Reverse Discrimination Case

[Daredevel7]

I think it's a logical assumption that tests are updated every certain years to a more modern language style and also to update the information to include the questions based on latest information (legal/fire/administrative process, procedure, tool, etc).

I meant "the new test" that would be better than the old test at removing cultural bias (or at least an attempt to..)

 

[Jiro]

I meant "the new test" that would be better than the old test at removing cultural bias (or at least an attempt to..)

ah... a very good question indeed

 

[Jiro]

Oh, puleeze! I have already posted some of the statistics, but I guess you don't recognize them when you see them. Likewise, this is not a corporation, it is a forum. Thirdly, what would you know about statistical analysis for a corporation?

You promised to post the RESULT "soon." Whether or not if this is a corporation or forum, you used your qualification card in here numbers of time. Maybe you forget that this is a forum where we all can agree to disagree instead of condescending others and asserting your qualification. So am I to understand that you're a flaker?

I don't work for AD. But it is certainly beginning to look as if you might. You don't appear to be doing much work anywhere else.

and this isn't your statistic classroom either. I believe darkdog does not need your statistic lecture (#237).

A few intelligent posters are mistaken on their assumptions. Please point me to the mistakes that you have corrected. I have virtually no recall of anything you have stated on this topic that is accurrate, from a misunderstanding of the statistical concepts, to a misunderstanding of the issue before the courts, to a failure to know that the U.S. Supreme court will not hear a case until the State Supreme Court has already heard it and handed down a decision, to confusing this issue with Affirmative Action, to attempting to bring an unrelated discussion on heirarchy into the case.

and even you can make mistakes on your part & assumptions <gasp!!>

1. your post #252

Two lower courts, including the State Supreme Court, disagree with you. They both dismissed the white firefighters lawsuit.

and I corrected you that State Supreme Court has not made any decision so how did you come to the point where State Supreme Court would disagree with me?

2. my posts questioning/correcting your false assumptions #248 / #253 / #263 / #266 (especially the part where I've never ever mentioned anything about U.S. Supreme Court which you have claimed that I did). See your post

another thing - I must ask... when you say "soon"... exactly how long is "soon" in your way? I've never had people especially those who work for me telling me "it's almost done soon" that would takes more than 2 hours.

 

[naisho]

Nope, that isn't what I said at all. Those are not the figures I used. And I will provide you with the range as soon as I finish calculations. Right now I can tell you that based on the combined scores using all of the participants, the mean score is 70.98 with a standard deviation of 19.15. That makes the range 61.80-80.10 within 1 SD.

I ran these figures through the SPSS, I'm not getting the same values as you are, either you or I am doing something wrong. I based the data input off Daredevel7's #236 post,

AllDeaf.com - View Single Post - Reverse Discrimination Case
Which the data of the 77 Firefighters were found here:
New Haven Firefighters File Reverse Discrimination Lawsuit

Here is a preliminary show of the data for you (if you want to double check), but trust me it is correct.

Here are the results:

??? How did you get your numbers.

 

[jillio]

Here's my statistical analysis, you already said it before. The mean was right around a 70. Looks right to me. As I said many times, I am in favor of not focusing on race since it is so easily misinterpreted, you are the one that is hung up on it. As far as I'm concerned, 77 men took a test, and some did better than others. That's how tests are.

And I don't think that using smilies to "clarify" your disdain at others' posts or the fact that you consider them laughable is necessary in a civil, adult discussion. If you think their posts are so funny, it shouldn't be so hard for you to discuss the points they bring up, instead of taking cheap shots at the posters and avoiding saying anything meaningful.

Sorry. You are using raw scores, and you are using only the combined score. Raw scores are meaningless; you need z-scores, and then, if you wish to compare further, you will need t-scores. These must be computed for all participants in all domains and then plotted. If you don't compute across all domains, you don't see the influence of weight given to subsets.

I personally don't think that a lot of what you post is necessary in civil, adult discussion...but it all goes back to roomfor interpretation, now, doesn't it?

 

[jillio]

byrdie and I were talking about employers and the trainings... not laws. Where in heaven did I challenge him in law subject in this thread? Are you having trouble following this thread? You've made NUMBER of mistakes which I have repeatedly corrected you. Perhaps you should stick with one task at a time.... such as finishing the statistical analysis that you have promised us.

oye oye.... how unbecoming of you, dear, to sucker-punch me with cheap-shots and irrelevant redirections...

btw - it doesn't take a professional degree nor law degree nor statistical course to understand this simple case

You question, very obviously, his knowledge regarding empoyer/employee rights and accommodations.

Again, I ask you to point out the exact mistakes that I have made that you have corrected. You have given opinion, but you have provided virtually nothing to back it up, and therefore, have been able to refute anything I have said.

 

[jillio]

You promised to post the RESULT "soon." Whether or not if this is a corporation or forum, you used your qualification card in here numbers of time. Maybe you forget that this is a forum where we all can agree to disagree instead of condescending others and asserting your qualification. So am I to understand that you're a flaker?


and this isn't your statistic classroom either. I believe darkdog does not need your statistic lecture (#237).


and even you can make mistakes on your part & assumptions <gasp!!>

1. your post #252

and I corrected you that State Supreme Court has not made any decision so how did you come to the point where State Supreme Court would disagree with me?

2. my posts questioning/correcting your false assumptions #248 / #253 / #263 / #266 (especially the part where I've never ever mentioned anything about U.S. Supreme Court which you have claimed that I did). See your post

another thing - I must ask... when you say "soon"... exactly how long is "soon" in your way? I've never had people especially those who work for me telling me "it's almost done soon" that would takes more than 2 hours.

And that is where you are wrong, Jiro. The case is currently before the U.S. Supreme Court. That would not be possible if the State Supreme Court had not already handed down a decision.

The Supreme Court hears arguments today in a Connecticut firefighters' civil rights case that has the potential to change hiring practices nationwide.

A federal appeals court in New York upheld a lower court ruling dismissing the lawsuit.

A case must exhaust all hearings before state courts, including the district court and the state supreme court, before going to a federal appeals court and the US supreme court.

 

[jillio]

I ran these figures through the SPSS, I'm not getting the same values as you are, either you or I am doing something wrong. I based the data input off Daredevel7's #236 post,

AllDeaf.com - View Single Post - Reverse Discrimination Case
Which the data of the 77 Firefighters were found here:
New Haven Firefighters File Reverse Discrimination Lawsuit

Here is a preliminary show of the data for you (if you want to double check), but trust me it is correct.

Here are the results:

??? How did you get your numbers.

This is meaningless. You are using the wrong statistical analysis. If you want to use SPSS, you need to obtain first your mean based on raw scores. You then need to obtain your standard deviation. Following that you need to obtain your z scores and your t scores. This needs to be done across all domains. You then need to do a scatter plot or a histogram based on z scores and t scores. You then need to sort by race. It doesn't appear that you have even entered your data into SPSS in the correct way that will allow you to run the applicable statistical analysis. You are running stats for hypothesis testing, and we are not testing a hypothesis. We are indicating frequency distribution as it applies to validity.

But to get the figures I have already posted on combined scores for the whole population, not sorted by race:

The sum of (X-M)squared divided by N. Then the square root of that figure. That will give you your SD. To achieve a normal curve, the majority of scores (68%) must fall around the mean of 70.98 in the range of 61.83-80.13.

If you check the raw scores and the way they are distributed, you will discover that you have a postive skew in the raw scores. When converted to z-scores, the scores are still distributed in a postive skew. When you sort by race, and domain, you will find a positive skew in all domains for the minority races, with the greatest postive skew for blacks in the written subset, and the greatest positive skew for Hispanics in the oral subset. However, because more weight was given to the written scores, the positive skew disparately shows with blacks moreso than Hispanics in the combined scores. This indicates a problem with validity for the minority populations.

Additionally, if you check your z-scores in the combined subset and you will find that in the Caucasion scores, you have 16 scores between the mean and +2 SD. You have, in this same population, 9 scores between the mean and -2 SD. This has a slightly negative skew, but approximates a normal distribution and is not cause for concern.

Check your z-scores for the Black population in the combined subset and you will find that you have 2 scores that fall between the mean and +2 SD. You have 6 scores that fall between the mean and -3 SD. The majority fall in the area between -1 SD and -2 SD. That creates a postive skew in the distribution.

Check your z-scores for the Hispanic population in the combined subset and you will find that you have 3 scores falling between the mean and +2 SD. You have 5 scores that fall between the mean and -2 SD, with the majority falling between -1 SD and -2 SD. This again creates a positive skew in the distribution.

Additionally, when using raw scores, your mean for the written portion is 72.05 with an SD of 10.30. Your mean for the oral portion is 69.45 with an SD of 11.81.

With these positively skewed distribution occurring in the minority populations only, one must question the cross cultural validity of the instrument used to obtain the scores...in this case the Lt. exam.

BTW, I just noticed that you are also using the wrong # for N. The number you should have used was 41 as the scores reported were only for the Lt. exam. Nor do the scores you have entered for the subsets reflect the raw scores reported. For instance, rank # 1 showed a raw score of 89.52 on the oral exam, a raw score of 95 on the written exam, and a raw score of 93 on the combined subset. I think you must have failed to account for the different weights, and therefore, came up with an incorrect combined score. Either that, or you attempted to use data from something other than the Lt. exam. You also have rank #6 listed as white, and rank #6 is actually Hispanic. You need to re-enter all of your data as reported in raw scores, and check your race column.

You have also listed "written, oral, and combined" as variables. Again, we are not doing hypothesis testing.

Those are the reasons that your descriptive statistics are off.

 

[Jiro]

You question, very obviously, his knowledge regarding empoyer/employee rights and accommodations.

Again, I ask you to point out the exact mistakes that I have made that you have corrected. You have given opinion, but you have provided virtually nothing to back it up, and therefore, have been able to refute anything I have said.

again.... we did not talk about employer/employee rights and accommodations. we were talking about employer/employee trainings.

see post #343 to answer your question

 

[Jiro]

my question was left unanswered. I'll repost -

another thing - I must ask... when you say "soon"... exactly how long is "soon" in your way? I've never had people especially those who work for me telling me "it's almost done soon" that would takes more than 2 hours.

 

[naisho]

This is meaningless. You are using the wrong statistical analysis. If you want to use SPSS, you need to obtain first your mean based on raw scores. You then need to obtain your standard deviation. .

That's what I'm doing.. I have done this already in my previous post. What I am doing is calculating Standard Deviation and the mean of combined scores to make sure I have the data processed correctly. I am calculating the LT exam.

For the Mean of all Combined scores, I'm getting 68.25857 .
For the Standard Deviation of all Combined scores, I'm getting 9.4106

I know I'm not getting any errors because I'm using excel formulas to calculate it this time, rather than SPSS.

I used excel's formula functions to calculate standard deviation. It backs up the previous mean and standard deviation calculation from SPSS, which was

Right now I can tell you that based on the combined scores using all of the participants, the mean score is 70.98 with a standard deviation of 19.15. That makes the range 61.80-80.10 within 1 SD..

Unless I am still doing something wrong, but these are the exact values I am getting. 68.25857 for the mean, 9.4106 for SD of 77 combined tests. You've gotten70.98 for mean and 19.15 for standard deviation, why are our numbers off?

Either that, or you attempted to use data from something other than the Lt. exam. You also have rank #6 listed as white, and rank #6 is actually Hispanic. You need to re-enter all of your data as reported in raw scores, and check your race column.

Are you sure of this? I went to go re look at the website DD7 provided, #6 for the Captain's test is Hispanic. #6 for the Lieutenant's test is White..


I am pretty positive there is no mistake on my end, or excel is lying to me for some reason, because I have double and triple checked the math for both calculating a mean and SD.

 

[jillio]

That's what I'm doing.. I have done this already in my previous post. What I am doing is calculating Standard Deviation and the mean of combined scores to make sure I have the data processed correctly. I am calculating the LT exam.

For the Mean of all Combined scores, I'm getting 68.25857 .
For the Standard Deviation of all Combined scores, I'm getting 9.4106

I know I'm not getting any errors because I'm using excel formulas to calculate it this time, rather than SPSS.

I used excel's formula functions to calculate standard deviation. It backs up the previous mean and standard deviation calculation from SPSS, which was

Unless I am still doing something wrong, but these are the exact values I am getting. 68.25857 for the mean, 9.4106 for SD of 77 combined tests. You've gotten70.98 for mean and 19.15 for standard deviation, why are our numbers off?


Are you sure of this? I went to go re look at the website DD7 provided, #6 for the Captain's test is Hispanic. #6 for the Lieutenant's test is White..


I am pretty positive there is no mistake on my end, or excel is lying to me for some reason, because I have double and triple checked the math for both calculating a mean and SD.

You can't be calculating for the LT exam, as only 41 participants took the Lt exam. You are using an N of 77. My figures are based on scores obtained from the Lt exam only. What formula are you using to calculate the SD? Or are you just relying on a computer program to do it? If you are asking SPSS to do it for you, why is it not reported? You are only reporting for descriptive statistics, and again, you have variables listed that is throwing SPSS off. Re-enter the data for the LT exam only with ranks from 1-41, do not list the subsets as variables, and simply get a frequency distribution. You are still trying to do functions that are meant for hypothesis testing.

 

[darkdog]

Nope, that isn't what I said at all. Those are not the figures I used. And I will provide you with the range as soon as I finish calculations. Right now I can tell you that based on the combined scores using all of the participants, the mean score is 70.98 with a standard deviation of 19.15. That makes the range 61.80-80.10 within 1 SD.

I look forward to seeing what you come up with because I still have yet to get a clear answer. I asked what formula you use to test validity and you give me the % of populations in the various SDs and tell me that's the information I requested. What am I supposed to infer from that?

And your numbers were approximately correct. My numbers are precise up to 6 significant figures.

Ahh....intro stats.

Ahh.... you do realize the other book I referenced is a graduate level book, right?

"Sometimes referred to". I already stated that. Perhaps you need to go back and check my post regarding a normal distribution and laws of mathematical probability. You are simply repeating what I have alread stated.

So a Gaussian curve and a normal curve are the exact same thing. Except the Gaussian approximates the normal. And they both fall off differently towards +/- infinity. Or zero. Or something. Yeah, I think I got it. Except I don't. It's approximately clear. But not really.

So if a=b, then they're the exact same thing, and at the same time, a is approximately b? I mean, I can say 22/7 is approximately pi, but not the exact same. I can say say 22/7 is exactly 3 1/7, but I can't say they're approximately the same.

Again, Chi-Square is not a test used to determine reliability and validity of a testing instrument. Chi-Square is for hypothesis testing, and is used in experimental statistical analysis, not validity testing. It has no application here.

Then why do you keep bringing it up? I arbitrarily included it in my list of distributions a few posts back and then defended its very existence along with the student-t distribution. I've said nothing of its applicability here. You might as well keep telling me that the Rayleigh distribution is not applicable here, too. I get it.

I did not say that there was no such thing as a t-score distribution.

"Student-t is not a distribution." -jillio, April 27, 2009

There are numerous acceptable methods for determining validity, not the least of which are the correlation coefficient, Coefficient of Determination. The way that specific areas of validity are determined are numerous, and dependent upon the type of validity that you are attempting to measure.

I don't expect you to tell me everything in great detail, but I would be interested to hear about at least one method you would use in this case and how you would apply it.

The only people who seem to have a distrust are those that have had an intro stats course and have not yet learned the difference between hypothesis testing, post hoc testing, and testing for validity of an assessment.

I tried to ask you questions precisely because validating test results is something I don't know much about. I'm not professing any expertise. Quite the opposite- I'm professing ignorance on this particular topic and asking about it. So far, I've only gotten unclear answers and a condescending attitude. It's as if you're more interested in proclaiming your own superiority and everyone else's inferiority than helping me walk away from this with a clear understanding. To quote a wise man, "Communicating badly and then acting smug when you're misunderstood is not cleverness."

 

[naisho]

You can't be calculating for the LT exam, as only 41 participants took the Lt exam. You are using an N of 77. My figures are based on scores obtained from the Lt exam only. What formula are you using to calculate the SD?

Look at the website DD provided:
New Haven Firefighters File Reverse Discrimination Lawsuit


There are 77 participants in the Lieutenant exam. There are 41 participants in the Captain's Exam. I have a feeling you might be confusing the two together, but I thought right now we are supposed to be focusing on the LT exam? Because that's where as the site says, 19 blacks and 15 hispanics took the test.

To calculate SD, that is quite simple (to me) at least. I took the mean of 68.25857 from the 77 participants for the lieutenant's exam, then subtracted it from each of the individual 77 combined scores (You can see that in the 6th row from the left on excel for the last batch).

I then squared that number (7th column). Then add the sum of all of them up which I got, 6730.535. Dividing that by 76 (77-1), I end up with 88.55967. Squaring this for the Standard Deviation, I get 9.410615. that's it in a nutshell from my end.

I gotta head off for some reading, I'll check for more later.

 

[jillio]

I look forward to seeing what you come up with because I still have yet to get a clear answer. I asked what formula you use to test validity and you give me the % of populations in the various SDs and tell me that's the information I requested. What am I supposed to infer from that?

If you can't infer how the distribution affects issues of validity, I can only assume that you have never had a research methods course in your life. And most especially not one specialized in testing and assessment.
And your numbers were approximately correct. My numbers are precise up to 6 significant figures.

Funny. Statistical analysis for the behavioral sciences, which assessment and test validity fall into, only carries out 2 decimal places. If you are using 6 places, you have done the calculations incorrectly.

Ahh.... you do realize the other book I referenced is a graduate level book, right?

And what you referred me to is not applicable to the issue of validity of testing and assessment instruments.

So a Gaussian curve and a normal curve are the exact same thing. Except the Gaussian approximates the normal. And they both fall off differently towards +/- infinity. Or zero. Or something. Yeah, I think I got it. Except I don't. It's approximately clear. But not really.

Perhaps it will become clearer as you continue your education.

So if a=b, then they're the exact same thing, and at the same time, a is approximately b? I mean, I can say 22/7 is approximately pi, but not the exact same. I can say say 22/7 is exactly 3 1/7, but I can't say they're approximately the same.

That's because 22/7 is NOT 3.17. Check your calculation.


Then why do you keep bringing it up? I arbitrarily included it in my list of distributions a few posts back and then defended its very existence along with the student-t distribution. I've said nothing of its applicability here. You might as well keep telling me that the Rayleigh distribution is not applicable here, too. I get it.




"Student-t is not a distribution." -jillio, April 27, 2009

Student t is not a distribution. T-scores are used for comparing scores to peer group scores. T-scores have a mean of 50 and an SD of 10. Z-scores have a mean of zero and an SD of 1. That is why raw scores must be converted to z-scores and t-scores for interpretation of what a raw score actually means in comparison.
I don't expect you to tell me everything in great detail, but I would be interested to hear about at least one method you would use in this case and how you would apply it.

Check my posts. I have already done so. You, as well as naisho, are attempting to compute based on methods used for hypothesis testing. That is the wrong statistical application for looking at frequency distribution to determine disparities that are indicative of problems with validity in a testing instrument.

I tried to ask you questions precisely because validating test results is something I don't know much about. I'm not professing any expertise. Quite the opposite- I'm professing ignorance on this particular topic and asking about it. So far, I've only gotten unclear answers and a condescending attitude. It's as if you're more interested in proclaiming your own superiority and everyone else's inferiority than helping me walk away from this with a clear understanding. To quote a wise man, "Communicating badly and then acting smug when you're misunderstood is not cleverness."

And I have explained again and again why the things you were assuming were incorrect. I have explained in my posts to naisho why he keeps coming up with wrong figures. Go back and check those posts.

 

[jillio]

I meant "the new test" that would be better than the old test at removing cultural bias (or at least an attempt to..)

The first thing that needs to be changed is the way the subsets are weighted. Then raw scores need to be converted to at least a z-score prior to interpretation of what the raw score actually means.

 

[jillio]

Look at the website DD provided:
New Haven Firefighters File Reverse Discrimination Lawsuit


There are 77 participants in the Lieutenant exam. There are 41 participants in the Captain's Exam. I have a feeling you might be confusing the two together, but I thought right now we are supposed to be focusing on the LT exam? Because that's where as the site says, 19 blacks and 15 hispanics took the test.

To calculate SD, that is quite simple (to me) at least. I took the mean of 68.25857 from the 77 participants for the lieutenant's exam, then subtracted it from each of the individual 77 combined scores (You can see that in the 6th row from the left on excel for the last batch).

I then squared that number (7th column). Then add the sum of all of them up which I got, 6730.535. Dividing that by 76 (77-1), I end up with 88.55967. Squaring this for the Standard Deviation, I get 9.410615. that's it in a nutshell from my end.

I gotta head off for some reading, I'll check for more later.

My bad. I was using the scores for the Captain's exam. Sorry about that.
When calculating the SD for the raw scores, you do not use N-1. You simply use N. Maybe this will make it more clear. When we are looking at scores for the purpose for which we are looking at them in this case, we are norm referencing to determine where individual scores fall of the minority populations vs. the peer scores. That is why conversion to a a-score at the very least is necessary to interpret the meaning of the raw score. Raw scores do not give any information regarding relative position, and in this case, relative position is important.

 

[Jiro]

My bad. I was using the scores for the Captain's exam. Sorry about that.
When calculating the SD for the raw scores, you do not use N-1. You simply use N. Maybe this will make it more clear. When we are looking at scores for the purpose for which we are looking at them in this case, we are norm referencing to determine where individual scores fall of the minority populations vs. the overall scores.

so..... what's the result?

 

[jillio]

so..... what's the result?

I've already reported the results in a few posts back.

 

[Jiro]

I've already reported the results in a few posts back.

ah - the post #248. I see that you made a lengthy last-minute edit. it's about time. let's see if my mind can grasp it.