The total number of correctanswers is transformed to a T-score which has mean 50 andSD 20.
Between which I-scores will approx. 95% the
of population scores lie?
In normal distribution, the lower bound is at -1.96 SDs /orappr.2 SDS) below the mean and the
upper bound is at1.96 SDS above the mean. Thus, the 95%CI lies between a T-score of
50 11.96 28) 50 11.96 * IM*SDnew
-
=
10.8
=
and
+
20) 89.2 (10
+ =
and 90) new
Describe the distribution ofscores:Descriptives -
Explore +
"correct scores" as dependent
skeweness and kurtosis values should be divided by their
·
SES, this value should be compared to -
2 and 2.
Ifthe value for skeweness is larger than 2:distribution
is
negatively skewed
↳ If
t he value for skeweness is larger than 2:distribution
is positively skewed
-
8,975 If kurtosis value greater than -
2:peak
o fdistribution is
1,569
+00 flate
greater than 2:Peakis too sharp
skeweness 1-8,975):slightly negatively skewed butnotsign.!
->
Kurtosis(1,69):peak is sharp butn ot significantly!
Kolmogorox-smirnox test:is significantK.001), indicating a deviation from a normal distr.
ibution! unsignificant:normal distribution
1K.S.- testis very conservative!
calculate
the z-scores and the T-scores:
The Z-score is a standard score with a mean of0 and SD of 1, which is calculated using Raw
scores, the mean of the raw scores and sp of the raw scores. The T-score is a converted
Standardized score, intended to have values thatppl find easier to understand.
The Escore is convertedinto a new standard score IT-score) by multiplying the E-score with
the SD ofthe new score (28) and adding the mean ofthe new score (50)
1) Analyze, Descriptive Statistics' Descriptives X Save standardized variables (E- scores)
2.) Transform, compute to variable T
calculate
T RND
=
120x2-20r 50) +
T- scores based on raw scores
2-scores wereonly standardized, notnormalized
, percentile
2.5,97.5
calculate
9 5% interval of the scores using percentile ranks
1.) Analyze' Descriptive Statistics Explore: T-variable in dependentl ist
statistics X percentiles, Paste
2)I n syntax, change: / Percentiles (5,10,25,50,75,90,95) HAVERAGE
intO
↑Percentile (2.5,97.5) HAVERAGE to gett h e lowest and highest2.5% percentiles
The answer differs from a) bc lower bound is 7 andupper is 92 (VS.10190)
because ata) we assumed a normal distribution, while we DON'T assume a normal distrib-
ution when we use percentiles.
percentile rankS
#
To make norm scores, one can use percentile ranks andp-values thatstem from the standard normal
distribution:
both percentile ranks and p-values indicate the yof ppl with an equal or lower score.
percentiles:calculated using all the raw scores wo
making assumption aboutdistribution ofthe scores
p-values:calculated using only mean and sp ofraw scores and
assuming a standard normal
IP-values:normality assumption
distribution
whether you use percentiles or p-values depends on whether you can assume a normal distribution in the
population or not
p-value preferred by it's less influenced by sample fluctuations
When no information known aboutpopulation and whether it's normally distributed, percentile ranks best to use
calculate p-value stemming from the standard normal distribution (z-scores):
1) Transform, compute to calculate percentile ranks using the standard normal distribution
CDF. NORMAL (Enr cor, 0,1
mean SD
CDF:cumulative distribution function;needed to calculate
the p-value for a certain z- score.
we know thata standardnormal distribution is a perfectly norm. dist. With mean 0 andSD1
calculate
percentives for the number corrects cores (raw scores
1) Transform, Rank cases Variables:h r cor ranktypes:X
fractional rankas
INTERPRETATION:
The percentile rank for a grade of 3.9 is 18.34 and p-value is 0,17
3
15.34% ofthe students hada grade of3.9 or lower.
don't differ a lot:so we can say the distribution
1
17%of the students had a grade of3.9 or lower.
t he
of
grades is fairly normal
use p-values when we can safely assume the distribution ofscores to be normal!
Ifnot:use smith that's not
assuming normal distribution (e..:percentile ranks)
, .Normalized scores
#
normalized T-score has
A to be caculated: 50
Meannew= sDrew=20
O RMALIZATION:
M
1) compute directpercentile ranks Rank Cases
2) convert the percentile ranks into standard scores (Nar_20r)
where the actual normalization oft he scores takes place be the standard scores are now no
longer based on the raw scores (like z-scores), buton percentile ranks!
3) compute convertedstandard score with mean 50 and SD 20 +
ur -cor + 20 50
+
Difference btw F-Scores from I . andIII.:
·The T-scores and F-norm scores differ on same Grade (e.9.:Grace 6:61/63). They differ because
the T-scores were notn ormalized, they were only standardizedIZ-Scores). The T-norm scores were
both standardized and normalized. raw scores, z-scores transformation
·F scores:transformations oft he z-scores (Standardized, notnormalized) - use raw scores
Why Iscores have same distribution ofthe raw scores (thus notnecessarily norm all
·
F-norm scores:transformation t he
of normalized scores. perientile+ z-scures transformation
-
·Standard scores calculated based on assump. of a normal distribution
the course coordinator shouldprefer the normalized scores to be sure thatthe assumption of a
normal distribution ofthe scores is met.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller christinauhlenbruck. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.66. You're not tied to anything after your purchase.
