The question is: do you expect your data to follow a normal distribution? Do you know from earlier studies or logical reasoning that this kind of data is usually normally distributed?

Normality is an assumption for a t-test, which is no trivial thing. You explicitly "tell" your test that for each group, the further you move away from the mean in either direction, the less likely the observation. If you have good reason to assume that your data is indeed normal, and according to whichever test for normality (they all have their issues, especially with small sample size), your data indeed seems to be normal (or at least kind of symmetrically distributed around the mean), then the t-test is absolutely the way forward. In this way, you will have a lot more power to draw conclusions. 

I argue that for simple questions (I'm not talking about super high dimensional data, or machine learning), parametric testing is to be preferred if you have somewhat of an idea about where your data came from and what kind of distributions you expect.

Many people apply some kind of ad hoc method, where each set of observations is first tested for normality and depending on the outcome, a parametric or non-parametric test is chosen. There are several issues with this method. First, it leads to intellectual laziness by taking away the need for a scientist to wonder what kind of process generated his/her data. Next, it leads to a situation where outliers or deviations from expected distributions are overlooked ("hidden" behind a non-parametric test) and finally, just by the definition of many of those normality-tests, it will lead to the wrong choice of a test in about 5% of cases :)

Hi Cécilia,

It is better to use a non parametric test as the Mann-Whitney test to compare two population means or the Kruskall Wallis test which assesses for significant differences on a continuous dependent variable by a variable with three or more categories

HI Cheval, 

First, are the 8 observations in total or are they 8 observations for each set? if the former, what test did you use? If it's the Kolmogorov-Smirnov test, there is a high chance that the results of  the normality test were misleading as influenced by the sample size (see what answers were given in the first link below). The non-parametric option only becomes best if the data does not pass a normality test.

If it's the former (8 observations per test), you can use the student's t test or welch's two sample test (Welch's two sample test is better as it assumes unequal variances). I have attached a pdf document that might help. The second link might also help. 

I hope these answer your question.

http://stats.stackexchange.com/questions/13983/is-it-meaningful-to-test-for-normality-with-a-very-small-sample-size-e-g-n

http://daniellakens.blogspot.co.ke/2015/01/always-use-welchs-t-test-instead-of.html

I have 8 observations for each set. I used the Shapiro-Wilk test to assess the normality, I will have a look on the docs you sent, thank you very much.

The question is: do you expect your data to follow a normal distribution? Do you know from earlier studies or logical reasoning that this kind of data is usually normally distributed?

Normality is an assumption for a t-test, which is no trivial thing. You explicitly "tell" your test that for each group, the further you move away from the mean in either direction, the less likely the observation. If you have good reason to assume that your data is indeed normal, and according to whichever test for normality (they all have their issues, especially with small sample size), your data indeed seems to be normal (or at least kind of symmetrically distributed around the mean), then the t-test is absolutely the way forward. In this way, you will have a lot more power to draw conclusions. 

I argue that for simple questions (I'm not talking about super high dimensional data, or machine learning), parametric testing is to be preferred if you have somewhat of an idea about where your data came from and what kind of distributions you expect.

Many people apply some kind of ad hoc method, where each set of observations is first tested for normality and depending on the outcome, a parametric or non-parametric test is chosen. There are several issues with this method. First, it leads to intellectual laziness by taking away the need for a scientist to wonder what kind of process generated his/her data. Next, it leads to a situation where outliers or deviations from expected distributions are overlooked ("hidden" behind a non-parametric test) and finally, just by the definition of many of those normality-tests, it will lead to the wrong choice of a test in about 5% of cases :)

Dear Cécilia

I hope you can use Mann-Whitney or Kruskall Wallis test but try to verify that the sample appears to have  a Normal distribution.

Thank you

Marius

If the data is continuous and not censored, the t-test is probably robust enough to be valid.  Also look at non-parametric test, and if both agree, you should be fine. In any case, report what stat you used, and even better report the raw data in a table.

Its is ok to use a t test for such a number of observation... I did it even with less and compared the Ttest to other non parametric statistical test and the result was always the same.

If the p value is

Stephen, I'd like to stress that this point is wrong and very misleading:

"If the p value is

Hello Cécilia.  See Bland & Altman's (2009) BMJ Statistics Note linked below. One of their points is that frequently, researches know quite a lot about the variables from prior research, and do not have to rely only on what they can see in the sample from a particular study.  You appear to be drawing upon prior knowledge of your variable when you say "even though they follow a normal distribution".  That suggests to me that you should go ahead with your t-test.

The second link below is for a conference presentation in which I argued that formal testing for normality as a precursor to using a t-test is a rather silly and pointless exercise.  HTH.

http://www.bmj.com/content/338/bmj.a3166.long

Presentation Silly or Pointless Things People Do When Analyzing Data: 1. ...