Kaushik and Pradipta have done a very nice job of offering 2 approaches -- one relatively 'simple' and one relatively 'complete.'
Let's assume that you have historical data going back a few years, by month. If your typical product turns over in less than 1 month (time from shipment to outlet to customer purchase is under 1 month), then data by month is great.
Then your company managers want you to predict the sales rate for (all - many - some?) product lines. They _assume_ that these sales rates depend on outlet location, type of location, and floor area. This may be true, but it is also the only data you have.
So we need to develop an equation - a model - that can predict the sales rate for next month or year _before_ the month occurs. Maybe before the outlet is built (!).
This could be done with a multiple regression analysis, using (as Kaushik said) items 1, 2, & 3 as independent variables, and 4 as dependent variable. You would need to check the statistical results to assure yourself that yes, these independent variables actually do influence the sales rate. If you keep track of your data with a date flag, you may discover that there is a seasonal effect [In the northern USA, in the fall & winter you don't sell many lawn mowers but you do sell more snow blowers.]
Key point remember:If your data does not keep track of a factor, you will never learn if it influences your sales. So pick your choice of things to record carefully.
"multiple regression analysis" will be in your stat book. Intro books will discuss cases of all categorical factors (items 1, 2 below) under "analysis of variance - multiple factors." and all interval or ratio scale factors (item 3 below) as "multiple regression analysis." As a first cut, you can reduce item 3 to 2 categories, but that is only to find out if it really has an effect (and yes, it probably will.). You will need a more detailed book to cover both categorical and interval/ratio scale data at once.
Once you have completed this analysis, you will know which type of stores sell more per month, and you can predict a store's sales before it is built. Something valuable to know if you are picking sites for new outlets.
Now you can ask, "how do I keep the cot of delivering product to the outlet to a minimum?"
This gets into the "just-in-time" and "economic order quantity" issues that Pradipta touched on. If you sell a particular item at the rate of 25 per month (about 1 per working day including Saturdays), then you would like to get one item from the manufacturer and get it to the outlet quickly and sell it, so that you are ;holding onto it as little as possible. Your company has to pay interest on the loan that helped you buy the product,and you can't pay back the bank until you get the money form the customer. [If your company doesn't need a loan for working capital, they could have put the money in a bank to earn interest, and you can't earn interest on inventory -- so it still costs you carrying costs.]
This minimum would be to buy and ship to the outlet each day, only enough product to cover the sales for that day. That is Just-in-Time. But you don't know how many will be sold each day - some days it's 0, some it's 3. We can work out how many to have on hand, to cover sales for 98% of the days, IF AND ONLY IF you have data on how many were sold each day for most of a year or so. You don't like days? Try it for months, but you still need over 30 months. And you don't know yet, if each store is the same. I bet they're not.
Then there is the order & shipping cost. Suppliers like to ship large loads, and don't like to handle small orders. So they add a surcharge for small orders. They also may not like to ship an item directly, in 1 day, instead of taking their time and shipping a whole truck load once a month. They add fees for the fast ones again. You will need to work with your suppliers and shippers, to see what they can do for you. Say you promise to order a minimum number each month or year, and tell them as fast as possible when you need a new one - a text message may work great for that. INa ll of this, there will turn out to be a minimum order quantity and an order frequency. You want the conditions that will minimize the cost to your company of moving product from a supplier (manufacturer) to the customer. Those conditions will depend a good deal on the unit cost of your product(s), and the labor and fuel costs of transportation in your geographic area. If you are smart, you will then reduce your sale price some, and wind up with more sales in the bargain. Basically, that is what Walmart did in the USA.
Clearly, things are going to get very complicated as soon as you consider more than one product (different average and variation in sales rates, suppliers, transportation woes, etc.) But if you can set up your computer software and supplier agreements with one product, computers will do very nicely to let you do it for all the rest as well. The Operations Research folks have lots of equations for doing this; the LEAN production people know how to do it more completely than the Just-in-time people. The SAP people and ERP (Enterprise Requirements Planning) people all claim to do it in spades, with software. Industrial Engineers do it frequently also. I suggest you start with one small group of stores, and one large volume product.
My best wishes for your efforts,
Jay
On Mar 31, 2008, at 12:51:19 AM, nupur choudhury wrote:
My problem is that our company have a chain of retail outlets in various locations of guwahati.how can i give weights to the outlets based on
Location of the outlet like commercial area,residence area etc
Type of location like if its commercial area how important is that area compared to others.
Store area in terms of sq foot
Sale amount(monthly)
Based on these factors they want me to give weightage to the outlets so that they can use it to find out how much stock to be kept in the outlets which gives them maximum sale. Can u please guide as to what principles and formula should i use.
Forgot the famous last words? Access your message archive online.Click here.
Dear Nupur
In Operations Research there is a field called
inventory control and management. You can go to your
local library and find some elementary text book on
that subject.
The basic idea is as follows:
Case 1. If you have data on sales of these stores.
There are at least three types of costs - (a) ordering
cost (b) inventory carrying cost (if the company needs
to carry extra inventory) and (c) cost of lost sales
if the demand is not met. Obviously (b) and (c) work
in opposite directions. So you neither want to hold
too much of inventory nor do you want to lose a lot of
sales. Ordering cost can be very interesting. In the
simplest case it is just (unit cost) * (No. of items
ordered). But usually it is more complicated - for
example the supplier may give a discount for higher
volume. Net, you need to first understand the
ordering cost and set up a mathematical equation for
it. Similarly write down the mathematical equations
for inventory carrying cost (cost of renting
warehouses) and cost of lost sales (if customers
cannot find the item in the store). Then you can
write the sum of all relevant costs and minimize the
combined equation with respect to the total volume.
Any elementary Operations research book on Inventory
control will have the formulas for some simpler
models. Some of the key words to look for are
Economic Lot Size Production model. Check the
following website for some idea:
http://people.brunel.ac.uk/~mastjjb/jeb/or/invent.html
Case 2. If you do not know the sales of individual
stores. Then use location, size of stores etc. to
model the sales of the individual stores and then use
the techniques as in Case 1.
Now all of the above are traditional inventory
management system. In reality this type of problems
can be very complicated and advanced. Many companies
nowadays follow "Just in time" inventory system (You
have heard of supply chain logistics of Dell
Computers, right?). With the advancement in
information technology it is possible to reduce
inventory carrying cost very very low - use of barcode
scanning at the counter and transferring the
information to a central location in real time has
made the field very advanced.
I don't know how sophisticated your analysis needs to
be, but at an elementary level you can either use the
traditional methodologies or can write a simulation
program on top of the traditional analysis to take
care of some statistical uncertainty in the system.
For more advanced applications there are commercially
available software that can be used (can be
expensive).
Good luck and enjoy your volume forecasting project.
Thanks,
Pradipta.
--- nupur choudhury <me_nupur79@...> wrote:
---------------------------------
My problem is that our company have a chain of retail
outlets in various locations of guwahati.how can i
give weights to the outlets based on
Location of the outlet like commercial
area,residence area etc
Type of location like if its commercial area how
important is that area compared to others.
Store area in terms of sq foot
Sale amount(monthly)
Based on these factors they want me to give weightage
to the outlets so that they can use it to find out how
much stock to be kept in the outlets which gives them
maximum sale. Can u please guide as to what
principles and formula should i use.
---------------------------------
Forgot the famous last words? Access your message
archive online. Click here.
________________________________________________________________________________\
____
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just an immdiate reaction{not necesory to be all correct):
I think it is an inventory control prob & ur mgtment aprori knows 1,2&3 control demand -for whicgh the proxy is 4. 4 is ur dep variable & 1& 2 have to be in either nominal or in ordinal scale...but 3 is in ratio sclae..
I think u can go for a dummy variable regression ...
If you want to group the stores first u can think of cluster nanalysis....
I want to see what staticians say.....
Regds.
Kaushik
nupur choudhury <me_nupur79@...> wrote:
My problem is that our company have a chain of retail outlets in various locations of guwahati.how can i give weights to the outlets based on
Location of the outlet like commercial area,residence area etc
Type of location like if its commercial area how important is that area compared to others.
Store area in terms of sq foot
Sale amount(monthly)
Based on these factors they want me to give weightage to the outlets so that they can use it to find out how much stock to be kept in the outlets which gives them maximum sale. Can u please guide as to what principles and formula should i use.
Forgot the famous last words? Access your message archive
online. Click here.
Kaushik Bhattacharjee Research Scholar,2005-08 IIMT,ICFAI University Hyderabad-500034 Contact No.9347525284
I hope you of you doing well, I have data needs to do statistical analysis by using SPSS Software. could you please if there is any one willing to help me and do it for me . please contact me personal and i will send my data to him as soon as possible.
Mr.Zidan Mohamed Houmani Ph.D. Student
Nuclear Science Building School of Applied Physics Faculty of Science and Technology University of Kebangsaan Malaysia 43600 UKM Bangi Selangor D.E, Malaysia.
My problem is that our company have a chain of retail outlets in various locations of guwahati.how can i give weights to the outlets based on
Location of the outlet like commercial area,residence area etc
Type of location like if its commercial area how important is that area compared to others.
Store area in terms of sq foot
Sale amount(monthly)
Based on these factors they want me to give weightage to the outlets so that they can use it to find out how much stock to be kept in the outlets which gives them maximum sale. Can u please guide as to what principles and formula should i use.
Forgot the famous last words? Access your message archive online. Click here.
Dear All,
Statistica Sinica will host a special session on its new category
"Editor Invited Thesis Paper" at ICSA 2008 Applied Statistics
Symposium held on June 5-7 at Embassy Suite Hotel in
Piscataway, New Jersey.
The special session will feature "Tracking of Multiple Merging and
Splitting Targets: A Statistical Perspective" by Curtis Storlie etc,
with commentators Drs. Sumeetpal S. Singh, Patrick J. Wolf, and
Ying-Nian Wu.
This new category is designed to promote works by new PhDs.
Papers chosen for this category might not be perfect but show great
promise in important areas. Our invited experts will comment on
each paper for its further development.
The symposium is open for registration. The instructions for abstract
submissions and other details can be found at
http://stat.rutgers.edu/icsa2008/.
With all the best,
Karen Li---on behalf of the Co-Editors
Editorial Assistant
Statistica Sinica
Hi Prakash, This is Venkateswara Rao. I have completed my master degree in statistics in the year 2007. At present i am staying in Bang. I learn sas and the modules are base sas, sas sql, sas stat, sas etl, and a little bit in sas olap.
And what are the skill set required for the job. give me an information about the job to my mail or my phone 9986026273
hi prakash,
wat r the requirements for the job of data analyast?
i am a student of final year of B.Sc(H) Statistics.Do I stand any chance?
wat r the skill sets required?
Kindly reply asap.
Akanksha
On Fri, 28 Mar 2008 maxim dsouza wrote :
> Hi All,
> There are excellent openings for those with the skill
> set of time series or R or Splus with one of the
> investment resesarch companies.
> If you are keen, please send across your updated
> profile immediately. The position is based out in
> Bangalore.
>
> Regards
> Prakash.
>
> avaconsul_at <alice@...> wrote:
> URGENT NEED FOR DATA ANALYST
>
> US Citizen or Green Card only. H1-B visas NOT accepted.
>
> My name is Chelsea Moore and I am a recruiter at AVA
> Consulting. We
> are helping Capital One fill their full time Data
> Analyst openings in
> Plano, Texas. We reviewed your resume from the job
> boards and believe
> you may be a potential fit
>
> It's an exciting time to join Capital One, especially
> when the Auto
> Finance division is pursuing becoming the #1 Auto
> Lender in the
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>
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> Uses the power of numbers to solve real business
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> Mines data and provide strategic insights to the
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> Get trained on the latest tools SAS, SQL, Crystal
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> Work alongside the best in class talent and build
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> Has the best in compensation and benefits in the
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>
> ---------------------------------------------------------
> --
>
> I have two positions open:
>
> Data Analyst – we require a 4 year quantitative degree
> and some
> project work in data analytics
> To apply online:
> Please go to the Capital One career section:
> https://recruit.capitalone.com/index.html
> Enter 515223 to find the right job and add to job
> basket. Click "Apply
> for Jobs in Basket". If not registered you will need to
> register and
> go through the process.
>
>
> Senior Data Analyst - we require a 4 year quantitative
> degree and one
> year in a programming language like sas or sql
> To apply online:
> Please go to the Capital One career section:
> https://recruit.capitalone.com/index.html
> Enter 515773 to find the right job and add to job
> basket. Click "Apply
> for Jobs in Basket". If not registered you will need to
> register and
> go through the process.
>
> Hope to hear from you soon!
>
>
> Warm Regards,
> Chelsea Moore
> AVA Consulting
> E-mail: chelsea.moore@...
>
>
>
>
>
>
> ---------------------------------
> Save all your chat conversations. Find them online.
There are excellent openings for those with the skill set of time series or R or Splus with one of the investment resesarch companies.
If you are keen, please send across your updated profile immediately. The position is based out in Bangalore.
Regards
Prakash.
avaconsul_at <alice@...> wrote:
URGENT NEED FOR DATA ANALYST
US Citizen or Green Card only. H1-B visas NOT accepted.
My name is Chelsea Moore and I am a recruiter at AVA
Consulting. We are helping Capital One fill their full time Data Analyst openings in Plano, Texas. We reviewed your resume from the job boards and believe you may be a potential fit
It's an exciting time to join Capital One, especially when the Auto Finance division is pursuing becoming the #1 Auto Lender in the America. To be able to reach the goal, we need top talent like you to help us build strong, successful teams.
The Data Analyst at Capital One: Uses the power of numbers to solve real business problems. Mines data and provide strategic insights to the organization. Get trained on the latest tools SAS, SQL, Crystal Reports, Proclarity, Sagent, Teradata, Oracle. Supports marketing and solicitation initiatives through analytic projects. Successfully implements process improvements across the organization. Work alongside the best in class talent and build superior solutions. Has the best in compensation and
benefits in the industry + great environment to work in.
Data Analyst – we require a 4 year quantitative degree and some project work in data analytics To apply online: Please go to the Capital One career section: https://recruit.capitalone.com/index.html Enter 515223 to find the right job and add to job basket. Click "Apply for Jobs in Basket". If not registered you will need to register and go through the process.
Senior Data Analyst - we require a 4 year quantitative degree and one year in a programming language like sas or sql To apply online: Please go to the Capital One career section: https://recruit.capitalone.com/index.html Enter 515773 to
find the right job and add to job basket. Click "Apply for Jobs in Basket". If not registered you will need to register and go through the process.
under my company Biostatistics Consulting. This will supply all your data-analysis needs for rates you can afford which are completely negotiable. Please check out the site and fill out an enquiry form regarding your data analysis work. I have 3 yrs of MBBS, First Class Honours in Biostatistics, almost completed Masters in Biostatistics and Mphil in Biostastics. Please check out my site, heavy discounts apply for the analysis of publishable data.
Thanks, Mithilesh Dronavalli, Director of Biostatistics Consulting
under my company Biostatistics Consulting. This will supply all your data-analysis needs for rates you can afford which are completely negotiable. Please check out the site and fill out an enquiry form regarding your data analysis work. I have 3 yrs of MBBS, First Class Honours in Biostatistics, almost completed Masters in Biostatistics and Mphil in Biostastics. Please check out my site, heavy discounts apply for the analysis of publishable data.
Thanks, Mithilesh Dronavalli, Director of Biostatistics Consulting
Even if your native language is English and your membership in the American Statistical Association is up-to-date, you won't get all the words at first go, like any rap song.
Hi,
I give this address for anyone interested
in having access to a great variety of links to notes
covering many areas of statistics
http://statlink.tripod.com/
I dont want to use particularly any one technique in the market research. I want to learn those techniques so can you guide me in that or can you send me some write up on it ???
Thank you
Vishwesh
krishan pandey <krishankpandey@...> wrote:
Hi Vishwesh you should use STATISTICA, or MATLAB for exploring Nueral network in the field of Market research. It is easy to proceed by following simple help option in these softwares. krishan
vishwesh_s_h
<vishwesh_s_h@yahoo.co.in> wrote:
Hi Group,
I am working in the analytics team of a market research company. I wanted to learn application of data mining technique such as Nueral network, MARS, and lots other. If anybody is having good doccuments on it pls send to me. Or give yahoo or gmail id so that we can talk online. Pls do reply.
Hi Vishwesh you should use STATISTICA, or MATLAB for exploring Nueral network in the field of Market research. It is easy to proceed by following simple help option in these softwares. krishan
vishwesh_s_h <vishwesh_s_h@...> wrote:
Hi Group,
I am working in the analytics team of a market research company. I wanted to learn application of data mining technique such as Nueral network, MARS, and lots other. If anybody is having good doccuments on it pls send to me. Or give yahoo or gmail id so that we can talk
online. Pls do reply.
Hi Group,
I am working in the analytics team of a market research company.
I wanted to learn application of data mining technique such as Nueral
network, MARS, and lots other. If anybody is having good doccuments on
it pls send to me. Or give yahoo or gmail id so that we can talk
online. Pls do reply.
Thank you
Sub: Positions for Software
Engineers in all the disciplines.
We are very much glade to announce that our company Apple computers launching the branches in India.
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We are Establishing 8 branches through out India
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Delhi, Noida, Calcutta,
Mumbai),So, we have huge recruitment.
So, As we are hiring 4500 employees at a time we require BE
/B .Tech / B.Sc / M.Tech/MCA / MSC candidates
Positions are based on 1+ years of Experience in all the
disciplines (Java, Dot net, Testing, Oracle, SAP, Data warehousing….)
Note: Freshers also
can apply but they will be recruited based on the best performance.
üSend your updated profile to admin@... before April
15.
Indicate your discipline and years of Experiencein subject box
üNote :Freshers
also welcome but recruiting is based on the best performance.
DotNet:(1- 8 years)
Role:Senior
Developer(Dotnet) Skills:ASP.NET, C# or VB.NET,SQL Server
knowledge, ADO.NET,Knowledge in XML/XSL.ADO.NET,Microsoft SharePoint Portal
Server 2007,Microsoft C#,Net Compact Framework 2.0,.NET Framework 1.1,OOAD with
UML.
Job Description:
·Should be able to prepare and execute LLD from
HLD
* Plan and assign tasks to the team
* Generate weekly and monthly reports for team
C#.Net,
ASP.Net, Webforms,SQL Server 2005
Visual Source Safe, Ado.net, Oracle
Secondary
(Desirable) Technical Skills: Knowledge of programming (PL/SQL) on any RDBMS
SQL Developer:(1-8 years)
We havemultiple positions for Oracle/SQL Server
developers, who will be working in Business Intelligence and Data Warehousing
projects.
Candidate might be relocated to client sites in cities like Bangalore,
Mumbai, Delhi, Chennai, Pune and Hyderabad
as and when required Analysts may also be expected to work at international destinations
in USA, Europe,
South East Asia, Middle East and
Australia etc.
Detailed Description
1) Oracle/SQL Server developer with programming skills in SQL, PLSQL and
knowledge of RDBMS concepts will be working in BI and Data Warehousing
projects.
2) He/She should be skilled in database design concepts/tools to design data
warehouses and work on ETL assignments
3) He/She will work independently and in collaboration with other team
members.
C, C++ UNIX : (1 to 7 years)
Software Engineer / Sr. Software Engineer /
Module Lead / Team Lead / Technical Lead
- Should
have experience working in C++ on Unix OS or other flavors of UNIX and good in
Computer fundamentals like Data structures, Algorithms etc.
- Should have hands on development experience with STL, threads and processes,
memory management.
- Candidates applying for the Lead positions should have experience of leading
a team of 4-10 people
Oracle Applications:(1-10 years)
Oracle
App Functional: All core modules (Financials ,SCM, Distribution, Manufacturing,
HRMS, Project Accounting and self service modules)
Responsibilities:
Good domain knowledge (SAP Technical)
Good hands on capability - should develop good quality deliverable with little
guidance.
Understands SAP Business Processes.
Is able to communicate effectively and in a timely manner with Team lead, team
members and Client. Presents and discusses work results clearly.
Desired Profile:
Strong academic
performance
Good analytical, and problem-solving skills
Effective interpersonal, communication & presentation skills
SAP technical experience of 1-8 years with
Certification in the module will be preferred JD Edwards:(1-3
years)
JD
Edwards Functional: Distribution/Manufacturing/Finance, Experience in
EAM,CRM,APS, and Knowledgeof
latest releases 8.11/8.12 is a plus.
JD
Edwards Technical: Experience in developing Reports/Enhancements/Conversions,
and Interfaces using standard JDE tools set: ERW ,FDA,NER,C-BFSN,
knowledge of 8.11 and 8.12 tools , set and any middleware
(webmethods/Tibco/WSG) is in added advantage.
Send your updated profile to admin@... before April
15.
Selection process will be fallowed as:
1.CVsare to be short
listed.
2. last date for receiving the resume is15
April 2008.
3. Aptitude Tests/ Interviews are likely to be conducted at
following
centers in india
during the month of April and may 2008
Datawarehousing:( 1 - 6 years)
1.Business Objects Reporting
(Primary Skill)
2. Business Objects Designer
(Primary Skill)
3. Business
Objects Supervisor/Administration (Proficiency required)
4. Business
Objects Architecture (Desirable Skill)
Skills - BO, Oracle , Unix
Testing:(1 to 8 years)
Job Description:
Excellent skills in test designing, test planning, test data
preparation, various testing techniques,test
execution and defect management. Must be able write test approach, progress
plans, monitoring reports. Test automation.
Desired Candidate Profile:
1 year of experience in leading test teams. Fresher with testing knowledge also can apply.
Should have excellent verbal & written communication skill.
Should be committed and dedicated.
Should be sincere and hard working.
Peoplesoft
DBA:(1 – 6 years)
Job Description
Experience in
administering PeopleSoft Database on UNIX or windows NT
environment
Implementing Pure
Internet Architecture on Demo, Test, Development & Production
instances.
Sound knowledge in
PeopleSoft Internet architecture
Installation of
PeopleSoft
People Tools Patching.
Setting up development
environment for PeopleSoft Developers.
Thank you , i wish know which would be more effective like some of the centers are providing E-learning(online) certifications.. Whether these online certifications would be effective, like i wish to know whether it would be equivalent to doing the six sigma GB belt & BB belt in ISI institute, i.e ( doing the course in ISI or E-learning (online) Which would be more worth and effective) and also pleasse suggest me any institute that provide E-learning(online) certifications in chennai.... The main thing i wish to know is which would be worthful and effective studing GB & BB belt certifications in E-learning or doing it in regular i.e in ISI or any other institues.....
Thanks & Regards,
Sekaran.L thejasvi tv <tvthejasvi@...> wrote:
ISI provides GB & BB training at many of its centers, Bangalore center being the best. Their GB, BB & MBB courses are accredited by the quality council of India.
Hi Sekaran i think you should go for this in ISI Delhi. This is best place for such a programme.
sekaran L <sekarstats1984@yahoo.co.in> wrote:
Hi All,
This is sekaran, I was very much
interested in joining six sigma Green belt(GB) & also black belt(BB).... Can any one suggest any insitutions for GB or BB certifications in chennai... Apart from e-learning(online) is there any insitutions that provide regular classes, If so please inform me....
ISI provides GB & BB training at many of its centers, Bangalore center being the best. Their GB, BB & MBB courses are accredited by the quality council of India.
krishan pandey <krishankpandey@...> wrote:
Hi Sekaran i think you should go for this in ISI Delhi. This is best place for such a programme.
sekaran L <sekarstats1984@yahoo.co.in> wrote:
Hi All,
This is sekaran, I was very much interested in joining six sigma Green belt(GB) & also black belt(BB).... Can any one suggest any insitutions for GB or BB certifications in chennai... Apart from e-learning(online) is there any insitutions that provide regular classes, If so please inform me....
Hi Sekaran i think you should go for this in ISI Delhi. This is best place for such a programme.
sekaran L <sekarstats1984@...> wrote:
Hi All,
This is sekaran, I was very much interested in joining six sigma Green belt(GB) & also black belt(BB).... Can any one suggest any insitutions for GB or BB certifications in chennai... Apart from e-learning(online) is there any insitutions that provide regular classes, If so please inform me....
Hi friends,
This is venkateswara rao. I did my M.Sc in Statistics
from Banaras Hindu University. Now i am in bangalore. Give me an
information about oppourtunities for sas programmers. Or give me
suggitions towords searching for it.
Thanks Jay. I will be sure to pass your thoughts/suggestions on to
my supervisor as he has a better understanding of the mixed model
approach.
In regards to one of your questions
Is it possible to measure the _amount_ of airway collapse
following sleep onset?"
The hypopneas and apneas were scored by a sleep technician. The
scoring of these events are based on a set of rules e.g. drop in
respiratory flow, oxygen desaturations, length of event, presence of
an arousal. I defined each trial type on the presence of these
events in our data.
Could I measure the collapse of the airway? Not in the current
study. We do have techniques to measure how collapsible the airway
is i.e. what pressure is needed to collapse the airway. However, we
did not perform these techniques.
I guess respiratory flow rate is an indirect measurement of airway
collapsibility. When inspiratory flow rate is decreased, despite
increase ventilatory drive i.e. person is trying to breathe harder,
this indicates that the airway is getting smaller. Basically, this
is how the hypopneas and apneas are scored. But, a hypopnoea is
scored when there is any discernable decrease in flow accompanied by
a 3% decrease in oxygen saturation. In essence, a hypopnea could be
scored when flow decreases by 5% or 95%, as long as oxygen
saturation drops by 3%. However, a 95% decrease in flow would likely
indicate a more collapsed airway. So, we could perhaps look at:
1) stable breathing (no drop in flow)
2) 0-25% drop in flow (hypopnea)
3) 26%-50% drop in flow (hypopnea)
4) 51-75% drop in flow (hypopnea)
5) 76-95% drop in flow (hypopnea)
6) 96-100% drop in flow (apnea)
However, I would assume the numbers for each of these 6 events would
be very small.
Daniel
--- In Statisticians_group@..., Jay Warner
<quality@...> wrote:
>
> Without getting specific WRT analytical approach of mixed model,
> etc., etc. I have 2 generalized thoughts:
>
> 1) Is it possible to measure the _amount_ of airway collapse
> following sleep onset? You have selected three categories, no
> collapse, some, and complete collapse. I bet you treat them as
> categorical data, when in fact they are ordinal, and if you could
> report a finer scale (say 5 or more levels, not 3), then you
could
> have ratio scale data. the shift from ratio scale to categorical
> scale essentially _gives away_ information (or at best, never
> collects it).
>
> If you choose not to report a measure of collapse, then you might
> need to justify to the oversight board, or a reviewer, why you
chose
> the less informative approach.
>
> 2) As a guiding rule of data analysis, one should analyze the
> original data, with all the observations possible, and not try to
> analyze averages of subsets. Talk about giving away information!
>
> there is a variation (standard deviation) of the data within a
> subgroup that you plant o average. There is variation (standard
> deviation) between subgroup averages. On what basis do you
believe
> these standard deviations to be equal? You probably don't.
However,
> your analysis of the averages probably treats each average as a
> single measurement, and the hypothesis test will perhaps assume
that
> they are inherently equal - from which it will determine the stdev
of
> the averages, and hence compute the delta of some means divided by
a
> standard deviation that will become the test statistic. Thus,
the
> degrees of freedom will be sharply reduced (n is smaller than
your
> original data count) and the standard deviation in the test
> statistics will be from the averages, not the measurements. In
> general, I fear your hypothesis test will be less likely to detect
a
> difference in delta.
>
> If I wrote out the model equation, it would be much more clear
(he
> said). Also, if I used the 'proper' terms. Nonetheless,
reliance
> upon the guiding rule - use all your data for the analysis -
should
> prove helpful to you.
>
> Cheers,
> Jay
> On Mar 15, 2008, at 6:24:24 PM, swannies1983 wrote:
>
> > Hi there,
> >
> > This is my first post. I was just wondering if someone could
provide
> > an answer to my problem. This next bit may sound long winded but
> > hopefully it all makes sense.
> >
> > I have been looking at lung volume changes at sleep onset in
obese
> > male obstructive sleep apnea (OSA) patients and age-matched,
healthy-
> > weight controls. At sleep onset, particularly in the OSA
patients,
> > there are generally three types of events which follow sleep
onset:
> >
> > 1) They have stable breathing i.e. no hypopneas/apneas
> > 2) They have a hypopnea (airway partially collapses) not long
after
> > sleep onset
> > 3) They have an apnea (airway completely collapses) not long
after
> > sleep onset
> >
> > Therefore, I have separated out these events to see if there is
any
> > difference in lung volume between each of these conditions. See
Sleep
> > onset.jpg file under Daniel (mixed model) folder in Files area
for a
> > graph showing my current results.
> >
> > On the X-axis, we have breath number relative to sleep onset
> > (vertical line) and on the Y-axis we have change in lung volume.
The
> > change in lung volume for each breath is compared to a baseline
(the
> > mean of the 5 pre sleep onset breaths).
> >
> > So you can see that there looks to be a greater fall in lung
volume,
> > particularly at breath 3, when sleep onset is followed by an
> > obstructive event. I am in the process of looking to see if
there are
> > any differences in these lung volume changes between event type
and
> > breath number. I have been using mixed model analysis to see if
there
> > are any differences. However, I just need a little help with the
> > stats.
> >
> > For each patient, I have attempted to find 10 sleep onset events
for
> > each condition i.e. 10 sleep onsets followed by stable
breathing, 10
> > sleep onsets followed by a hypopnea and 10 events followed by an
> > apnea. In reality, it has been difficult to achieve these numbers
> > because some patients never experienced stable breathing
following
> > sleep onset while others didn't have any obstructive events.
> > Nevertheless, I did the best I could with these numbers.
> >
> > For the mixed model analysis, these are the variables I have:
> >
> > 1) Subject
> > 2) TrialType (stable breathing, hypopnea, apnea)
> > 3) Trial # (i.e. replicate measures within each subject)
> > 4) Breath # (three post sleep onset breaths)
> > 5) Change in lung volume (compared to baseline)
> >
> > Now, in regards to point three, there are two ways which I can
deal
> > with this, but I am unsure how to go about it.
> >
> > Please see Stats1.jpg for first way I have entered the data into
> > SPSS. This example shows that I have put in all trial data (in
> > reality there are more than two).
> >
> >
> > So in this example:
> > 1) Data from one subject
> > 2) Data from two trial types i.e. stable breathing and hypopnea
> > 3) Two replicate trials for each of the two trial types (can be
> > up to ten trials but I only put in two for this purpose)
> > 4) Change in lung volume for each post sleep onset breath for
> > each trial number
> >
> > Now the Stats2.jpg file shows that I have now averaged all
trials for
> > each of the two event types.
> >
> > If I put in all trials, I get a significant p value for trial
type
> > and breath number. However, if I average all trials first, there
are
> > no significant differences for anything. So the question is, do I
> > first need to average all trials for each condition before I do a
> > mixed model analysis OR can I put in every trial for each trial
type?
> > We generally do average trials first but we aren't quite sure
whether
> > this is essential.
> >
> > Thanks
> >
> >
> >
> > ------------------------------------
> >
> >
_____________________________________________________________________
_
> > __
> > NOTE: The Statisticians_group is for discussing on different
issues
> > related to the subject Statistics, Statistical softwares like
SAS,
> > SPSS etc. The users are encouraged to post jobs those are
> > exclusively for Statisticians like data analyst, business
analyst etc.
> >
> > Please don't post or send any SPAM!
> >
> > NOTE: Please don't use this mail for any personal discussion.
> >
> >
_____________________________________________________________________
_
> > __
> >
> > Yahoo! Groups Links
> >
> >
> >
> >
>
> Jay Warner
> Principal Scientist
> Warner Consulting, Inc.
> 4444 North Green Bay Road
> Racine, WI 53404-1216
> USA
>
> Ph: 262.634.9100
> Fax: 262.681.1133
> email: quality@...
> web: www.a2q.com
>
> The A2Q Method (tm) -- What do you want to improve today?
>
Without getting specific WRT analytical approach of mixed model,
etc., etc. I have 2 generalized thoughts:
1) Is it possible to measure the _amount_ of airway collapse
following sleep onset? You have selected three categories, no
collapse, some, and complete collapse. I bet you treat them as
categorical data, when in fact they are ordinal, and if you could
report a finer scale (say 5 or more levels, not 3), then you could
have ratio scale data. the shift from ratio scale to categorical
scale essentially _gives away_ information (or at best, never
collects it).
If you choose not to report a measure of collapse, then you might
need to justify to the oversight board, or a reviewer, why you chose
the less informative approach.
2) As a guiding rule of data analysis, one should analyze the
original data, with all the observations possible, and not try to
analyze averages of subsets. Talk about giving away information!
there is a variation (standard deviation) of the data within a
subgroup that you plant o average. There is variation (standard
deviation) between subgroup averages. On what basis do you believe
these standard deviations to be equal? You probably don't. However,
your analysis of the averages probably treats each average as a
single measurement, and the hypothesis test will perhaps assume that
they are inherently equal - from which it will determine the stdev of
the averages, and hence compute the delta of some means divided by a
standard deviation that will become the test statistic. Thus, the
degrees of freedom will be sharply reduced (n is smaller than your
original data count) and the standard deviation in the test
statistics will be from the averages, not the measurements. In
general, I fear your hypothesis test will be less likely to detect a
difference in delta.
If I wrote out the model equation, it would be much more clear (he
said). Also, if I used the 'proper' terms. Nonetheless, reliance
upon the guiding rule - use all your data for the analysis - should
prove helpful to you.
Cheers,
Jay
On Mar 15, 2008, at 6:24:24 PM, swannies1983 wrote:
> Hi there,
>
> This is my first post. I was just wondering if someone could provide
> an answer to my problem. This next bit may sound long winded but
> hopefully it all makes sense.
>
> I have been looking at lung volume changes at sleep onset in obese
> male obstructive sleep apnea (OSA) patients and age-matched, healthy-
> weight controls. At sleep onset, particularly in the OSA patients,
> there are generally three types of events which follow sleep onset:
>
> 1) They have stable breathing i.e. no hypopneas/apneas
> 2) They have a hypopnea (airway partially collapses) not long after
> sleep onset
> 3) They have an apnea (airway completely collapses) not long after
> sleep onset
>
> Therefore, I have separated out these events to see if there is any
> difference in lung volume between each of these conditions. See Sleep
> onset.jpg file under Daniel (mixed model) folder in Files area for a
> graph showing my current results.
>
> On the X-axis, we have breath number relative to sleep onset
> (vertical line) and on the Y-axis we have change in lung volume. The
> change in lung volume for each breath is compared to a baseline (the
> mean of the 5 pre sleep onset breaths).
>
> So you can see that there looks to be a greater fall in lung volume,
> particularly at breath 3, when sleep onset is followed by an
> obstructive event. I am in the process of looking to see if there are
> any differences in these lung volume changes between event type and
> breath number. I have been using mixed model analysis to see if there
> are any differences. However, I just need a little help with the
> stats.
>
> For each patient, I have attempted to find 10 sleep onset events for
> each condition i.e. 10 sleep onsets followed by stable breathing, 10
> sleep onsets followed by a hypopnea and 10 events followed by an
> apnea. In reality, it has been difficult to achieve these numbers
> because some patients never experienced stable breathing following
> sleep onset while others didn't have any obstructive events.
> Nevertheless, I did the best I could with these numbers.
>
> For the mixed model analysis, these are the variables I have:
>
> 1) Subject
> 2) TrialType (stable breathing, hypopnea, apnea)
> 3) Trial # (i.e. replicate measures within each subject)
> 4) Breath # (three post sleep onset breaths)
> 5) Change in lung volume (compared to baseline)
>
> Now, in regards to point three, there are two ways which I can deal
> with this, but I am unsure how to go about it.
>
> Please see Stats1.jpg for first way I have entered the data into
> SPSS. This example shows that I have put in all trial data (in
> reality there are more than two).
>
>
> So in this example:
> 1) Data from one subject
> 2) Data from two trial types i.e. stable breathing and hypopnea
> 3) Two replicate trials for each of the two trial types (can be
> up to ten trials but I only put in two for this purpose)
> 4) Change in lung volume for each post sleep onset breath for
> each trial number
>
> Now the Stats2.jpg file shows that I have now averaged all trials for
> each of the two event types.
>
> If I put in all trials, I get a significant p value for trial type
> and breath number. However, if I average all trials first, there are
> no significant differences for anything. So the question is, do I
> first need to average all trials for each condition before I do a
> mixed model analysis OR can I put in every trial for each trial type?
> We generally do average trials first but we aren't quite sure whether
> this is essential.
>
> Thanks
>
>
>
> ------------------------------------
>
> ______________________________________________________________________
> __
> NOTE: The Statisticians_group is for discussing on different issues
> related to the subject Statistics, Statistical softwares like SAS,
> SPSS etc. The users are encouraged to post jobs those are
> exclusively for Statisticians like data analyst, business analyst etc.
>
> Please don't post or send any SPAM!
>
> NOTE: Please don't use this mail for any personal discussion.
>
> ______________________________________________________________________
> __
>
> Yahoo! Groups Links
>
>
>
>
Jay Warner
Principal Scientist
Warner Consulting, Inc.
4444 North Green Bay Road
Racine, WI 53404-1216
USA
Ph: 262.634.9100
Fax: 262.681.1133
email: quality@...
web: www.a2q.com
The A2Q Method (tm) -- What do you want to improve today?
Hi, According to my knowledge I think that you should not go for analysis of average what you can do is that you can get average and then using graphs you can get ideas of interection effects and each treatment effects. Thanks,
swannies1983 <split_city@...> wrote:
Hi there,
This is my first post. I was just wondering if someone could provide an answer to my problem. This next bit may sound long winded but hopefully it all makes sense.
I have been looking at lung volume changes at sleep onset in
obese male obstructive sleep apnea (OSA) patients and age-matched, healthy- weight controls. At sleep onset, particularly in the OSA patients, there are generally three types of events which follow sleep onset:
1) They have stable breathing i.e. no hypopneas/apneas 2) They have a hypopnea (airway partially collapses) not long after sleep onset 3) They have an apnea (airway completely collapses) not long after sleep onset
Therefore, I have separated out these events to see if there is any difference in lung volume between each of these conditions. See Sleep onset.jpg file under Daniel (mixed model) folder in Files area for a graph showing my current results.
On the X-axis, we have breath number relative to sleep onset (vertical line) and on the Y-axis we have change in lung volume. The change in lung volume for each breath is compared to a baseline (the mean of the 5 pre sleep onset
breaths).
So you can see that there looks to be a greater fall in lung volume, particularly at breath 3, when sleep onset is followed by an obstructive event. I am in the process of looking to see if there are any differences in these lung volume changes between event type and breath number. I have been using mixed model analysis to see if there are any differences. However, I just need a little help with the stats.
For each patient, I have attempted to find 10 sleep onset events for each condition i.e. 10 sleep onsets followed by stable breathing, 10 sleep onsets followed by a hypopnea and 10 events followed by an apnea. In reality, it has been difficult to achieve these numbers because some patients never experienced stable breathing following sleep onset while others didn't have any obstructive events. Nevertheless, I did the best I could with these numbers.
For the mixed model
analysis, these are the variables I have:
1) Subject 2) TrialType (stable breathing, hypopnea, apnea) 3) Trial # (i.e. replicate measures within each subject) 4) Breath # (three post sleep onset breaths) 5) Change in lung volume (compared to baseline)
Now, in regards to point three, there are two ways which I can deal with this, but I am unsure how to go about it.
Please see Stats1.jpg for first way I have entered the data into SPSS. This example shows that I have put in all trial data (in reality there are more than two).
So in this example: 1) Data from one subject 2) Data from two trial types i.e. stable breathing and hypopnea 3) Two replicate trials for each of the two trial types (can be up to ten trials but I only put in two for this purpose) 4) Change in lung volume for each post sleep onset breath for each trial number
Now the Stats2.jpg file shows that I have now
averaged all trials for each of the two event types.
If I put in all trials, I get a significant p value for trial type and breath number. However, if I average all trials first, there are no significant differences for anything. So the question is, do I first need to average all trials for each condition before I do a mixed model analysis OR can I put in every trial for each trial type? We generally do average trials first but we aren't quite sure whether this is essential.
This is sekaran, I was very much interested in joining six sigma Green belt(GB) & also black belt(BB).... Can any one suggest any insitutions for GB or BB certifications in chennai... Apart from e-learning(online) is there any insitutions that provide regular classes, If so please inform me....
Hi there,
This is my first post. I was just wondering if someone could provide
an answer to my problem. This next bit may sound long winded but
hopefully it all makes sense.
I have been looking at lung volume changes at sleep onset in obese
male obstructive sleep apnea (OSA) patients and age-matched, healthy-
weight controls. At sleep onset, particularly in the OSA patients,
there are generally three types of events which follow sleep onset:
1) They have stable breathing i.e. no hypopneas/apneas
2) They have a hypopnea (airway partially collapses) not long after
sleep onset
3) They have an apnea (airway completely collapses) not long after
sleep onset
Therefore, I have separated out these events to see if there is any
difference in lung volume between each of these conditions. See Sleep
onset.jpg file under Daniel (mixed model) folder in Files area for a
graph showing my current results.
On the X-axis, we have breath number relative to sleep onset
(vertical line) and on the Y-axis we have change in lung volume. The
change in lung volume for each breath is compared to a baseline (the
mean of the 5 pre sleep onset breaths).
So you can see that there looks to be a greater fall in lung volume,
particularly at breath 3, when sleep onset is followed by an
obstructive event. I am in the process of looking to see if there are
any differences in these lung volume changes between event type and
breath number. I have been using mixed model analysis to see if there
are any differences. However, I just need a little help with the
stats.
For each patient, I have attempted to find 10 sleep onset events for
each condition i.e. 10 sleep onsets followed by stable breathing, 10
sleep onsets followed by a hypopnea and 10 events followed by an
apnea. In reality, it has been difficult to achieve these numbers
because some patients never experienced stable breathing following
sleep onset while others didn't have any obstructive events.
Nevertheless, I did the best I could with these numbers.
For the mixed model analysis, these are the variables I have:
1) Subject
2) TrialType (stable breathing, hypopnea, apnea)
3) Trial # (i.e. replicate measures within each subject)
4) Breath # (three post sleep onset breaths)
5) Change in lung volume (compared to baseline)
Now, in regards to point three, there are two ways which I can deal
with this, but I am unsure how to go about it.
Please see Stats1.jpg for first way I have entered the data into
SPSS. This example shows that I have put in all trial data (in
reality there are more than two).
So in this example:
1) Data from one subject
2) Data from two trial types i.e. stable breathing and hypopnea
3) Two replicate trials for each of the two trial types (can be
up to ten trials but I only put in two for this purpose)
4) Change in lung volume for each post sleep onset breath for
each trial number
Now the Stats2.jpg file shows that I have now averaged all trials for
each of the two event types.
If I put in all trials, I get a significant p value for trial type
and breath number. However, if I average all trials first, there are
no significant differences for anything. So the question is, do I
first need to average all trials for each condition before I do a
mixed model analysis OR can I put in every trial for each trial type?
We generally do average trials first but we aren't quite sure whether
this is essential.
Thanks
Respected sir, This is venkateswara rao from hyderabad. Sir here i am attaching my resume along with this message. Sir i already make some conversation with you by phone one day ago. Sir i did my post graduation in statistics from banaras hindu university. Sir, i am coming to bangolore with in next two to 3 days, my request to you is please send me the details about the consultencies which recruites the sas analysts or statistical analysts. Thanking You sir
--- sarwat_bqau <sarwat_bqau@...> wrote:
> Can some body explain me what do you mean by semi
> log sigmoidal shape
> graph. I shall be very thankful to you.
> I am completely new to the statistics and graph.
>
>
Get the freedom to save as many mails as you wish. To know how, go to
http://help.yahoo.com/l/in/yahoo/mail/yahoomail/tools/tools-08.html
Prerequisite Learning Modules: Basic Graphing, Linear Relations
This module consists of a written script, supplemental graphs and a posttest (obtained in the SLC).
The objectives of this module are to:
1) Present semi-logarithmic paper as a means of constructing semi-logarithmic plots of data.
2) Discuss some background information on logarithms to aid in understanding the construction of semi-logarithmic paper.
3) Discuss some of the aspects of interpreting linear semi-logarithmic graphs and to point out at the same time some of the advantages and disadvantages of using this method of constructing semi-logarithmic plots.
At the end of this module you should be able to:
1) choose the type of semi-log paper appropriate to a set of data,
2) construct a semi-log plot of the data, and
3) for linear plots, be able to determine the equation for the line.
Directions
This learning module consists of a written script and examples of graphs that help to illustrate the points covered in the text. Be sure you understand the examples provided in the module before proceeding further. At some point you will be asked to work examples for yourself. Complete these and make sure you understand them before continuing. At the end of the module obtain a posttest from the assistant in the Science Learning Center and the graphing materials you need. When you have completed the posttest, return all materials and be sure to have the posttest checked and recorded. If you make a mistake on the posttest, you may retake the posttest until you have completed it satisfactorily. In some of the exercises and on the posttest you may need to find the log of a number; feel free to use your calculator to make this conversion. If you do not have a calculator that takes logs, the assistant in the Science Learning Center will provide you with one.
Introduction
In the process of constructing graphs of sets of data, the appropriate type of graph paper must be selected. The most common type of paper used is shown below. This type of paper is referred to as quadrille ruled paper. This means that the spacing between one line and the next is repeated exactly in both the horizontal and vertical directions.
In these examples, note that the size of the squares is different for each of the types of paper shown. (The dimensions of the squares are shown on each type.) The size of the squares is determined by the spacing between the lines.
Semi-Logarithmic Grids
In certain cases the quadrille ruled grid may not be satisfactory. This can be due to:
1) the nature of the data (e.g. data covering a very wide range),
2) the need to construct a plot for statistical purposes, or
3) the need to transform a complex function into a linear one.
In instances as those cited above, it is often necessary to construct a semi-logarithmic plot of the data. An example of using semi-logarithmic paper to transform a nonlinear data relation into a linear one is shown below in Figures 1 and 2.
Data Table 1: Concentration of X as a function of reaction time
Concentration of X (M)
Time (sec)
0.1000
0
0.0707
50
0.0500
100
0.0250
200
0.0125
300
Figure 1 and Data Table 1 include a set of data and a graph of that data. Note that this graph does not result in a straight line. It is possible to convert this relation into a linear one by constructing a semi-logarithmic (semi-log) plot of this data using semi-log paper.
The graph above, Figure 2, has the same set of data as shown in Data Table 1, but note that is has been graphed using semi-log paper rather than quadrille ruled paper. Note that the relation now results in a straight line. (See Transformations of Exponential Equations into Linear Equations Learning Module for the mathematical justification of this process of using logs to convert exponential relations to a linear form.).
Thus for a variety of reasons as stated above it may sometimes be necessary to use semi-log paper to graph data. To understand the use and construction of this type of paper, let us begin by examining the ruling on the paper and the nature of logarithms.
On Figure 2 above note the two scales
. The horizontal scale has equal spacing between the lines (i.e., it is the quadrille ruled scale). The vertical scale, however, does not have equal spacing between lines for either the major or minor divisions. Instead, the lines have been ruled such that the spacing between the lines is proportion to the difference of the logarithms of the numbers that are placed along this axis.
It should be noted that we will be using common (base 10 or Briggian) logarithms since our number scale is based on multiples of 10. Natural (Naperian) logarithms can easily be converted to common logs so the principles here can be applies to either type of logarithm. An example may serve to clarify the nature of this scaling.
Consider the table and scale shown below, both of which show the numbers from 1 to 10 along with their corresponding logarithms (logs). In the first column of the table the difference between each number is equal, namely 1. Therefore, if we wished to graph these numbers we would choose a grid with equal spacing between the lines (a quadrille ruled scale). If, on the other hand, we wished to graph the logs of these numbers (without actually looking up the numerical values of the logs as was done to construct the table ) we would have to choose a scale on which the spacing between the lines was equal to the difference between the logs of the numbers to be graphed.
This is illustrated by the scale shown above. Note that when we space the numbers from 1 to 10 according to their logarithms the numbers are no longer equally spaced. Instead, the spacing between numbers is relatively large for the smaller numbers (1, 2, 3…) and becomes closer together for the larger numbers as we approach 10 at the top of the column. Note in the table that, if we look at the difference between logarithms, the same pattern of spacing occurs. Therefore, if one of the axes on is ruled in the same manner as the scale, the axis would then be termed logarithmic and we could use it to graph the logs of numbers.
To further understand the log scaling on semi-log paper, examine an actual semi-log grid.
Compare the spacing sequence of lines along the vertical axis on this piece of semi-log paper with the scale that was given before. The spacing sequence follows the same pattern. As an example, note that on the table above the log of 2 is 0.301 which is a little less that one-third the total difference between the log of 1 (0) and the log of 10 (1). Therefore, the second line of the grid, rather than coming about two-tenths the total distance between 1 and 10 as on the quadrille ruled paper, comes about a third the distance between the first and the tenth lines. The same rationale could be used to justify the placement of the other lines on the log grid. Note that as the numbers in the table approach ten, the logs get closer together, and so does the spacing of the lines on the log scale. Using a log scale on a grid allows you to utilize the logs of numbers without looking up the actual log values. It does not provide you with the numerical value of the number's log. You must calculate that if it is needed, as was done to construct the table above.
The type of semi-log paper shown above is termed one-cycle since it can be used only to graph numbers which vary from one another within one order of magnitude (or 101)
. A cycle begins with the lines spaced very far apart.
Data Table: Table of number and log value for the graphs A, B and C below.
GRAPH A
GRAPH B
GRAPH C
Number
Log
Number
Log
Number
Log
1.00
0.0000
10.0
1.0000
100
2.0000
2.00
0.3010
20.0
1.3010
200
2.3010
3.00
0.4771
30.0
1.4771
300
2.4771
4.00
0.6021
40.0
1.6021
400
2.6021
5.00
0.6990
50.0
1.6990
500
2.6990
6.00
0.7782
60.0
1.7782
600
2.7782
7.00
0.8451
70.0
1.8451
700
2.8451
8.00
0.9031
80.0
1.9031
800
2.9031
9.00
0.9542
90.0
1.9542
900
2.9542
10.00
1.0000
100.0
2.0000
1000
3.0000
Several vertical log scales are shown above. On the scale labeled A, the log scale has been used to cover the order of magnitude from 100 (or 1.00) to 101 (or 10.00). Note how the numbers have been written along the axis. This type of one-cycle scale could just as easily be used to cover any order of magnitude. On the scale labeled B it has been used to cover the order of magnitude from 101 (or 10.0) to 102 (100.0). On the scale labeled C it has been used to cover the order of magnitude from 102 (or 100) to 103 (or 1000). Note, again, the numbers showing the order of magnitude are written along the axis.
Note below each of the scales the numbers appearing on the axes are shown in tabular form along with the actual logarithms of each number.
This has been done to:
1) point out that the spacing does not depend on the order of magnitude of the number used, and
2) illustrate the fact that the decimal portion of the log does not vary for numbers that differ only by orders of magnitude.
Compare the decimal portion of the log of 20 with the decimal portion of the log of 200. Both have a decimal portion of '.3010'. Another example may help to clarify this.
Log 20
=
1
.310
characteristic
mantissa
Above the two portions that make up the logarithm of 20 are labeled. The characteristic is the integer portion of the log and is determined by the order of magnitude. The mantissa is the decimal portion of the log and is determined by the nature of the number, e.g. the mantissa of 20 and 30 are not the same. Stop a moment and consider the logs of 2.00, 20.0 and 200 to see that the mantissas are the same:
Log 2.00 =
0.3010
Log 20.0 =
1.3010
Log 200 =
2.3010
ALL MANTISSAS ARE THE SAME
The characteristic for each of these numbers is different and depends on their order of magnitude. Since it is the mantissa that determines the spacing between the lines, the log scale can be used regardless of the order of magnitude of the numbers being graphed.
In all the examples thus far, relatively large numbers (greater than 1) have been used. These same principles can be applied to relatively small numbers (less than 1).
On the graph paper above, the log scale has been used to cover the order of magnitude from 0.001 (or 10-3) to 0.100 (or 10-2). Since scientific work often deals with relatively large and small numbers this type of paper often proves to be quite useful.
If a set of data values ranged from 2.39 to 970 more than one order of magnitude is covered by the data and more than one cycle semi-log paper would be required. In this example, since three orders of magnitude (100 to 103) are involved, paper with at least three cycles would be needed.
The scale on the left side shows an example of the log axis of three cycle semi-log paper. Note that the line spacing sequence repeats itself three times. The middle scale is an example of five cycle semi-log paper and the scale on the right side shows two cycle paper. These would be applicable to graphing data that covers five and two orders of magnitude respectively. Therefore, the type of semi-log paper you choose depends on the range of the data to be placed on the log scale.
Problem Set 1:
DATA SET A:
DATA SET B:
Concentration HA (M)*
pH
Concentration (M)*
Time (min)
1.00
2.4
1.00
0.0
0.100
2.9
0.80
1.0
0.0100
3.4
0.63
2.0
0.00100
3.8
0.50
3.0
0.40
4.0
0.32
5.0
* Denotes data for the logarithmic scale
Two sets of data are given above. For each (a) determine the type of semi-log paper that would be required for each and (b) determine how you would scale the log axis on the paper. When you have completed this check your answers at the end of the learning module. Be sure you understand the answers before continuing.
Plotting Semi-Logarithmic Graphs
The first step in plotting any graph, once the appropriate paper has been chosen, is to scale each of the axes so that the range of each set of data values to be graphed is encompassed by the scales used.
Scaling the axes on the semi-log paper is exactly the same as what you are used to doing for the horizontal quadrille ruled scale. Scaling the log axis is almost as easy, maybe more so, since part of the numbers that will be used are already printed on the log axis.
Note on the grids of graph paper above (5, 3 and 2 cycle paper representations) that the numbers from '1' to '10' run along the vertical axis for each cycle, repeating with each of the next cycles. Each cycle ends with the '1' that begins the next cycle. On the scales on each of these cycles the appropriate number of zeroes must be placed to encompass the data to be graphed. On grids such as these that contain more than one cycle, often the "1's" that come further up on the paper are followed by increasing numbers of zeros. The reason for this should become evident as we actually scale one of the axes if it is not already evident.
Data Table: Relationship Between Median Survival Time and Temperature for Brook Trout Acclimated at 15 ° C.
MST
Median Survival Time
(min)
T
Temperature
(° C)
28
28.5
47
28.0
85
27.5
150
27.0
250
26.5
440
26.0
800
25.5
Above is a set of data that will be plotted (in this case to attain a straight line) on a semi-log grid. The values of the median survival time will be placed on the log (vertical) axis and the temperature values will be placed on the linear (horizontal) axis.
Since the median survival time values cover two orders of magnitude (from 101 to 103) at least two-cycle paper is required. Above a piece of two-cycle paper is shown. Since all the data values come between 10 (101) and 1000 (103), we begin by scaling the log scale at the bottom by making the first line correspond to 10. This is shown on the vertical scale. The second line (or major divisions) then corresponds to 20 (done by adding a 0 to the '2' already there), the third line (major division then represents 30 and so on until we reach a printed '1' again. The first cycle ends with 100 and the second cycle begins. The '2' of the second cycle then represents 200 and we place zeros on the paper accordingly. The third major division is 300 and so on to the top of the paper where the last '1' becomes 1000. All these numbers have been placed on the axis above. Be sure you understand their placement before proceeding.
The next step in plotting the graph is actually to begin to plot the data points on the grid.
With semi-log paper this is done just as on quadrille ruled paper, the only difference is that by using the log scale we are automatically plotting the logs rather than the numbers we use to locate the points.
The mechanics of the plotting are basically the same. One must use some care, however, on the log scale since the value of the minor divisions does change as one moves up a cycle. Note on the figure above that between '10' and '20' each of the minor divisions is worth '0.5' whereas between '90' and '100' each is worth '1'. Until you are familiar with the log scale and locating the points along this scale be sure to do this carefully in order to avoid any error in locating a point.
The graph below shows the first three data points plotted. For purposes of illustration the coordinates are shown by each point. Examine the placement of each data point and be sure to understand its location.
In the figure below the rest of the data points are placed on the grid (examine the last four and check their placement). The graph has been completed by drawing the line of best fit, labeling the axes, and giving the graph a title. Note that in the title the fact that logs have been used for the survival time data is indicated along with the means for doing this, i.e. "Semi-Logarithmic Plot…". The y-axis has been labeled "MST" not "Log of MST" since the numerical values displayed along the axis are survival times and not log values.
Since it is impossible to take the log of a physical quantity (mass, volume, etc.) when we deal with the log of the numbers that measure these quantities, we can treat only the numerical value and not the unit of measure. Therefore values of logarithms will not be dimensioned with units, for example, if A = 2.0000 g then log A = 0.3010 (unitless). Keep this in mind when actually working with log values.
Interpreting Linear Semi-Logarithmic Plots
Although we will be limiting the following discussion to linear semi-log plots, many of the general ideas presented in the following section can be applied to nonlinear plots as well.
Plotting appropriate sets of data on semi-log paper has the distinct advantage that one does not have to look up logs to work with logarithmic functions. One does need to have the right kind of semi-log paper, however. With this method, if you need to determine the slope or the y-intercept of the line, you do not need to look up logs. This fact should be kept in mind when calculating the slope and the y-intercept of a semi-log plot in the process of deriving the equation for the line.
Below is the semi-log plot that was used earlier in the module. Since the semi-log plot yields a straight line, we can derive the equation for the line by simply calculating the slope and the y-intercept. Since the time axis begins at zero, we can easily determine the y-intercept from the graph. Remember that the y-intercept is the point where the line crosses the y-axis provided that the x-axis begins at zero. Such is the case here. The one caution one must observe is that a straight line was obtained using the log scale so that when we determine the y-intercept it is the log of y (or here concentration) and not the simple concentration value that appears along the axis.
Note here that the line crosses the y-axis (or concentration axis) at 0.1000. The y-intercept is, therefore the log of 0.1000 or -1.000 since this was read off the log ruled axis. IT MUST BE CONVERTED TO A LOGARITHM. The y-intercept is shown on the graph above.
The next step is to calculate the numerical value for the slope of the line. The general definition for the slope is:
Slope = D Y/D X
The exact definition of the slope as applies to this graph is:
Slope = D log C/D t
Note that the D Y term is equal to D log C and not D C. Since these values are again read off the log axis we must use logs, i.e., convert the values read off the log axis to logarithms. On the graph the points used to calculate the slope are shown. The slope calculations are as follows:
POINTS USED IN CALCULATIONS:
C2 = 0.0600 M
C1 = 0.0200 M
Log C2 = -1.2218
Log C1 = -1.6990
t2 = 75 sec
t1 = 233 sec
Slope = (-1.2218 - (-1.6690))/(75 sec - 233 sec)
Slope = -0.00302 sec-1
Note that if the concentration values had not been converted to log values the slope would not have the same numerical value
. On this type of graph if the slope is not calculated correctly any value derived from this value will also be in error. Therefore, one must use some thought with this type of grid and the calculated values derived from it.
To complete the equation for the line we need now only substitute the slope and y-intercept into the general equation for a straight line and replace the general y and x terms with the specific dependent and independent variables used in the experiment. This process is shown below:
SINCE:
Y = log C
X = t
Y-INTERCEPT = -1.0000
SLOPE = -0.00302 sec-1
THEN:
Y
=
M
X
+
B
log C
=
-0.00302 sec-1
t
+
-1.0000
OR
Log C =
-0.00302 sec-1t - 1.0000
We now have a quantitative expression that relates concentration and time. Note that the y-term or dependent variable is the log C, not C, for the same reasons used earlier in the calculation of the y-intercept and the slope.
While there are disadvantages, the use of semi-log paper has an added advantage in the processes of extrapolation and interpolation. For example, suppose one needed to know the concentration at 150 seconds. We could use the equation defined above (and here to find the concentration value we would have to solve the equation for log C then take the antilog to find C) or we could read C directly from the graph without taking an antilog since the numbers along the y-axis are concentration values (and not logs).
Both of the methods are shown here. The graph above shows the direct method of reading off the graph.The calculations below show the method using the equation of the line:
At t = 150 sec
Log C = -0.00302 sec-1 t - 1.0000
Log C = -0.00302 sec-1 (150) - 1.0000
Log C = -0.453 - 1.0000 = -1.453
C = 0.0352 M
Both methods give the same answer but direct reading of the value in this case might be easier and faster.
One final comment should be made about interpreting semi-log plots. You may encounter cases where the graph of a set of data does NOT include the point x = 0 on the x-axis. An example of such a graph is shown below:
On the graph above the pH axis begins at 2.4 and not 0. In such an instance the value of the y-intercept cannot be directly read from the graph as was done in the previous example.
In a case like this the value of the y-intercept must be calculated from the equation for a line. That is:
If: y = mx + b
Then: b = y - mx
To calculate the y-intercept the following steps need to be carried out:
1) Calculate the slope of the line. For the graph above:
M = D log [HA]/D pH
M = (log [HA2] - LOG [HA1])/(pH2 - pH1)
[HA2] = 0.700
[HA1] = 0.0250
log [HA2] = -0.1549
LOG [HA1] = -1.6020
pH2 = 2.48
pH1 = 3.20
M = (-0.1549 - (-1.6020))/(2.48 - 3.20) = (1.4471/-0.72)
M = -2.0
2) Pick a point on the line and read off the y and x coordinates. Note the y value read from the graph must be converted to a log value but the x coordinate is used as is. Any point could be used, but for convenience you may wish to use one of the points used to calculate the slope. In the example, the first set of coordinates is used.
3) Substitute the slope value and the set of coordinates into the general equation for the line and calculate the value of b. For the example this is shown below:
IF:
Y
=
M
X
+
B
THEN:
B
=
Y
-
M
X
OR:
B
=
Log [HA]
-
M
pH
Calculation of y-intercept:
SLOPE: M = -2.0
Log of y value: log [HA] = -0.1549
X value: pH = 2.48
B = -0.1549 - (-2.0)(2.48)
B = 4.8
4) Write the completed equation
COMPLETED EQUATION: log [HA] = -2.0 pH + 4.8
This equation showing the notation between concentration of HA and pH is now complete.
The utility of such a type of graphing makes it a relatively common practice. Its disadvantages can easily be overcome as long as one understands how and why the grid is constructed as it is and uses it accordingly.
SUMMARY OF INFORMATION ON CONSTRUCTING AND USING SEMI-LOGARITHMIC PLOTS:
1) Examine the data to be plotted and determine the number of orders of magnitude covered by the data to be plotted on the logarithmic axis.
2) Select the semi-logarithmic paper with a number of cycles appropriate to the range of data to be placed on this axis.
3) construct a semi-logarithmic plot of the data following all the rules for constructing an appropriate graph. Remember in plotting the points that the value of the division on the logarithmic scale changes as one moves along this axis.
4) In labeling the logarithmic axis remember that the numbers appearing along this scale are NOT log values.
5) In titling the graph be sure to indicate that the plot is semi-logarithmic in nature.
6) For linear plots from which one will derive the equation for the line, remember:
In calculating the slope, the values read off the logarithmic scale must be converted to logs before the slope is calculated.
In determining the y-intercept, if this value is read off the log scale (when x = 0 is part of the x-axis) then this value must be converted to a log before it is substituted for the y-intercept in the general equation for a straight line.
When the point x = 0 is not included on the x-axis, one can not read the y-intercept off the y-axis. Solve for the y-intercept using the equation for a straight line: y = mx + b. First solve for m, then pick any point on the line and substitute the x-value for x and the log of the y-value for y. Then rearrange the equation and solve or b.
Once you feel you understand the points presented in this module, obtain a posttest from the assistant in the Science Learning Center. When you have completed the posttest return all graphing materials that you have been given and be sure to have the posttest checked out and recorded.
Problem Set 1 Answers:
Data Set A:
a) At least 3 cycle paper should be used since the concentration data covers the orders of magnitude from 10-3 to 100.
b) The logarithmic axis should be scaled to read from 0.00100 at the bottom to 1.00 at the top.
Data Set B:
a) One cycle paper should be used since the concentration data covers only one order of magnitude from 10-1 to 100.
b) The logarithmic axis should be scaled to read from 0.10 at the bottom to 1.00 at the top.
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Vijay Shinde 
Consider the table and scale shown below, both of which show the numbers from 1 to 10 along with their corresponding logarithms (logs). In the first column of the table the difference between each number is equal, namely 1. Therefore, if we wished to graph these numbers we would choose a grid with equal spacing between the lines (a quadrille ruled scale). If, on the other hand, we wished to graph the logs of these numbers (without actually looking up the numerical values of the logs as was done to construct the table ) we would have to choose a scale on which the spacing between the lines was equal to the difference between the logs of the numbers to be graphed.
The graph below shows the first three data points plotted. For purposes of illustration the coordinates are shown by each point. Examine the placement of each data point and be sure to understand its location.
