ever really know that the variances are equal?) – Dave Jun 29 '21 at 15:58
  • i find it confusing the flow according to my samples is areTwoSample related -No-> areTwosamplesetSameSize(10 each)--yes--> EqualVarianceT-test . – sherpaurgen Jun 29 '21 at 16:01
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    Some people argue that the unequal variance issue is less of an issue when the sample sizes are equal. I avoid this by defaulting to the unequal variance test, so my decision tree would be "are the two samples related" -> yes -> paired t-test, "are the two samples related" -> no -> unequal variance t-test. (Maybe that's more like a decision "V" than a decision "tree".) – Dave Jun 29 '21 at 16:02
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    WARNING: This may be at odds with what your instructor sees as the right answer on a quiz, so make sure you get the points in your class, even if you know the full-credit answer is incorrect. – Dave Jun 29 '21 at 16:07
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    This flow chart is erroneous: equality of sample sizes is completely irrelevant to deciding whether an equal-variance version of the test is needed. It is also misleading. For instance, "same or related" literally means paired, which is far more general than most people would infer from that phrase. – whuber Jun 29 '21 at 16:28
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    The ordinary independent samples t-test is quite robust to inequality of variances when sample sizes are equal (or you have more data for the sample that has larger variance). There's nothing wrong with using the unequal variance test, though, just be aware that it is more conservative.

    When you're trying to "get to know" a test, it's worth simulating fake data in R or Python with different parameters and see how the test performs.

     – rishi-k Jun 29 '21 at 17:27
  • @Dave: Whe there are pre-existing groups, groups that where not created in the study by randomization, there might seldom be equal variances. But in a properly randomized study, under the null hypothesis of no treatment effect, there should be equal variances! Unequal sample variances will indicate that the null is false see https://stats.stackexchange.com/questions/434928/unequal-variance-in-randomized-experiments-to-compare-treatment-with-control – kjetil b halvorsen Jun 29 '21 at 22:32

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