September 11, 2012 – Lesson on Testing the Difference between Two Means (Small Samples) and Proportion

It is Tuesday, and here we are again at the four corners of our classroom in Advanced Statistics discussing our new lesson. Our new lesson is not that new because we have already discussed hypothesis testing, yet for every lesson within this topic, there are some changes in the formulas and to what kind of test we will conduct, of what table are we going to use or what degree of freedom is recommended.

Testing the Difference between two Means: Small Independent Samples

If the problem falls on small Independent samples – we still need to conduct the F-test in order to determine the if the variances of the populations are equal or not equal. If the variances are unequal we will this formula for the t-test:

For the degree of freedom the formula is: d.f.= the smaller of n₁ – 1 or n₂ – 1.

However, if the Variances are equal we need to use this formula:

And the d.f.= n₁+ n₂-2

Testing the Difference between two Means: Small Dependent Samples

Small dependent samples are used for problems that involve Pretest and Post test administered to the same people.

µ_D, this symbol is for the expected mean of the differences of the matched pairs.

Here are the possible Hypotheses for Difference of two Means of Small Dependents Samples:

When we are finding the test value of Small Dependent Samples, we are going to conduct a much longer process than that of the Small Independent samples.

First thing to do is to find the differences of the values of the pairs of data (x₁-x₂). Secondly we will find the Mean of the differences by adding all the values and the dividing the answer by the total population of the given data. Then find the standard deviation of the differences. Next is to find the estimated standard error of the differences. Last is to find the test value.

Posted By: Kent Spencer Manalo Mendez

                III-Gold