Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Statistical Tests Means and Medians One Sample tTest Small Sample Size  
See also: survey on statistical tests, large samples, twosample ttest  
OneSample tTest  Small SamplesFor small sample sizes, the mean shows a tdistribution (compare the case for large samples: in this case the means are distributed according to a normal distribution). The reason for this is that the estimate s of the standard deviation is not accurate enough. But again the assumption is that the distribution of the data is approximately normal. The only difference from the derivation for the large sample case is that, instead of the zscores, we will use the tscores, which we can obtain from statistical tables, or by using the distribution calculator. The tdistribution depends on the number of samples. Its parameter is called degrees of freedom, and it is equal to the number of samples minus 1: df = n  1. For a detailed description of how to perform a ttest, please have a look at the ztest section.
The prerequisite for the onesample ttest is that the sample is normally distributed.


Home Statistical Tests Means and Medians One Sample tTest Small Sample Size 