Def: The independent t-test, also called the two-sample t-test, independent-samples t-test or student’s t-test, is an inferential statistical test that determines whether there is a statistically significant difference between the means in two unrelated groups.

In probability, two events are said to be independent if the probability of one is not affected by the occurrence or non-occurrence of the other. This definition requires further explanation, so consider the following example.

Earlier in this module we considered data from a population of N=100 men who had both a PSA test and a biopsy for prostate cancer. Suppose we have a different test for prostate cancer. This prostate test produces a numerical risk that classifies a man as at low, moderate or high risk for prostate cancer. A sample of 100 men underwent the new test and had a biopsy. The data from the biopsy results are summarized below.

Prostate Test Risk Prostate Cancer No Prostate Cancer Total
Low 10 50 60
Moderate 6 30 36
High 4 20 24
Over All 20 100 120
  • The probability that a man has prostate cancer given he has a low risk is P (Prostate Cancer | Low Risk) = 10/60 = 0.167.
  • The probability that a man has prostate cancer given he has a moderate risk is P (Prostate Cancer | Moderate Risk) = 6/36 = 0.167.
  • The probability that a man has prostate cancer given he has a high risk is P (Prostate Cancer | High Risk) = 4/24 = 0.167.

Note that regardless of whether the hypothetical Prostate Test was low, moderate, or high, the probability that a subject had cancer was 0.167. In other words, knowing a man’s prostate test result does not affect the likelihood that he has prostate cancer in this example. In this case, the probability that a man has prostate cancer is independent of his prostate test result.

Dhasaratharaman

Mr. T. Dhasaratharaman

Assistant Manager – Statistician

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