Business Statistics CONTENTS The role of data The data matrix - - PowerPoint PPT Presentation

DATA

Business Statistics

The role of data The data matrix Data types Aspects of data Obtaining data Further study CONTENTS

Data refers to observed facts

▪ “there are 82 persons in this train” ▪ “the weight of this pizza is 283 gram” ▪ “this museum hosts paintings by Picasso”

Data helps

▪ to suggest theories (“pizzas with a high price are less popular”) ▪ to test hypotheses (“advertising increase sales”) ▪ to calibrate coefficients of theories (“𝑟 = 𝑏 − 𝑐𝑞, but what are 𝑏 and 𝑐?”)

THE ROLE OF DATA

Columns: variables (may have identifying name like “age”) Rows: subjects/cases (may have identifying name like “John”) Cells: observations Entire table: data matrix THE DATA MATRIX

Observation Subject/Case Variable

THE DATA MATRIX

Variable name Variable unit Numerical data Nominal data Ordinal data Binary data Missing

• bservation

Subject name

Information to extract from a data matrix ▪ One variable

▪ mean age at inauguration ▪ odds of republicans vs. democrats ▪ univariate analysis

▪ Two variables

▪ association between handedness and party ▪ correlation between age and number of terms ▪ bivariate analysis

▪ Many variables

▪ predict terms as a function of height and handednes ▪ multivariate analysis

THE DATA MATRIX

The data matrix can represent: ▪ all data (the population)

▪ a list of all US presidents

▪ a non-random selection of data

▪ a list of all US presidents since 1969

▪ a random selection of data (a sample)

▪ a subset of randomly picked presidents from the full list

▪ descriptive statistics is applicable to all three cases ▪ inferential statistics focuses on how to draw conclusions for a population on the basis of information on a random sample THE DATA MATRIX

You find data on the body size of 5 men and 5 women Organize these data in a data matrix EXERCISE 1

▪ Type of data

▪ categorical, numerical

▪ Countability

▪ discrete, continuous

▪ Range

▪ restricted, infinite, semi-infinite

▪ Coded

▪ numbers for text

▪ Recoded

▪ text for ranges of numbers (or ranges of texts)

ASPECTS OF DATA

Type of data ▪ categorical

▪ e.g., dog, cat, horse

▪ numerical (cardinal)

▪ e.g., 12, 45.29

Has consequences for:

▪ transformations (income per capita vs. car type per capita) ▪ statistical summaries (average income vs. average car type)

Special cases

▪ Likert scale (5 or 7-point scale: “strongly agree”, “somewhat agree”, etc.) ▪ binary variable (0/1, yes/no, Dutch/foreign)

ASPECTS OF DATA

Countability ▪ discrete

▪ e.g., eggs

▪ (semi-)continuous

▪ e.g., waiting time

Has consequences for:

▪ recoding (“binning”) ▪ statistical summaries (modal income vs. median income)

ASPECTS OF DATA

Range ▪ (semi-)infinite

▪ e.g., income

▪ restricted

▪ e.g., percentage of satisfied customers

Has consequences for:

▪ dealing with outliers (exceptional data points)

ASPECTS OF DATA

Coding ▪ replacing nominal categories by numbers

▪ e.g., Ford=1, Audi=2, Volkswagen=3, Opel=4

▪ replacing ordinal categories by numbers

▪ e.g., tiny=1, small=2, normal=3, big=4, huge=5

Has consequences for:

▪ preventing recording mistakes (e.g., Vlokswgaen) ▪ preparing for statistical calculations (SPSS, Stata, R, etc)

ASPECTS OF DATA

Recoding ▪ grouping categorical data

▪ e.g., “Volkswagen”+“Audi”+“Opel”=“German car”

▪ grouping numerical data

▪ e.g., 𝑦 ∈ 20.000,25.000 =“middle income”

Has consequences for:

▪ statistical summaries (histograms, modal values)

ASPECTS OF DATA

Coding of categories into numbers ASPECTS OF DATA

Coding of categories into several binary variables ▪ using dummy variables (or dummies for short) ▪ 𝑜dummies = 𝑜categories (redundant!) ▪ 𝑜dummies = 𝑜categories − 1 (with omitted category) ASPECTS OF DATA

Some pitfalls: ▪ missing data

▪ blank? 0? 99?

▪ treating coded categories or number-like categories as numbers

▪ e.g., if Volkswage=1, Audi=2, BMW=3, the average car in this street 1.92?

▪ units of data

▪ see Math course

▪ decimals

▪ see Math course

ASPECTS OF DATA

Describe the appropriate data characteristic (categorical,

• rdinal, nominal, numerical, continuous, discrete, dummy,

etc.) for

• a. body size (171, 184, etc.)
• b. pet (cat, dog, rabbit)
• c. righthandedness (0, 1)
• d. income group (low, medium, high)
• e. number of children (0, 1, 2, etc.)

EXERCISE 2

Typing

▪ from books, etc.

Downloading

▪ from online databases (like CBS) ▪ from general webpages (like Wikipedia)

OBTAINING DATA

Purchasing

▪ commercial databases

OBTAINING DATA

Generating

▪ from secondary sources ▪ combining multiple sources ▪ by primary research ▪ doing interviews ▪ doing observations ▪ doing experiments

OBTAINING DATA

Doane & Seward 5/E 2.1-2.2 Tutorial exercises week 1 data FURTHER STUDY