How to perform F-test?

Question

Im currently working on a statistical lab (analytical chemistry) and I am not sure how to chose which way to calculate the F-value. Initial thought was to calculate Spool for 2-11, and get F-calculated to then compare it to the F-table. The more I dove into the F-critical, F-calculated etc etc, the more confused I got. Im not sure at all how to go about this problem. Realising I probably misunderstood the whole concept of F-testing.

Answer 1

Let's clear things up a bit: A= Set (2-7) B= Set 8 $n_A=6$ (b/c you have set 2-7) $n_B=1$ (b/c you only have set 8) $s^2_A$ is the variance of set 2-7 $s^2_B$ is the variance of set 8 Does this answer your question?

Answer 2

Im comparing 6 sets (pooled) with one single set. Basically, when calculating the sA^2 value for the s-pooled used in tcalculated, do I get the s^2 for the 6 sets by calculating this first (second pic) and then taking that value to the power of two, which will equal my sA^2 ? I have to pool the pool?

Answer 3

Jananas said: Hi again, Im now calculating the t-calculated. It is ment to compare a pooled set (2-7) with set 8. I have done so according to this formula: View attachment 44465 I have set the A values as the pooled sets. When calculating the spool for t, I have taken the already variance-pooled value for the sA^2 (I used the formula for spooled but didn't square it). Then I took the (nA-1) pooled as well = (4(sample size)-1)*6-6. I inserted this in the formula. However Im getting a very high number... seems wrong (around 6E4)... the tcritical is around 1.7. What am I missing? Click to expand... I don't have the data so I can't speak to what mistake you made.

Answer 4

Hi again, Im now calculating the t-calculated. It is ment to compare a pooled set (2-7) with set 8. I have done so according to this formula: I have set the A values as the pooled sets. When calculating the spool for t, I have taken the already variance-pooled value for the sA^2 (I used the formula for spooled but didn't square it). Then I took the (nA-1) pooled as well = (4(sample size)-1)*6-6. I inserted this in the formula. However Im getting a very high number... seems wrong (around 6E4)... the tcritical is around 1.7. What am I missing?

Answer 5

Jananas said: For context this is the main task; Water is being transfered from its source (e.g a river) to a lab and all samples must be analysed during the travel to the lab, which is 1h. This is done 11 times during the trip, taking 4 determinations for each time. The concentration of aluminium is measured, and the goal is to keep it as close to the initial value as possible during the whole trip; View attachment 44458 Which checks out removing nr 1since its not statistically comparable with the rest. Will need to see what this means practically though... Click to expand... From task 2, you've concluded that the variability of the sample (1) is statistically different from other samples. Therefore, during the first 4 minutes, the sample will be unstable. If you were the researcher, you should wait longer than 4 minutes for the sample to stabilize before proceeding any further.

Answer 6

For context this is the main task; Water is being transfered from its source (e.g a river) to a lab and all samples must be analysed during the travel to the lab, which is 1h. This is done 11 times during the trip, taking 4 determinations for each time. The concentration of aluminium is measured, and the goal is to keep it as close to the initial value as possible during the whole trip; Which checks out removing nr 1since its not statistically comparable with the rest. Will need to see what this means practically though...

Answer 7

Jananas said: Thanks for the answer! I have calculated the Spool (from 2 to 11) = Sx^2 and also Sy^2 for set 1. When I compared that with the F-table, The F-calc was larger. This means it was a significant difference in variance, which is why I can discard it, right? That's what they ment under "TIP1"? I want to make sure Im on the right track. Click to expand... An F-statistic greater than the critical value is equivalent to a p-value less than alpha and both mean that you reject the null hypothesis. In other words, the variances of the 2 populations are statistically different. The samples were not drawn from the same normal distribution with the same variability. As far as discarding it, I'm not sure what task is being asked is, but if you were asked to discard, you can justify removing group 1 due to the reason stated above.

Answer 8

SupremeCookie said: The F-test is used to test whether 2 normal populations have the same variance. As you can see from the diagram, the variance of the population (1) is much wider than (2-11). That is the point the text is trying to make. To perform the F-test, you need to compute the F-statistic: View attachment 44456 Once you have the F-statistic, compare it to the F-distribution and determine whether the variances are statistically significant based on your selected alpha level. Click to expand... Thanks for the answer! I have calculated the Spool (from 2 to 11) = Sx^2 and also Sy^2 for set 1. When I compared that with the F-table, The F-calc was larger. This means it was a significant difference in variance, which is why I can discard it, right? That's what they ment under "TIP1"? I want to make sure Im on the right track.

Answer 9

The F-test is used to test whether 2 normal populations have the same variance. As you can see from the diagram, the variance of the population (1) is much wider than (2-11). That is the point the text is trying to make. To perform the F-test, you need to compute the F-statistic: Once you have the F-statistic, compare it to the F-distribution and determine whether the variances are statistically significant based on your selected alpha level.