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Stats Notes 4c: Z-test Application in Excel

Question: What is Z test? How do we understand Z-test w/o too many formulas?
When do we need to apply Z-test? What's the difference from T-test?

Answer: Z test is also called proportion test, it's mainly used to compare two proportions' output under two different settings. Theorically, it's based on the second fundamental theorem of probability, the "Bible" Theorem--Central Limit Theorem.

Example: We use the following example to demonstrate: assume there are two groups of patients, one group under the treatment A, and the other under treatment B, we want to see whether there are significant difference between those two treatments' effects.

For the group of patients under treatment A, we assume everybody has the probability of p1 to get positive result; similarly, p2 for the probability to get positive result for patients under treatment B. We want to compare how different between p1 and p2.

Only God knows the true values of p1 and p2, but he will not tell us, right? we need to estimate them as close as possible by the testing samples. One good choice would be the number of patients with positive result devided by the total number of patients in that group. Related Articles you might be interested:
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Ģ 4a. Paried T-test Fundamental
Ģ 4b. Paried T-test Example
Ģ 4c. Z-test Application in Excel
Ģ 5. Bootstrapping example in SAS
Ģ 6. Elasticity: Theory and Application-1
Ģ 6. Elasticity: Theory and Application-2