Types of Statistics
(a) Descriptive Statistics:
Methods of organizing, summarizing, and presenting data in an informative
way.
(b) Inferential Statistics:
A decision, estimate, prediction, or generalization about a population, based
on a sample.
A population is a collection of all possible individuals, objects, or
measurements of interest. A sample is a portion, or part, of the population
of interest
Applications in Business and Economics
A. Accounting Public accounting firms use statistical sampling procedures
when conducting audits for their clients.
B. Finance Financial advisors use a variety of statistical information,
including price-earnings ratios and dividend yields, to guide their investment
recommendations.
C. Marketing Electronic point-of-sale scanners at retail checkout counters
are being used to collect data for a variety of marketing research
applications.
D. Production A variety of statistical quality control charts are used to
monitor the output of a production process.
E. Economics Economists use statistical information in making forecasts
about the future of the economy or some aspect of it.
A. Elements, Variables, and Observations
i. The elements are the entities on which data are collected.
ii. A variable is a characteristic of interest for the elements.
iii. The set of measurements collected for a particular element is called an
observation .
iv. The total number of data values in a data set is the number of elements
multiplied by thnumber of variables. Data, Data Sets, Elements, Variables,
and bservations are shown in the following figure.
Nominal:
• Data are labels or names used to identify an attribute of the element.
• A nonnumeric label or a numeric code may be used.
• Data that is classified into categories and cannot be arranged in any
particular order. Such as students of a university are classified by the
faculty in which they are enrolled using a nonnumeric label such as
Business, Humanities, Education, and so on. Alternatively, a numeric code
could be used for the faculty variable (e.g. 1 denotes Business, 2 denote
Humanities, 3 denote Education, and so on).
Ordinal:
The data have the properties of nominal data and the order or rank of the
data is meaningful . A nonnumeric label or a numeric code may be used.
Ordinal data are usually obtained by observing, such as quality rating (high,
medium, low), clothes size group (small, medium, large)…etc.
Interval
The data have the properties of ordinal data and the interval between
observations is expressed in terms of a fixed unit of measure. Interval data
are always numeric . Such as temperature on the Fahrenheit scale.
Ratio
The ratio level is the interval levels with an inherent zero starting point.
Differences and ratios are meaningful for this level of measurement. Such as
Monthly income of a person, or distance traveled by manufacturer’s
representatives per month.
Advantages of Written Questionnaires
Questionnaires are very cost effective when compared to face-to-face
interviews. This is especially true for studies involving large sample sizes
and large geographic areas. Written questionnaires become even more cost
effective as the number of research questions increases.
Questionnaires are easy to analyze. Data entry and tabulation for nearly all
surveys can be easily done with many computer software packages.
Questionnaires are familiar to most people. Nearly everyone has had some
experience completing questionnaires and they generally do not make people
apprehensive.
Questionnaires reduce bias. There is uniform question presentation and no
middle-man bias. The researcher's own opinions will not influence the
respondent to answer questions in a certain manner. There are no verbal or
visual clues to influence the respondent.
Questionnaires are less intrusive than telephone or face-to-face surveys.
When a respondent receives a questionnaire in the mail, he is free to
complete the questionnaire on his own time-table. Unlike other research
methods, the respondent is not interrupted by the research instrument.
Disadvantages Of Written Questionnaires
One major disadvantage of written questionnaires is the possibility of low
response rates. Low response is the curse of statistical analysis. It can
dramatically lower our confidence in the results. Response rates vary widely
from one questionnaire to another (10% - 90%), however, well- designed
studies consistently produce high response rates.
Another disadvantage of questionnaires is the inability to probe responses.
Questionnaires are structured instruments. They allow little flexibility to the
respondent with respect to response format. In essence, they often lose the
"flavor of the response" (i.e., respondents often want to qualify their
answers). By allowing frequent space for comments, the researcher can
partially overcome this disadvantage. Comments are among the most helpful
of all the information on the questionnaire, and they usually provide
insightful information that would have otherwise been lost.
C omputer Assisted Research Methods
• Paper-based methods have mainly been replaced by computer-based
methods (except for postal questionnaires)
• Questionnaire is a program. Questions appear on screen and responses are
entered. Program can check responses immediately. Program displays next
appropriate question.
• Masses of acronyms!
Sampling Methods
Probability Sampling
Simple random sampling
Stratified random sampling
Systematic sampling
Cluster (area) sampling
Multistage sampling
Deliberate (quota) sampling
Convenience sampling
Purposive sampling
Equal probability
Techniques
Non-Probability Sampling
Deliberate (quota) sam
Convenience sampling
Purposive sampling
Simple Random Sampling
Equal probability
Techniques
Fishbowl (with replacement & w/o replacement)
Table of random numbers
Advantage
Most representative group
Disadvantage
Difficult to identify every member of a population
Technique
Stratified Random Sampling
Divide population into various strata
Randomly sample within each strata
Sample from each strata should be proportional
Advantage
Better in achieving representative ness on control variable
Disadvantage
Difficult to pick appropriate strata
Difficult to ID every member in population
Technique
Systematic Sampling
Use “system” to select sample (e.g., every 5th item in alphabetized list,
every 10th name in phone book)
Advantage
Quick, efficient, saves time and energy
Disadvantage
Not entirely bias free; each item does not have equal chance to be selected
System for selecting subjects may introduce systematic error
Cannot generalize beyond pop actually sampled
Cluster (Area) Sampling
Randomly select groups (cluster) – all members of groups are subjects
Appropriate when
you can’t obtain a list of the members of the population
have little knowledge of pop characteristics
Pop is scattered over large geographic area
Advantage
More practical, less costly
Conclusions should be stated in terms of cluster (sample unit – school)
Sample size is # of clusters
Stage 1
Multistage Sampling
randomly sample clusters (schools)
Stage 2
randomly sample individuals from the schools selected Deliberate (Quota)
Sampling
Similar to stratified random sampling
Technique
Quotas set using some characteristic of the population thought to be
relevant
Subjects selected non-randomly to meet quotas (usu. convenience sampling)
Disadvantage
selection bias
Cannot set quotas for all characteristics important to study
Convenience Sampling
“Take them where you find them” - nonrandom
Intact classes, volunteers, survey respondents (low return), a typical group,
a typical person
Disadvantage: Selection bias
Use post hoc analysis to show groups were equal at the start