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Topic Trying to Understand ANOVA F Crit

Trying to Understand ANOVA F Crit

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This topic contains 11 replies, has 3 voices, and was last updated by Profile photo of Andrew Ciccarelli Ciccarelli 1 year, 2 months ago.

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  • #203549 Reply

    Hello – I’m trying to get a more complete understanding of ANOVA. MS is easy: SS/df

    F ratio seems much more complex and time-consuming based on what I see here: http://en.wikipedia.org/wiki/F-test

    How do I determine the “f crit” value in ANOVA? I wasn’t able to find a good explanation for this, based on some basic googling?

    Based on some basic googling, p-value is a lookup in the “table of f crit values” by f-ratio/stat, if I understand correctly. Is “table of f crit values” the official name for this lookup table? I looked through the back of my ASQ CSSBB handbook and I couldn’t find a lookup table with this name. All I found were several “f-distribution” tables for different confidence levels?

    #203597 Reply

    ok, so consider the example above:

    * df = 1
    * f-ratio = 2.82

    The following table is titled “f-distribution critical values for p=0.10″:

    http://www.medcalc.org/manual/f-table.php

    The name and contents of this table appear to indicate that it can be used to look up an f-crit value based on an f-ratio and df. Can you please explain how I would use this table (if this is a valid assumption) to identify the f-crit value for the scenario described at the top of this post?

    #203599 Reply

    http://www.itl.nist.gov/div898/handbook/prc/section4/prc433.htm

    You need to decide what alpha risk (p-value) you want…then look at the attachment to understand the numerator/denominator and where they come from. You find the f-crit knowing the p-value and the DF for both num and denom. Read the attachment and it’s clear where the df comes from.

    You are also confusing the matter by asking questions more advanced than a one way ANOVA. Your attachment isn’t a one-way anova anaysis.

    #203611 Reply

    Thanks for your feedback everyone! The following video also helped me put the pieces together:

    Using the anova table does not seem that complicated. Here’s a simple reference table I put together for my cssbb exam:

    https://www.dropbox.com/s/eqd6tgfi5z3ab38/anova%20lookup.png

    #203613 Reply

    Oops, upon further review, it looks like the table I included in my last post has all of the correct formulas, except for p-value. Here’s the original anova table that I was trying to solve:

    https://www.dropbox.com/s/qbt46gl55xvt497/anova%20problem.png

    The correct answers for the p-values in this table are:

    p – value = 0.168
    p – value = 0.004
    p – value = 0.009

    Can someone please explain how those p-values are calculated? I think I’ve done most of the work for this table by identifying the formulas required for the other fields, in my last post. The p-value calculation is the last missing piece….

    #203615 Reply

    Actually, it looks like the answer options provided for the p-values for this problem are more general. I’m guessing this should make the problem easier to solve, based on a table lookup or other heuristic, without having to use a complex formula:

    (4) = 0.10 < P < 1
    (8) = 0 < P < 0.005
    (12) = 0.005 < P < 0.01

    Can someone please explain the logic behind these answers provided for the p-values for the anova table in this url?:

    https://www.dropbox.com/s/qbt46gl55xvt497/anova%20problem.png

    #203619 Reply

    The p-value is the area under the curve to the right of the F value you found. The total area under the F-curve is 1.0

    #203627 Reply

    “The p-value is the area under the curve to the right of the F value you found. The total area under the F-curve is 1.0″

    Yes, I understand that, in concept. And it appears that P-values can be specified as a relative range between ? F-table lookups. Here’s a fully-populated anova table:

    https://www.dropbox.com/s/lpm1wpkheytfg1e/populated%20anova%20table.png

    All 3 treatments have df=1 and f-crit=4.54. However, the p-values are all different between treatments. This appears to indicate that MS and/or F-ratio are used, in some way, to calculate the p-value.

    However, I’m not clear on *how* the MS and/or F-ratio are used to calculate the p-value. I’m assuming the data is somehow used as part of an f-table lookup, but I’m not sure how. Can you please explain the missing link to me?

    #203667 Reply

    This has been explained to you a couple of times. Get out of the #$$^^&!@#%& table and try to listen and understand the concept. The F value is a calculated number using the Signal/Noise ratio. First understand that the numerator is the average squares of the distance between the group means and the grand mean of the group means. The denominator is the average squares of the distance between the individual group values and the group means. In other words, ratio of the Between group variation (Signal) and the Within group variation (noise/error). This value is overlaid on the F Distribution (forget the table and picture a distribution). The area to the right is the probability that the value can occur (p value). It is the risk you have of being wrong if you reject the null hypothesis. Your F crit or alpha value is the risk that you are willing to be wrong in rejecting the null. The higher the F value, the smaller the remaining area to the right and thus the p value. If the p value is smaller than your F crit or alpha then you can feel comfortable in rejecting the null and claiming that there is a difference in the means. If the Signal is much larger than the Error/Noise then the ratio will be large and the p value small. If you chose an alpha value of .05 (common) and you calculated an F value that was large, then the p value might end up being 0. Now if you reject the null you have a 0 chance of being wrong. You were willing to be wrong 5% of the time. So reject the null. And frankly, with the “advent” of the p value I never worry about the F crit. That’s just the F value for your selected alpha. So as I said, get out of the table and start understanding what is going on conceptually and with the formulas.

    #203701 Reply

    @Darth :)

    @7sigma You need to read more critically the help you’ve been given. To answer your final expaserated? question….The p-value is different for the 3 factors you’ve looked at because the F-ratio is different for all even though all use the same curve. The one with the largest F is the farthest to the right on the curve so the area under the curve is the smallest.

    Let me be more blunt since this is a blog. Quit confusing F-crit and p-value…they are related in the way that the area to the right of the F-crit is your alpha risk (typically 5%). The p-value is as you’ve said you understood (area under the curve to the right of the Fratio)…hope this helps.

    #203831 Reply

    sure – I can tell by looking at the populated table in my previous post that a higher F-ratio leads to a lower p-value, and I can visualize that in a distribution. I also found this nifty online calculator that will give me the p-value based on df1, df2 and f-value. I ran the numbers based on the populated anova table in my previous post, and all of the correct p-values were calculated as expected. This calculator gives me some clarity and confidence, because it gives me the correct p-values I need based on a specific subset of parameters.

    However, I need to be able to figure out the p-value during the cssbb exam, where I can only use some type of lookup table, or a basic calculator like a TI-30XA. This url describes how to do the calculation on the TI-30XA:

    http://csetmathguru.weebly.com/calculator-tips-for-the-ti-83-family.html

    I can probably do some more googling to find better instructions that are more clear. I’m not sure why no one in this thread mentioned that p-value could be obtained through a calculator. Can you recommend a calculator that would simplify this calculation for me as much as possible, but still be legal for the cssbb exam?

    Or can the p-value be easily obtained through some type of lookup chart? If rgw p-value can be easily obtained through a lookup chart, then I would really appreciate it if you could post an image of that chart for the populated anova table I posted, with the red circles to highlight key attributes, intersections, etc, that are used to obtain the p-value from the chart?

    #204007 Reply

    @Robert – I ordered, and received, TCGS. I was eager to see how they addressed the calculation of p-values, steps for me to follow during my cssbb exam.

    p.141: “We computed this p-value the modern way, using a statistical software package”

    dammit. statistical software packages are not allowed as part of the cssbb exam :(

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