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Cindy is in the same class as Bill, Mary, and Pedro. On the mathematics test, she received a stanine score of9. Her mother wants to know just how high that score is-what percent of pupils perform less well than Cindy. Ms. Billingsley tells Cindy's mother that 96 percent of students in Cindy's grade performed less well than Cindy. Is this an accurate statement of Cindy's percentile rank?

No. The ninth stanine is not the 96th percentile. The lower limit of the ninth sta­ nine is the 96th percentile, but the upper limit is plus infinity. Any performance above the 96th percentile is the 9th stanine. Cindy may have scored far above the 96th percentile and received a stanine of 9. The same is true at the other end of the scale for a stanine of 1.A person with a stanine score of 1 may be as high as the 4th percentile, or very much lower.

Alfonso's stanine score is 7. Mr. Rivera is more familiar with standard scores than sta­ nines. He asked Ms. Billingsley how many standard deviations above the mean a stanine score of7 was. Ms. Billingsley imme­ diately responded, "One." Does Ms. Billingsley have a trick for remembering such things so well?

Yes. Three easy landmarks for relat­ ing stanines to standard scores ·are the mean and plus and minus one standard deviation. The mean is in the middle of the fifth stanine. Plus one standard deviation is in the middle of the seventh stanine. Minusone standard deviation is in the middle of the third stanine.

Mr. Rivera decided that Ms. Billingsley really knew her sta­ nines. So he pushed his luck and asked her what percent of students got stanine scores of7. Ms. Billingsley thought for a moment. Then she replied, "In a normal distribution, 12 per­ cent of the scores will be in the seventh stanine." Taken aback by the speed of her response, Mr. Rivera asked whether an­ other trick was involved. Was there?

Yes. Ms. Billingsley used the Rule of Four. With stanines, a close approxima­ tion to the distribution of scores can beremembered as starting with 4 percent in either stanine 1 or 9, then adding 4 percent for the next stanine each time up to stanine 5 and then subtracting 4 percent for each to the end of the scale. Thus, the percent of the scores that are assigned I, 2, 3, ...9 are verycloseto4,8, 12, 16,20, 16, 12,8,and4, respectively. So Ms. Billingsley said to her­ self, "Four percent for stanine 9, 8 percent for stanine 8, and 12 percent for stanine 7." Then she had her answer. She could have started with stanine 5, saying to herself,"Twenty percent in stanine 5, 16 percent in stanine 6, and 12 percent in stanine 7," reaching the same result.

Mr. Tatnall overheard the conversation between Ms. Bill­ ingsley and Mr. Rivera and decided to contribute another guide. He suggested that sta­ nines were the same as deciles. So, he said, the first stanine would be the same as the first decile, the second stanine and the second decile would be equivalent, and so on. Is Mr. Tatnall correct?

No. First, to be correct a decile is a point, not a range. The first decile is the score that separates the lowest scoring JO percent of scores from the highest scoring 90 percent, for example. The name for the lowest JO percent is the lowest tenth, or the first tenth, not the first decile. Beyond that, the first tenth is the lowest scoring JO per­ cent, but the first stanine is the lowest scor­ ing 4 percent, a much lower scoring group, on the average. In general, the only corres­ pondence between tenths of a distribution (or "deciles") and stanines is that tenths and stanines above 5 are high scoring and below 5 are low scoring. The differences between tenths and stanines reflect different as­ sumptions about the distribution of scores. Tenths are based on the assumption that scores have a rectangular or flat distribu­ tion. Stanines are based on the more realis­ tic assumption that scores are distributed normally.

Mr. Rivera decided to ask one more question. He has found that most of his students receive the same stanine scores in the fifth grade that they got in the fourth grade or even the third grade. He concluded that they are not making much pro­ gress in school. ls that correct?

No. Tests that use stanine scores refer these scores to students in a particular grade, not to students in general or to people in general. So a student who regularly receives stanine scores of 5 in a subject from year to year can be assumed to be making normal progress. He stays in the middle of the distribution. Another student who con­ tinually makes scores of stanine 7 stays about I standard deviation above the mean and makes normal progress also. Normal progress with stanines (or with percentiles or standard scores) is shown by earning the same score over time, not higher scores year by year.

Mr. Tatnall asked what should he do about Patricia, who went down from the fifth stanine last year to the fourth stanine this year in reading comprehension? Should Mr. Tatnall be worried about this?

No. Mr. Tatnall does not need to worry much about a change from one sta­ nine score to the adjacent stanine score. One question fewer correct could move a person one stanine down if his score was at the bottom of the range for that stanine. This is one of the problems with stanine scores. A person's performance can be anywhere in a range of scores but receive the same stanine. If Patricia scored at the lower edge of the fifth stanine, a trivial difference in performance could change her score to the next lower stanine.

Mr. Rivera then asked about his student, Elena, whose stanine score in reading com­ prehension went up from the fourth stanine to the sixth sta­ nine. Is that big a difference important?

Yes. When scores differ by two sta­ nines, we tend to think of there being a real difference, not an error of measurement. Other things being equal, for tests with satisfactory reliabilities (.90), such differen­ ces are expected to occur only about one time in ten. Therefore, differences that large deserve further investigation. Perhaps Elena has benefitted from some effective teaching, or she may have become more motivated, or she may have found more time to read, or something in her life that was impeding !}er progress may have been removed. A difference that large is unlikely to be an accident.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Understanding standardised assessment. OpenStax CNX. Apr 06, 2013 Download for free at http://cnx.org/content/col11511/1.6
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