Example 1 - Comparing 2 populations

You produced parts using 2 production machines (red and blue). When measuring the breaking strength of the parts you produced, the following result was obtained:

Based on previous information we would believe that the parts produced by the red machine would be more resistant than those produced by the blue machine.

Question: Does the red machine produces a significantly higher average of products than the blue machine?

Enter the data in Ellistat

Then select the inferential statistics menu (on the left). In the adapted test selection menu (table at the top), select your Y (values here) and your X (colour here).

Inappropriate tests will then be greyed out and the only choices left are population comparison tests; test t, test F, etc...

Click on one of the tests to see its result:

Left hand table- Depending on the comparison to be carried out: if you want to compare the average of two independent samples, then you would use test t.

Right hand table - Depending on the type of variable: Y is the value for one part between 30 and 52 (quantitative) depending on (X) the kind of machine (qualitative). Therefore a population comparison is used.

We then obtain the following result:

According to the results of different statistical tests:

ANAVAR and test T, that allow for the comparison of the average of two samples, show the difference between the averages as, respectively, very significant and significant. The average for the Red machine is not the same as the average for the Blue machine.

Test F, that enables you to compare the standard deviations of 2 samples, shows the comparison of the standard deviations to be insignificant. The Blue machine has the same dispersion as the Red machine.

The Red machine produces parts well that are, on average, significantly more resistant than the Blue machine.