F-test for two-tailed?

[niederme]

I am trying to determine if two sample sets are "Statistically Different" from one another. My dataset is comprised of groundwater laboratory results from a stream, one upstream and one downstream. There are 54 individual parameters that comprise my entire dataset. I will be comparing each parameter between the two sampling locations (e.g., water temp upstream vs. water temp. downstream, dissolved iron concentrations upstream vs. downstream, etc.). I filtered my data to omit any individual parameter's data where we didn't not have at least 6 data points from each location and also had levels above the lab's detection limit (DL) for at least 70% of the samples. When both of these requirements were met, I initially assigned values below the DL to be equal to 0.5*DL.


1. I assume I have to run a two-tailed t-test, because I don't have a sense of whether one location is going to have greater concentrations than the other.

2. I ran an F-Test, making sure that I choose my datasets in such an order to have the variance for the first group to be larger than that of the second. Once that was confirmed, I compared the F_critical value to the F value, as I understand that the F_critical must be larger than the F for the variances to be equal.

Now for the Excel question part...

The results I get when I run an "F-Test for Two Sample Variance" in Excel, shows results associated with a "one-tail" test:

[TABLE="width: 474"]
<tbody>[TR]
[TD="colspan: 2"]F-Test Two-Sample for Variances[/TD]
[TD][/TD]
[/TR]
[TR]
[TD][/TD]
[TD]Variable 1[/TD]
[TD]Variable 2[/TD]
[/TR]
[TR]
[TD]Mean[/TD]
[TD="align: right"]0.0073[/TD]
[TD="align: right"]0.007877778[/TD]
[/TR]
[TR]
[TD]Variance[/TD]
[TD="align: right"]9.4575E-06[/TD]
[TD="align: right"]5.28194E-06[/TD]
[/TR]
[TR]
[TD]Observations[/TD]
[TD="align: right"]9[/TD]
[TD="align: right"]9[/TD]
[/TR]
[TR]
[TD]df[/TD]
[TD="align: right"]8[/TD]
[TD="align: right"]8[/TD]
[/TR]
[TR]
[TD]F[/TD]
[TD="align: right"]1.790533789[/TD]
[TD][/TD]
[/TR]
[TR]
[TD]P(F<=f) one-tail[/TD]
[TD="align: right"]0.213842357[/TD]
[TD][/TD]
[/TR]
[TR]
[TD]F Critical one-tail[/TD]
[TD="align: right"]3.438101233[/TD]
[TD][/TD]
[/TR]
</tbody>[/TABLE]

Once Variance 1 > Variance 2, then you can compare the F and F_crit. values. And if F>F_crit., then the two samples can be said to have generally the same variance, and so you apply a t-Test for equal variances, otherwise, if F_crit. > F, you have unequal variances and so chose to apply a t-Test for unequal variances in Excel.

Am I supposed to be running a different F-Test that can provide a two-tailed results? Is it valid to go forward with the results of equal or unequal variances using the F-Test I already applied?

And one last question...
I saw somewhere that when running the t-Tests I am to set the "Hypothesized Mean Difference" to zero. Why and how come?

 

[AhoyNC]

Maybe the attached links will be of help.
To get a two F critical you can divided your significance level (alpha) by 2. If your alpha is .05 then divided by 2 for .025 when you run the test from Data Analysis.
Since P value is for one tail multiply by 2.

The Hypothesized Mean dif. is usually set to 0 as the Null Hypoth. usually states there is no difference between the samples.

How to run a t test two sample assuming unequal variances in Excel 2013 - YouTube
Two Sample Hypothesis Testing to Compare Variances | Real Statistics Using Excel

You may also want to take a look at this open source statistics text. Page 194 explains the F test.

https://www.openintro.org/stat/textbook.php