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Ventilation Design Handbook on Animal Research Facilities Using Static Microisolators 
The resulting estimate of the standard deviation of differences between means is called the 
standard error of the difference and can be interpreted in a manner similar to the standard error of 
means. For example, the probability of obtaining a difference between means that is outside the 
-1.96 to +1.96 range is 5 out of 100. 
The standard error of the difference is computed by taking the square root of the sum of the 
standard error of the means (SEM) for group one squared and the standard error of the means for 
group two squared. 
standard error of the difference = square root (group one SEM 2 + group two SEM 2 ) 
6.1.7 T-Test 
The t-test is defined as the difference between the two sample means divided by the standard 
error of the difference. 
t-test = (mean one-mean two)/standard error of the difference 
Thus, a t-test result can be interpreted as a z-score. For example, a t-value of 2.4 would be 
significant, since its probability is less than 5 out of 100. To be precise, the p-values associated 
with a given t-value depend upon the degrees of freedom that in turn depend upon sample sizes. 
The previous formula is for situations in which the samples being compared are independent 
samples. Other situations arise wherein two measurements are made on the same sample of 
people. When the two sets of scores are from the same sample, such as in a pre-test/post-test 
situation, the proper t-test is the t-test for correlated samples (sometimes called the t-test for 
paired samples or dependent samples). 
