# What undertone: beauty is in the eye of the

What

is a model? A

Model is an external and explicit representation of a part of reality, as it is

seen by individuals who wish to use this model to understand, change, manage

and control that part of reality.

“Why

are so many models designed and so few used?” is a question often

discussed within the Quantitative Modeling (QM) community. The formulation of

the question seems simple, but the concepts and theories that must be mobilized

to give it an answer are far more sophisticated. Would there be a selection

process from “many models designed” to “few models used”

and, if so, which particular properties do the “happy few” have? This

site first analyzes the various definitions of “models” presented in

the QM literature and proposes a synthesis of the functions a model can handle.

Then, the concept of “implementation” is defined, and we

progressively shift from a traditional “design then implementation”

standpoint to a more general theory of a model design/implementation, seen as a

cross-construction process between the model and the organization in which it

is implemented. Consequently, the organization is considered not as a simple

context, but as an active component in the design of models. This leads

logically to six models of model implementation: the technocratic model, the

political model, the managerial model, the self-learning model, the conquest

model and the experimental model.

Modeling for Forecasting:

Accuracy and Validation Assessments

Forecasting is a necessary input to planning,

whether in business, or government. Often, forecasts are generated subjectively

and at great cost by group discussion, even when relatively simple quantitative

methods can perform just as well or, at very least; provide an informed input

to such discussions.

Data Gathering for Verification of Model: Data gathering is often considered

“expensive”. Indeed, technology “softens” the mind, in that

we become reliant on devices; however, reliable data are needed to verify a

quantitative model. Mathematical models, no matter how elegant, sometimes

escape the appreciation of the decision-maker. In other words, some people

think algebraically; others see geometrically. When the data are complex or

multidimensional, there is the more reason for working with equations, though

appealing to the intellect has a more down-to-earth undertone: beauty is in the

eye of the other beholder – not you; yourself.

Statistical

Forecasting: The selection and implementation of the

proper forecast methodology has always been an important planning and control

issue for most firms and agencies. Often, the financial well-being of the

entire operation rely on the accuracy of the forecast since such information

will likely be used to make interrelated budgetary and operative decisions in

areas of personnel management, purchasing, marketing and advertising, capital

financing, etc. For example, any significant over-or-under sales forecast error

may cause the firm to be overly burdened with excess inventory carrying costs

or else create lost sales revenue through unanticipated item shortages. When

demand is fairly stable, e.g., unchanging or else growing or declining at a

known constant rate, making an accurate forecast is less difficult. If, on the

other hand, the firm has historically experienced an up-and-down sales pattern,

then the complexity of the forecasting task is compounded.

There are two main

approaches to forecasting. Either the estimate of future value is based on an

analysis of factors which are believed to influence future values, i.e., the

explanatory method, or else the prediction is based on an inferred study of

past general data behavior over time, i.e., the extrapolation method. For example,

the belief that the sale of doll clothing will increase from current levels

because of a recent advertising blitz rather than proximity to Christmas

illustrates the difference between the two philosophies. It is possible that

both approaches will lead to the creation of accurate and useful forecasts, but

it must be remembered that, even for a modest degree of desired accuracy, the

former method is often more difficult to implement and validate than the latter

approach.

Step

4: Selecting a Sample of Respondents

Identify the

accessible population.

Avoid using samples of convenience.

Simple random sampling is a desirable method of sampling.

Systematic sampling is an acceptable method of sampling.

Stratification may reduce sampling errors.

Consider using random cluster sampling when every member of a population

belongs to a group.

Consider using multistage sampling to select respondents from large

populations.

Consider the importance of getting precise results when determining sample

size.

Remember that using a large sample does not compensate for a bias in sampling.

Consider sampling non respondents to get information on the nature of a bias.

The bias in the mean is the difference of the population means for respondents

and non respondents multiplied by the population nonresponse rate.

General Sampling Techniques

From

the food you eat to the TV you watch, from political elections to school board

actions, much of your life is regulated by the results of sample surveys. In

the information age of today and tomorrow, it is increasingly important that

sample survey design and analysis be understood by many so as to produce good

data for decision making and to recognize questionable data when it arises.

Relevant topics are: Simple Random Sampling, Stratified Random Sampling,

Cluster Sampling, Systematic Sampling, Ratio and Regression Estimation,

Estimating a Population Size, Sampling a Continuum of Time, Area or Volume,

Questionnaire Design, Errors in Surveys.

A

sample is a group of units selected from a larger group (the population). By

studying the sample it is hoped to draw valid conclusions about the larger

group.

A

sample is generally selected for study because the population is too large to

study in its entirety. The sample should be representative of the general

population. This is often best achieved by random sampling. Also, before

collecting the sample, it is important that the researcher carefully and

completely defines the population, including a description of the members to be

included.

Random Sampling: Random sampling of size n from a population size N. Unbiased

estimate for variance of is

Var()

= S2(1-n/N)/n, where n/N is the sampling fraction. For sampling

fraction less than 10% the finite population correction factor (N-n)/(N-1) is

almost 1.

The

total T is estimated by N. ,

its variance is N2Var().

For

0, 1, (binary) type variables, variation in estimated proportion p is:

S2 = p.(1-p).(1-n/N)/(n-1).

For

ratio r = Sxi/Syi= / ,

the variation for r is

(N-n)(r2S2x + S2y -2

r Cov(x, y)/n(N-1).2.

Stratified Sampling: Stratified sampling can be used whenever the population can

be partitioned into smaller sub-populations, each of, which is homogeneous

according to the particular characteristic of interest.

s = S Wt.

Bxart, over t=1, 2, ..L (strata), and t is SXit/nt.

Its

variance is:

SW2t /(Nt-nt)S2t/nt(Nt-1)

Population

total T is estimated by N. s,

its variance is

SN2t(Nt-nt)S2t/nt(Nt-1).

Since

the survey usually measures several attributes for each population member, it

is impossible to find an allocation that is simultaneously optimal for each of

those variables. Therefore, in such a case we use the popular method of

allocation which use the same sampling fraction in each stratum. This yield

optimal allocation given the variation of the strata are all the same.

Determination

of sample sizes (n) with regard to binary data: Smallest integer greater than

or equal to:

t2 N

p(1-p) / t2 p(1-p) + a2 (N-1)

with

N being the size of the total number of cases, n being the sample size, a the expected error, t being the value

taken from the t distribution corresponding to a certain confidence interval,

and p being the probability of an event.

Cross-Sectional Sampling: Cross-Sectional Study the observation of a defined

population at a single point in time or time interval. Exposure and outcome are

determined simultaneously.

Quota

Sampling: Quota sampling is

availability sampling, but with the constraint that proportionality by strata

be preserved. Thus the interviewer will be told to interview so many white male

smokers, so many black female nonsmokers, and so on, to improve the

representatives of the sample. Maximum variation sampling is a variant of quota

sampling, in which the researcher purposively and non-randomly tries to select

a set of cases, which exhibit maximal differences on variables of interest.

Further variations include extreme or deviant case sampling or typical case

sampling.

What is a statistical instrument? A statistical instrument is any process

that aim at describing a phenomena by using any instrument or device, however

the results may be used as a control tool. Examples of statistical instruments

are questionnaire and surveys sampling.

What is grab sampling technique? The grab sampling technique is to take a

relatively small sample over a very short period of time, the result obtained

are usually instantaneous. However, the Passive Sampling is a

technique where a sampling device is used for an extended time under similar

conditions. Depending on the desirable statistical investigation, the Passive

Sampling may be a useful alternative or even more appropriate than grab

sampling. However, a passive sampling technique needs to be developed and

tested in the field.

Sample Size Determination

The

question of how large a sample to take arises early in the planning of any

survey. This is an important question that should be treated lightly. To take a

large sample than is needed to achieve the desired results is wasteful of

resources whereas very small samples often lead to that are no practical use of

making good decision. The main objective is to obtain both a desirable accuracy

and a desirable confidence level with minimum cost.

Pilot

Sample: A pilot or

preliminary sample must be drawn from the population and the statistics

computed from this sample are used in determination of the sample size.

Observations used in the pilot sample may be counted as part of the final

sample, so that the computed sample size minus the pilot sample size is the

number of observations needed to satisfy the total sample size requirement.