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re: "Half the schools are below average" - not always true
Posted on 9/30/14 at 10:56 am to SpidermanTUba
Posted on 9/30/14 at 10:56 am to SpidermanTUba
quote:
The test scores of students within a school are NOT INDEPENDENT variables. OBVIOUSLY.
They arent even variables...they are measurements of a variable
How are you this stupid?
quote:
They have the same teachers, the same learning conditions, the same fellow students to study with (or not).
Every student is the same? Every student has the same teacher in a whole school? wow. Thats gotta be one big class.....you fricking tart.
quote:
You are populating your samples based on which school a student attends - NOT RANDOM.
No. THE SAMPLING UNIT is a student. Where that student attends school is not a decision, that I, as the researcher control, that is we can consider it a random chance he will be at the school he attends.
Jesus man, you really are fricking stupid.
Under your idiotic assumption one could never compare differences in fish between 2 lakes because the fish already live in that specific lake.
1
Posted on 9/30/14 at 10:58 am to SpidermanTUba
quote:
A school's worth of students.
NO.
The sampling unit. The unit to which a treatment is applied and measured that controls the underlying variability in this example is the student.
The treatment is the EXAM.
Posted on 9/30/14 at 11:02 am to CptBengal
quote:
Where that student attends school is not a decision, that I, as the researcher control, that is we can consider it a random chance he will be at the school he attends.
YES BUT HIS TEST SCORE IS PARTIALLY DEPENDENT ON WHICH SCHOOL HE ATTENDS FOR frick'S SAKE
: Your logic would apply if we were measuring students heights It does not apply in the case of test scores.
This post was edited on 9/30/14 at 11:05 am
Posted on 9/30/14 at 11:08 am to SpidermanTUba
The word average is ambiguous. People who don't deal with statistics on a regular basis will not recall the differences between mean, median, and mode but they can all be correctly called an average.
Posted on 9/30/14 at 11:10 am to AUin02
quote:
People who don't deal with statistics on a regular basis will not recall the differences between mean, median, and mode but they can all be correctly called an average.
We should hold journalists - and NGT - to a higher standard.
Though - to be clear - I doubt the headline "Half the school are below average" is meant to imply something about the distribution - its actually meant to cause alarm - so it is stupid in that context - as a normal distribution is actually a good thing.
Posted on 9/30/14 at 11:54 am to SpidermanTUba
quote:
"Half the school are below average" - not always true
Ironic
Posted on 9/30/14 at 1:54 pm to RockyMtnTigerWDE
HOw did that go un-noticed so long?
Posted on 9/30/14 at 5:11 pm to SpidermanTUba
quote:
YES BUT HIS TEST SCORE IS PARTIALLY DEPENDENT ON WHICH SCHOOL HE ATTENDS FOR frick'S SAKE
Apology in advance for any grammar/spelling errors; I am on my phone.
As cptbengal said this is a nested design. Therefore one would use heirachical-linear modeling (goes by a number of names) to account for the between-school differences (or between-classroom differences as well for a three-level design) by allowing students' to vary within the nested units(can allow slopes, intercepts, or both to randomly vary). These analyses are frequently used.
In addition, while it is true in your small sample example that only 25% were below average, as has been pointed out, with a large enough sample, the mean will be approximately normally distributed, regardless of the distribution; you can downplay it but it is an important component to the argument.
I'm addition, although you are right that many variables do not have an underlying normal distribution, that is an irrelevant argument in this case due to the variables of measurment. In particular, because the tests are attempting to measure a latent construct (e.g., math achievement) that cannot be directly observed, they have to create and norm items and scales then psychometrically evaluate them (individually items are usually based on item-response theory, then factor analysis for larger constructs). They then ensure that the tests are normally distributed. Therefore, the underlying distribution is normal and the law of large numbers will enable a large sample to approximate to its expected value (the mean of that normal distribution).
Basically your whole premise is fundamentally flawed. In addition, although I am no expert on statistics, I know enough to believe that you don't know as much as you seem to think.
This post was edited on 9/30/14 at 5:26 pm
Posted on 9/30/14 at 6:55 pm to SpidermanTUba
quote:
NOT GENERALLY TRUE This only happens if the underlying distribution of scores is normal.
Well since the normal distribution is the the most commonly occurring distribution and not the only distribution that the mean is a measure of central tendency and the expected value, then it is often true. So generally is an appropriate description.
Not only have you incorrectly argued most of the concepts with cptbengal while throwing out unnecessary insults, your argument isn't even theoretically correct. In other words, you are talking about a sample from a population; however, a general statement that half of the schools will be below the average, we are actually talking about the whole population itself.
Posted on 9/30/14 at 6:58 pm to SpidermanTUba
quote:Almost everyone will give the wrong answer almost every time.
According to Taleb (I forget if he cites a source or not) - doctors will give the wrong answer almost every time.
The general public has a tough time figuring out 20% of 150 of the top of their heads; they darned sure aren't gonna get that question right.
Posted on 9/30/14 at 7:02 pm to SettleDown
quote:
Almost everyone will give the wrong answer almost every time. The general public has a tough time figuring out 20% of 150 of the top of their heads; they darned sure aren't gonna get that question right.
PhD level mathematicians and statisticians thought Savant incorrectly solved the Monty Hall problem. Conditional and Bayesian probability is often difficult to reason quickly.
Posted on 10/1/14 at 10:03 am to buckeye_vol
quote:
Apology in advance for any grammar/spelling errors; I am on my phone.
As cptbengal said this is a nested design. Therefore one would use heirachical-linear modeling (goes by a number of names) to account for the between-school differences (or between-classroom differences as well for a three-level design) by allowing students' to vary within the nested units(can allow slopes, intercepts, or both to randomly vary). These analyses are frequently used.
In addition, while it is true in your small sample example that only 25% were below average, as has been pointed out, with a large enough sample, the mean will be approximately normally distributed, regardless of the distribution; you can downplay it but it is an important component to the argument.
I'm addition, although you are right that many variables do not have an underlying normal distribution, that is an irrelevant argument in this case due to the variables of measurment. In particular, because the tests are attempting to measure a latent construct (e.g., math achievement) that cannot be directly observed, they have to create and norm items and scales then psychometrically evaluate them (individually items are usually based on item-response theory, then factor analysis for larger constructs). They then ensure that the tests are normally distributed. Therefore, the underlying distribution is normal and the law of large numbers will enable a large sample to approximate to its expected value (the mean of that normal distribution).
Basically your whole premise is fundamentally flawed. In addition, although I am no expert on statistics, I know enough to believe that you don't know as much as you seem to think.
Nice long read with big words.
Like CptBengal, you're neglecting the fact that selecting the sample based on school is not a RANDOM SAMPLE
This post was edited on 10/1/14 at 10:04 am
Posted on 10/1/14 at 10:04 am to SpidermanTUba
quote:
Nice long read with big words.
Like CptBengal, you're neglecting the fact that selecting the sample based on school is not a RANDOM SAMPLE
you still dont get it.
Posted on 10/1/14 at 10:07 am to SpidermanTUba
quote:
Half the schools are below average" - not always true
Print the shirts!!!
Posted on 10/1/14 at 10:08 am to buckeye_vol
quote:
Well since the normal distribution is the the most commonly occurring distribution and not the only distribution that the mean is a measure of central tendency and the expected value, then it is often true. So generally is an appropriate description.
Actually nature is usually more skewed than normal. The stock market learned that the hard way in 1987. Simply presuming a normal distribution without evidence is a serious folly.
Posted on 10/1/14 at 10:12 am to SpidermanTUba
quote:
Simply presuming a normal distribution without evidence is a serious folly.
You do know that there are many other distributions than the normal with the mean as the central measure, right?
You also know that many of these distributions are not symmetrical or unimodal, right?
Of course you did
Posted on 10/1/14 at 10:18 am to CptBengal
quote:
You do know that there are many other distributions than the normal with the mean as the central measure, right?
Ya dude. Point?
This post was edited on 10/1/14 at 10:20 am
Posted on 10/1/14 at 10:20 am to SpidermanTUba
Just go back to posting "k"....you don't look as stupid when you do that.
Posted on 10/1/14 at 10:22 am to CptBengal
Wouldn't do any good.
You'll still assert the distribution of differences in performances of different schools is due entirely to random selection of students.
Which is fricking stupid.
You'll still assert the distribution of differences in performances of different schools is due entirely to random selection of students.
Which is fricking stupid.
This post was edited on 10/1/14 at 10:39 am
Posted on 10/1/14 at 10:39 am to CptBengal
quote:
Let {X1, ..., X_N} be a
This post was edited on 10/1/14 at 10:40 am
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