Sample Size t tests

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Like all studies, when conducting an analysis using the T Test, it is important to consider the study’s power and sample size and how they affect the accuracy of the test itself. By evaluating the characteristics of both groups of data and determining the power needed for the study, we can calculate the minimum sample size needed for the T Test to identify true differences. 


This requires six pieces of information:


  1. The mean value of Group 1
  2. The standard deviation of Group 1
  3. The mean value of Group 2
  4. The standard deviation of Group 2
  5. The Significance level alpha error leve
  6. Power level
    • Also known as 1 - beta error probability or 1 - type 2 error or 1 - false negative error


Worked Example:

A dataset with Mean Group 1 = 10 (SD of 1) and Mean Group 2 = 12 (SD of 2), a Significance level of 0.05 and a Power of 0.8. This generates the results below.

Two-sample t test power calculation 

              n = 10.86076

          delta = 1.264911

             sd = 1

      sig.level = 0.05

          power = 0.8

    alternative = two.sided

NOTE: n is number in *each* group

This means that 10.86 pieces of data (which means at least 11) is required to be in each group in order for the T Test to generate valid results at P=0.05 significance level.


Benefits & Drawbacks

Extra calculation is needed to ascertain minimum sample size for valid statistical analysis.


Written By Ka Siu Fan & Ka Hay Fan





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