When do I use which stats test?

[Chaste]

Hi all, I have a homework question as follows:

A technician in a clinical lab is released to do routine glucose analyses when the data obtained by the trainee agree @ 90% CL with those experienced technologist. If the following results were obtained in 2 separate measurements:


The solution is to use F-test and then pooled t-test. But I don't understand why we have to use F test at all.
Firstly, their variances are test in a 2 tailed F-test in which the null hypothesis is accepted and then a pooled t test is performed. Why pooled?

My attempt at the question would be to perform a t-test right away with my null hypothesis being, the mean of analyses obtained by the trainee agree with 90% of those experienced technologist.

The alternative hypothesis is the mean of the analyses done by trainee differs from the technologist.

Can't I just solve the question based on my own attempt?

Please enlighten me thanks.

[dipika]

F-test is used for testing equality of 2 population variances.So your hypothesis is (2tailed)

Ho:- their variances are equal v/s H1: not Ho

In this case your , Ho is retained it means the variances are equal i.e. the samples are drawn from normal populations with same/common variance.

Since , we have verified the assumption of common variance using F-test , we use pooled estimate for independent samples t-test(comparing means).

Hope this answers your doubt.

[Chaste]

F-test is used for testing equality of 2 population variances.So your hypothesis is (2tailed)

Ho:- their variances are equal v/s H1: not Ho

In this case your , Ho is retained it means the variances are equal i.e. the samples are drawn from normal populations with same/common variance.

Since , we have verified the assumption of common variance using F-test , we use pooled estimate for independent samples t-test(comparing means).

Hope this answers your doubt.

Why do we need to find if they have the same variance in the first place? Why is a common variance the interested quantity?

[dipika]

We cant directly conclude /assume that they have same variance . Hence, we use F-test to verify if the variances differ significantly. You can look upon F-test as diagnostic procedure to check the assumption of common variance, before using t-test. In the above example , since the values of variances are given we check if they differ significantly & then proceed for t-test with pooled estimate of variance.

[gianmarco]

Hi,
just to remind that Welch's test can be used instead of t-test when equality of variance is not met.

Regards,
gm