Mark B. answered • 04/15/18
Tutor
New to Wyzant
PhD Candidate and Math Tutor with 20 Years of Experience: All levels.
Good Morning, Brenda,
There is a short answer to your question, and a longer explanation. I will address both since I spend the majority of my time in statistical analysis in my discipline. In addition, as a tutor, I feel an obligation to provide some further analysis versus just giving you the answer, so you may better understand the issue down the road when you ultimately encounter it. My apologies in advance for the length. With that said, I shall begin.
The short answer as to why the researcher knows immediately that she made a mistake is due to the F obtained value being negative.
The longer explanation, of necessity is below:
If you ask any statistician whether an F obtained value can be negative, you are likely to hear the immediate answer I provided you above. Why? Because statisticians are assuming the value reported is due to an F-Statistic being calculated coupled with the context meaning this particular F-Statistic. I bring this up because in population genetics, there is an F-Statistic being of value, however that particular F-Statistic is related to something entirely different.
Here is a quote from the page I just pulled up for you:
"F statistics: The F statistics in population genetics has [sic] nothing to do the F statistics evaluating differences in variances. Here F stands for fixation index, fixation being increased homozygosity resulting from inbreeding. ...
...The value of FIS ranges between -1 and +1. Negative FIS values indicate heterozygote excess (outbreeding) and positive values indicate heterozygote deficiency (inbreeding) compared with HWE expectations."
Yes, I realize it is confusing, however please note that the term F-Statistic is used but it stands for fixation index.
However, my suspicion is that this is not what you are referencing in your question above, and yet the possibility exists that you are in a biostats class, so I wanted to provide you with that information.
On the other hand, it is not possible to get a negative F-statistic of the type that occurs in statistics. Think about what an F-statistic is. All F-statistics are of the form:
F=MS effect
------------
MS residual
where MS is mean square, effect is best looked upon as error, and residual is interpreted as "a measure of the amount of error remaining between the regression function and the data set."
Therefore, the value can only be negative if and only if one of those values were negative. But all mean squares are of the form:
MS = SS
----
df
Remember: MS is mean squares, SS is sum of the squares, and df is the "degrees of freedom" in the analysis.
Consider further, if you will:
SS = ∑i (xi - x bar)2
and
df = N - number of parameters estimated.
Squaring any value yields a positive value. I suppose you could say that if you were estimating more parameters than you had data, then you would get a negative df, and thus ultimately a negative F, but such a model would be unidentifiable, so this could not be done.
Therefore, any F-statistic will always be non-negative.
For a given sample, it is possible to get 0 if all conditional means are identical, or undefined if all data exactly equal the conditional means, but these are extremely unlikely to happen in practice even if the null hypothesis is completely true.
When working with data repeatedly, as I find myself doing, and as you will likely be doing if you find yourself in any social scientific field, or field reliant upon statistics, this will become second nature to you.
While I hope I did not come across as pompous, arrogant, and overwhelming with the amount of information supplied to you, I do believe I have a professional responsibility to answer your question while providing you with all pertinet information related to that question, allowing you to make an informed decision as to whether the data is corrupt, the analysis miscalculated, or whether the finding is due to what we term artifact.
Interestingly, an F value for two groups is equal to a t-value for two groups squared. In other words, F = t2
Please remember though: This assumption applies only if you are comparing two groups.
I sincerely hope I have not only answered your question, but also provided you further information which may assist you down the road. I also hope I have not overwhelmed you with information. This is precisely why I provided you the short answer as well as the lengthier explanation.
Have a great Sunday and upcoming week. Please leave any feedback, or questions below the post so I can answer back for you.
There is a short answer to your question, and a longer explanation. I will address both since I spend the majority of my time in statistical analysis in my discipline. In addition, as a tutor, I feel an obligation to provide some further analysis versus just giving you the answer, so you may better understand the issue down the road when you ultimately encounter it. My apologies in advance for the length. With that said, I shall begin.
The short answer as to why the researcher knows immediately that she made a mistake is due to the F obtained value being negative.
The longer explanation, of necessity is below:
If you ask any statistician whether an F obtained value can be negative, you are likely to hear the immediate answer I provided you above. Why? Because statisticians are assuming the value reported is due to an F-Statistic being calculated coupled with the context meaning this particular F-Statistic. I bring this up because in population genetics, there is an F-Statistic being of value, however that particular F-Statistic is related to something entirely different.
Here is a quote from the page I just pulled up for you:
"F statistics: The F statistics in population genetics has [sic] nothing to do the F statistics evaluating differences in variances. Here F stands for fixation index, fixation being increased homozygosity resulting from inbreeding. ...
...The value of FIS ranges between -1 and +1. Negative FIS values indicate heterozygote excess (outbreeding) and positive values indicate heterozygote deficiency (inbreeding) compared with HWE expectations."
Yes, I realize it is confusing, however please note that the term F-Statistic is used but it stands for fixation index.
However, my suspicion is that this is not what you are referencing in your question above, and yet the possibility exists that you are in a biostats class, so I wanted to provide you with that information.
On the other hand, it is not possible to get a negative F-statistic of the type that occurs in statistics. Think about what an F-statistic is. All F-statistics are of the form:
F=MS effect
------------
MS residual
where MS is mean square, effect is best looked upon as error, and residual is interpreted as "a measure of the amount of error remaining between the regression function and the data set."
Therefore, the value can only be negative if and only if one of those values were negative. But all mean squares are of the form:
MS = SS
----
df
Remember: MS is mean squares, SS is sum of the squares, and df is the "degrees of freedom" in the analysis.
Consider further, if you will:
SS = ∑i (xi - x bar)2
and
df = N - number of parameters estimated.
Squaring any value yields a positive value. I suppose you could say that if you were estimating more parameters than you had data, then you would get a negative df, and thus ultimately a negative F, but such a model would be unidentifiable, so this could not be done.
Therefore, any F-statistic will always be non-negative.
For a given sample, it is possible to get 0 if all conditional means are identical, or undefined if all data exactly equal the conditional means, but these are extremely unlikely to happen in practice even if the null hypothesis is completely true.
When working with data repeatedly, as I find myself doing, and as you will likely be doing if you find yourself in any social scientific field, or field reliant upon statistics, this will become second nature to you.
While I hope I did not come across as pompous, arrogant, and overwhelming with the amount of information supplied to you, I do believe I have a professional responsibility to answer your question while providing you with all pertinet information related to that question, allowing you to make an informed decision as to whether the data is corrupt, the analysis miscalculated, or whether the finding is due to what we term artifact.
Interestingly, an F value for two groups is equal to a t-value for two groups squared. In other words, F = t2
Please remember though: This assumption applies only if you are comparing two groups.
I sincerely hope I have not only answered your question, but also provided you further information which may assist you down the road. I also hope I have not overwhelmed you with information. This is precisely why I provided you the short answer as well as the lengthier explanation.
Have a great Sunday and upcoming week. Please leave any feedback, or questions below the post so I can answer back for you.
This is the link for the information I provided you regarding the F-Statistic standing for "fixation index" in biostatistical analysis. http://www.dorak.info/genetics/popgen.html
Mark B.
My apologies for neglecting to provide you with the link where I obtained the quote for F statistic meaning "fixation index" in population genetics.
http://www.dorak.info/genetics/popgen.html
04/15/18