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Summary Statistics for Pre-MSc (EBS027A05)

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Summary of the book: Anderson, Sweeney, Williams, Camm, Cochran, Freeman, and Shoesmith (2020),Statistics for Business & Economics; Fifth Edition for the course Statistics for Pre-MSc. Chapters 1-5, 7, 8, 9.

Voorbeeld 4 van de 43  pagina's

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  • Hoofdstuk 1 t/m 5, 7, 8, 9
  • 13 september 2024
  • 43
  • 2023/2024
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Voorbeeld van de inhoud

Sta$s$cs for business and economics
Chapter 1 – Data and Sta/s/cs
§1.2 Data
Sta$s$cs is the art and science of collec$ng, analyzing, presen$ng and interpre$ng data.

Data are the facts and figures collected, analyzed and summarized for presenta$on and
interpreta$on. All the data collected in a par$cular study are referred to as the data set for
the study.

Elements, variables and observa$ons
Elements are the en$$es on which data are collected. A variable is a characteris$c of interest
for the elements. Measurements collected on each variable for every element in a study
provide the data. The set of measurements obtained for a par$cular element is called an
observa/on.

Scales of measurement
Data collec$on requires one of the following scales of measurement: nominal, ordinal,
interval or ra$o. The scale of measurement determines the amount of informa$on contained
in the data and indicates the most appropriate data summariza$on and sta$s$cal analyses.

When the data of a variable consist of labels or names used to iden$fy an aEribute of the
element, the scale of measurement is considered a nominal scale.
The scale of measurement for a variable is called an ordinal scale if the data exhibit the
proper$es of nominal data and the order or rand of the data is meaningful.
The scale of measurement for a variable becomes an interval scale if the data show the
proper$es of ordinal data and the interval between values is expressed in terms of a fixed
unit of measure. Interval data are always numeric.
The scale of measurement for a variable is a ra/o scale if the data have all the proper$es of
interval data and the ra$o of two values is meaningful. Variables such as distance, height,
weight and $me use the ra$o scale of measurement.

Categorical and quan4ta4ve data
Data can be further classified as either categorical or quan$ta$ve. Categorical data include
labels or names used to iden$fy an aEribute of each element. Categorical data use either the
nominal or ordinal scale of measurement and may be non-numeric or numeric.

Quan$ta$ve data require numeric values that indicate how much or how many. Quan$ta$ve
data are obtained using either the interval or ra$o scale of measurement.

A categorical variable is a variable with categorical data, and a quan$ta$ve variable is a
variable with quan$ta$ve data. The sta$s$cal analysis appropriate for a par$cular variable
depends upon whether the variable is categorical or quan$ta$ve. If the variable is
categorical, the sta$s$cal analysis is rather limited.

,Cross-sec4onal and 4me series data
For purposes of sta$s$cal analysis, dis$nguishing between cross-sec$onal data and $me
series data is important. Cross-sec/onal data are data collected at the same or approximately
the same point in $me.
Time series data are data collected over several $me periods. Quan$ta$ve data that measure
how many are discrete. Quan$ta$ve data that measure how much are con$nuous because
no separa$on occurs between the possible data values.

§1.3 Data sources
Data can be obtained from exis$ng sources or from surveys and experimental studies
designed to collect new data.

Exis$ng sources – in some cases, data needed for a par$cular applica$on already exist.
Companies maintain a variety of databases about their employees, customers and business
opera$ons.

Sta1s1cal studies
Some$mes the data needed for a par$cular applica$on are not available through exis$ng
sources. In such cases, the data can oNen be obtained by conduc$ng a sta$s$cal study.
Sta$s$cal studies can be classified as either experimental or observa$onal.

In an experimental study, a variable of interest is first iden$fied. The one or more other
variables are iden$fied and controlled so that data can be obtained about how they influence
the variable of interest.

Example: a pharmaceu.cal firm might be interested in conduc.ng an experiment to learn about how
a new drug affects blood pressure. Blood pressure is the variable of interest in the study. The dosage
level of the new drug is another variable that is hoped to have a causal effect on blood pressure. To
obtain data about the effect of the new drug, researchers select a sample of individuals. The dosage
level of the new drug is controlled, as different groups of individuals are given different dosage levels.
Sta.s.cal analysis of the experimental data can help determine how the new drug affects blood
pressure.

Observa/onal or non-experimental sta$s$cal studies make no aEempt to control the
variables of interest. A survey is perhaps the most common type of observa$onal study. For
instance, in a personal interview survey, research ques$ons are first iden$fied. Then a
ques$onnaire is designed and administered to a sample of individuals.

§1.4 Descrip1ve sta1s1cs
Summaries of data, which may be tabular, graphical or numerical, are referred to as
descrip$ve sta$s$cs. Methods of descrip$ve sta$s$cs can be used to provide summaries of
the informa$on in this data set.

In addi$on to tabular and graphical display, numerical descrip$ve sta$s$cs are used to
summarize data. The most common numerical descrip$ve sta$s$c is the average, or mean.

,§1.5 Sta1s1cal inference
Many situa$ons require data for a large group of elements. Because of $me, cost and other
considera$ons, data can be collected from only a small por$on of the group. The larger
group of elements in a par$cular study is called the popula$on, and the smaller group is
called the sample.

A popula/on is the set of all elements of interest in a par$cular study. A sample is a subset of
the popula$on.

The process of conduc$ng a survey to collect data for the en$re popula$on is called a census.
The process of conduc$ng a survey to collect data for a sample is called a sample survey. As
one of its major contribu$ons, sta$s$cs uses data from a sample to make es$mates and test
hypotheses about the characteris$cs of a popula$on through a process referred to as
sta/s/cal inference.

§1.6 Analy1cs
Analy/cs is the scien$fic process of transforming data into insight for making beEer
decisions. Analy$cs is used for data-driven or fact-based decision making, which is oNen seen
as more objec$ve than alterna$ve approaches to decision making.

Analy$cs can involve a variety of techniques from simple reports to the most advanced
op$miza$on techniques. Analy$cs is now generally thought to comprise three broad
categories of techniques:
- Descrip/ve analy/cs encompasses the set of analy$cal techniques that describe what
has happened in the past. Examples of these types of techniques are data queries,
reports, descrip$ve sta$s$cs, data visualiza$on, data dashboard and what-if
spreadsheets.
- Predic/ve analy/cs consists of analy$cal techniques that use models constructed
from past data to predict the future or to assess the impact of one variable on
another. For example, past data on sales of a product may be used to construct a
mathema$cal model that predicts future sales.
- Prescrip/ve analy/cs is the set of analy$cal techniques that yield a best course of
ac$on. Op$miza$on models, which generate solu$ons that maximize or minimize
some objec$ve subject to a set of constraints, fall into the category of prescrip$ve
models.

Prescrip$ve analy$cs differs greatly from descrip$ve or predic$ve analy$cs. What
dis$nguishes prescrip$ve analy$cs is that prescrip$ve models yield a best course of ac$on to
take. That is, the output of a prescrip$ve model is a best decision.

§1.7 Big data
Larger and more complex data sets are now oNen referred to as big data. Although there
does not seem to be a universally accepted defini$on of big data, many think of it as a set of
data that cannot be managed, processed or analyzed with commonly available soNware in a
reasonable amount of $me.

, Many data analysts define big data by referring to the three v’s of data: volume, velocity and
variety.

Volume refers to the amount of available data; velocity refers to the speed at which data are
collected and processed; and variety refers to the different data types.

Data warehousing – term to refer to the process of capturing, storing and maintaining the
data.

The subject of data mining deals with methods for developing useful decision-making
informa$on from large databases. Using a combina$on of procedures from sta$s$cs,
mathema$cs and computer science, analysts ‘mine the data’ in the warehouse to convert it
into useful informa$on.

Data mining is a technology that relies heavily on sta$s$cal methodology such as mul$ple
regression, logis$c regression and correla$on. But it takes a crea$ve integra$on of all these
methods and computer science technologies involving ar$ficial intelligence and machine
learning to make data mining effec$ve.

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