Download Fuzzy1_24_08

Fuzzy
How to calculate the
st. dev?
How to calculate the
range?
How to calculate the
variance?
What is variance?
√
What’s Fuzzy JANUARY 24, 2008
Responses
See Meier: pages 101-102
See Meier: page. 99
See Meier: page 102, step 5 of st. dev.
SPSS calculates these measurements of dispersions. See
Analyze> Descriptive Statistics> Frequencies> Statistics.
Variance is the sum of the squared deviations from the mean
divided by the number of observations being analyzed. (Meier,
page 102; 1036/5= 207.2). By itself it is a meaningless number.
However, the square root (√) of the variance is the standard
deviation which is used to identify if a value is close to the mean
(what you would expect at random) or far from the norm, which
may be significant.
Examples of st.
deviation? √
Examples are found on the in-class exercise of January 24th.
We will complete this exercise on Feb. 1st. Also see
http://psych.colorado.edu/~mcclella/java/normal/normz.html
This is from the class web page titled, Playing with Standard
Errors.
Interpreting st. dev.
once it is calculated?
√
Standard deviations allow one to exam how close or far an
observation is from the norm. For example let’s say the norm for
LSAT scores is 1000 and the standard deviation is 100. Then
the typical, run of the mill applicant will have a score of 900 to
1100. The difference between 900 and 1100 is random error.
A law school that wants high performers on LSAT exams may
elect to only consider applicants that are 2 standard deviations
above the norm (1100 +) knowing that will discourage
applications from 84% of all LSAT test takers.
Could you identify
terms and how can
we best learn
definitions such as
deductive, inductive
reasoning?
A general rule is that large st. deviations (compared to their
means) indicate less certainty about the norm while small
standard deviations indicate greater certainty. Drug A has 87%
effectiveness as its mean with a standard deviation or 4 but drug
B has 87% effectiveness and a standard deviation of 2. FDA will
prefer drug B to A. In some cases the size of the standard
deviation away from the norm will determine if a drug may be
sold over the counter (small standard deviation) or must be sold
by prescription.
There is a Glossary in Meier beginning on page 535. The other
terms will be found in a college level dictionary rather than in online WORD subprograms.
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What is the
difference between
valid percent and
cumulative
percent?
These are terms used by SPSS for output from Descriptive
Statistics>Frequency table.
I get confuse
calculating mean,
median, and mode
for grouped data. I
am also confused
about calculating
standard deviations
for grouped data.
We will use SPSS to calculate the mean, median, mode,
variance, range and standard deviation. Since the computer has
no problem with large sets of numbers there is no reason to use
grouped data calculations. Grouped calculations are used as a
short hand by those who just don’t want to add up a column of
numbers with a 1000 plus items. However, since most
organization use computers the need for “grouped data”
calculations has passed. Skip this discussion in Meier.
When writing a good
hypothesis should
you attempt to try to
predict? E.g. Young
persons are more
likely to vote?
A “good” hypothesis describes the relationship between the
independent and dependent variables. A good hypothesis could
be:
 Age is an indicator of voting.
 As age rises voting among citizens increases
A valid percent is a response divided by all responses. For
example, if there are 100 responses and 10 of these responses
were “1” then the valid percentage is 10% (10/100). If the next
response is “2” and there are 15 (2 responses) the valid
percentage is (15/100) or 15%. The cumulative percentage of
both the first and the second is 25% (10+15). Cumulative
percentages work ONLY with interval/ratio and ordinal data.
In the first case there is no “direction” and a test of statistical
significance would be 2 tailed. The outcome could go either
way: rise with age or fall with age. In the second case there is
direction and it is a one tailed test. The researcher is looking not
only for an influence but for an influence in a particular direction.
Both are ‘good’ hypotheses.
I am having difficulty
understanding the
researcher’s
hypothesis and the
inferential
relationship. These
were the first and last
questions on the
purple sheet.
See discussion of “hypothesis” noted above. The inferential
question on the purple sheet concerned the specifics provided in
the example. The example indicated that the key belief of the
researcher was that as age increased opposition to gay
adoptions increased. This was the inference the researcher
believed the independent would have on the dependent. The
general relationship in this specific example was that age
influenced views on gay adoptions.
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Jargon- or being
able to decipher the
different terms that
are asking for the
same information in
different ways.
The jargon is a challenge. The reason is that statistics texts are
written by different disciplines that have different ways of
addressing their discipline. In public administration we borrow
heavily from sociology, psych, economics, political science, etc.
In addition, SPSS has its own terms for concepts. I like to use
SPSS terms or common English because these are the terms we
use in practice.
Example: Norm = typical= central tendency= mean, median and
mode. See 5 questions handout for some of the linkages.
Please ask in class if terms are overlapping.
Still struggling with
conceptual
definitions versus
operational. √ √
See Fuzzy chart for January 17, visit me in my office during office
hours and/or set up an appointment if the office hours are not
viable for you.
Generally speaking conceptual definitions are found in
dictionaries and operational definitions are identified by the
researcher in the methodology sections that describes what
variables were used and how the data was collected. E.g.
Liberty conceptually means citizens setting their own rules for
self government. The operational definition might be Liberty is
the response of citizens to questions 106-111 on an NES survey
that address participation in public affairs.
Struggling with the
relationship of
nominal, ordinal and
interval to mean,
median and mode.
Level
Mode
Median
Mean
Nominal
*
Ordinal
*
*
Interval/Ratio
*
*
*
* indicates one can use statistic for specified level of
measurement.
Confused about the
scale and it
relationship to
measurement. What
scale level should be
linked to what
measurement?
Scale is an SPSS word that means, not nominal or ordinal. In
some statistics books this would be called parametric data or
continuous data but SPSS abbreviates the concept by using the
term “scale”. Scale should be linked—at least in theory—to
interval and ratio measuring systems.
Can you create a
description of the
standard deviation
chart (normal curve)
naming what each
line/curve means?
Try http://www.mnstate.edu/wasson/ed602lesson7.htm and scroll
down to the picture of a ‘normal’ curve which is about a third of
the way down the page. The title of the picture is Percentages of
Cases Under Portions of the Normal Curve. Here is the curve
and a definition of the lines and spaces under the curve. “0”
equals the mean.
However, since the measure column (last column on the right in
the variable view) doesn’t control any subprogram in SPSS
researchers (GSS, NES, Census) use ‘scale’ as a default and it
could mean anything!
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Click on box next
to this fuzzy cell
and it should reveal
the curve and its
values. (it make take
a moment or two to
load)
Also try:
www.ms.uky.edu/~mai/java/stat/GaltonMachine.html This
web page introduces you to Gauss, the inventor of the
‘curve’. Relax and watch the curve develop. It is a great
stress reducer.
Please explain the
tails and skewness.
The picture above is a Gaussian, bell shaped curve of random
events and as you can see there are two tails which are equal.
The mean, median and mode are all in the same place (0).
However, the model is not like the real world and the distribution
may indicate lumpiness on the left and a long tail on the right.
A tail on the right means the data is positively skewed and that
the mean will be larger than the median. A tail on the left means
the data is negatively skewed and the mean will be smaller than
the median.
Project requirements
for LAWA
Still having trouble
with data
interpretation and
how to assign
variables.
Badly skewed data has policy implications. For example the US
economy is in-- or is headed to-- a recession. Over the past 2
decades productivity and income has soared. However, the
distribution of that wealth has gone primarily to the top 1% of all
income earners in the U.S. Consequently if you look at mean
change in GDP, wealth, stocks, etc. The U.S. looks like it is
booming. However, if you look at the skewness of the data you
see that the norm (in this case the median income of $42000)
has remained virtually stagnant while only a few have reaped the
benefits. This is the reason that Clinton and Bush tax cuts for the
top 1 to 5% of income earners makes sense politically but not
economically in terms of balancing the overall economy.
I would like to meet with the LAWA team next week at a time that
is viable for our 9 members. We can then discuss what each
person will do in the overall project.
Question is not specific. Please come to office hours and/or set
up a time to clear up this confusion.
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