Basic Business Statistics Concepts and Applications 14th Ediition - MAS202 chap1

Copyright © 2020 Pearson Education Ltd. A LWAY S L E A R N I N G Slide 1

Defining and Collecting Data

Chapter 1


ObjectivesIn this chapter you learn: To understand issues that arise when defining

variables. How to define variables. To understand the different measurement scales. How to collect data. To identify different ways to collect a sample. To understand the issues involved in data

preparation. To understand the types of survey errors.


Classifying Variables By Type

Categorical (qualitative) variables take categories as their values such as “yes”, “no”, or “blue”, “brown”, “green”.

Numerical (quantitative) variables have values that represent a counted or measured quantity. Discrete variables arise from a counting process. Continuous variables arise from a measuring process.

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Examples of Types of VariablesDCOVA

Question Responses Variable Type

Do you have a Facebook profile? Yes or No Categorical

How many text messages have you sent in the past three days?

---------------Numerical(discrete)

How long did the mobile app update take to download?

---------------Numerical(continuous)


Types of VariablesDCOVA

Variables

Categorical Numerical

Discrete Continuous

Examples: Marital Status Political Party Eye Color(Defined Categories)

Examples: Number of Children Defects per hour(Counted items)

Examples: Weight Voltage(Measuredcharacteristics)

Nominal Ordinal

Examples: Ratings Good, Better,

Best Low, Med, High(Ordered Categories)


Measurement Scales

A nominal scale classifies data into distinct categories in which no ranking is implied.

Categorical Variables Categories

Do you have a Facebook profile?

Type of investment

Cellular Provider

Yes, No

AT&T, Sprint, Verizon, Other, None

Growth, Value, Other

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EX: Four different beverages are sold at a fast-food restaurant: softdrinks, tea, coffee, and bottled water.


Measurement Scales (con’t.)An ordinal scale classifies data into distinct categories in which ranking is implied.

Categorical Variable Ordered Categories

Student class designation Freshman, Sophomore, Junior, Senior

Product satisfaction Very unsatisfied, Fairly unsatisfied, Neutral, Fairly satisfied, Very satisfied

Faculty rank Professor, Associate Professor, Assistant Professor, Instructor

Standard & Poor’s bond ratings AAA, AA, A, BBB, BB, B, CCC, CC, C, DDD, DD, D

Student Grades A, B, C, D, F

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U.S. businesses are listed by size: small, medium, and large


Measurement Scales (con’t.)

An interval scale is an ordered scale in which the difference between measurements is a meaningful quantity but the measurements do not have a true zero point.

A ratio scale is an ordered scale in which the difference between the measurements is a meaningful quantity and the measurements have a true zero point. EX: The time it takes to download a video from the Internet is measured.

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Interval and Ratio ScalesDCOVA


For each of the following variables, determine whether the variable is categorical or numerical and determine its measurement scale. If the variable is numerical, determine whether the variable is discrete or continuous.a. Number of cellphones in the householdb. Monthly data usage (in MB)c. Number of text messages exchanged per monthd. Voice usage per month (in minutes)e. Whether the cellphone is used for email (yes / no)

Exercise 1:


Suppose the following information is collected from RobertKeeler on his application for a home mortgage loan at the MetroCounty Savings and Loan Association.a. Monthly payments: $2,227b. Number of jobs in past 10 years: 1c. Annual family income: $96,000d. Marital status: Married

Classify each of the responses by type of data and measurementscale.

Exercise 2:


For each of the following variables, determine whether thevariable is categorical or numerical and determine its measurementscale. If the variable is numerical, determine whether the variableis discrete or continuous.a. Name of Internet service providerb. Time, in hours, spent surfing the Internet per weekc. Whether the individual uses a mobile phone to connect to theInternet d. Amount of money spent on clothing in the past monthe. Favorite department storef. Most likely time period during which shopping for clothingtakes place (weekday, weeknight, or weekend)g. Number of pairs of shoes owned.

Exercise 3:


Data Is Collected From Either A Population or A Sample

POPULATIONA population contains all of the items or individuals of interest that you seek to study.

SAMPLEA sample contains only a portion of a population of interest.

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Population vs. Sample

All the items or individuals about which you want to draw conclusion(s).

A portion of the population of items or individuals.

Population Sample

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A Population of Size 40 A Sample of Size 4


Collecting Data Via Sampling Is Used When Doing So Is

Less time consuming than selecting every item in the population.

Less costly than selecting every item in the population.

Less cumbersome and more practical than analyzing the entire population.

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Parameter or Statistic?

A population parameter summarizes the value of a specific variable for a population.

A sample statistic summarizes the value of a specific variable for sample data.

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1. Parameter: There are exactly 100 Senators in the 109th Congress of the United States, and 55% of them are Republicans. The figure of 55% is a parameter because it is based on the entire population of all 100 Senators.

2. Statistic: In 1936, Literary Digest polled 2.3 million adults in the United States, and 57% said that they would vote for Alf Landon for the presidency.That figure of 57% is a statistic because it is based on a sample, not the entire population of all adults in the United States.


Sources Of Data Arise From The Following Activities

Capturing data generated by ongoing business activities.

Distributing data compiled by an organization or individual.

Compiling the responses from a survey.

Conducting a designed experiment and recording the outcomes.

Conducting an observational study and recording the results.

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Examples of Data Collected From Ongoing Business Activities

A bank studies years of financial transactions to help them identify patterns of fraud.

Economists utilize data on searches done via Google to help forecast future economic conditions.

Marketing companies use tracking data to evaluate the effectiveness of a web site.

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Examples Of Data Distributed By An Organization or Individual

Financial data on a company provided by investment services.

Industry or market data from market research firms and trade associations.

Stock prices, weather conditions, and sports statistics in daily newspapers.

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Examples of Survey Data

A survey asking people which laundry detergent has the best stain-removing abilities.

Political polls of registered voters during political campaigns.

People being surveyed to determine their satisfaction with a recent product or service experience.

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Examples of Data From A Designed Experiment

Consumer testing of different versions of a product to help determine which product should be pursued further.

Material testing to determine which supplier’s material should be used in a product.

Market testing on alternative product promotions to determine which promotion to use more broadly.

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Examples of Data Collected From Observational Studies

Market researchers utilizing focus groups to elicit unstructured responses to open-ended questions.

Measuring the time it takes for customers to be served in a fast food establishment.

Measuring the volume of traffic through an intersection to determine if some form of advertising at the intersection is justified.

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Observational Studies & Designed Experiments Have A Common Objective

Both are attempting to quantify the effect that a process change (called a treatment) has on a variable of interest.

In an observational study, there is no direct control over which items receive the treatment.

In a designed experiment, there is direct control over which items receive the treatment.

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Sources of Data

Primary Sources: The data collector is the one using the data for analysis: Data from a political survey. Data collected from an experiment. Observed data.

Secondary Sources: The person performing data analysis is not the data collector: Analyzing census data. Examining data from print journals or data published

on the internet.

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1. The American Community Survey (www.census.gov/acs) provides data every year about communities in the United States. Addresses are randomly selected, and respondents are required to supply answers to a series of questions.a. Which of the sources of data best describe the American Community Survey?b. Is the American Community Survey based on a sample or apopulation?

http://www.census.gov/acs


A Sampling Process Begins With A Sampling Frame

The sampling frame is a listing of items that make up the population.

Frames are data sources such as population lists, directories, or maps.

Inaccurate or biased results can result if a frame excludes certain groups or portions of the population.

Using different frames to generate data can lead to dissimilar conclusions.

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Types of Samples

Samples

Non Probability Samples

Judgment

Probability Samples

Simple Random

Systematic

Stratified

Cluster

Convenience

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Types of Samples:Nonprobability Sample

In a nonprobability sample, items included are chosen without regard to their probability of occurrence.

In convenience sampling, items are selected based only on the fact that they are easy, inexpensive, or convenient to sample.

In a judgment sample, you get the opinions of pre-selected experts in the subject matter.

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Types of Samples:Probability Sample

In a probability sample, items in the sample are chosen on the basis of known probabilities.

Probability Samples

Simple

RandomSystematic Stratified Cluster

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Probability Sample:Simple Random Sample

Every individual or item from the frame has an equal chance of being selected.

Selection may be with replacement (selected individual is returned to frame for possible reselection) or without replacement (selected individual isn’t returned to the frame).

Samples obtained from table of random numbers or computer random number generators.

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Selecting a Simple Random Sample Using A Random Number Table

Sampling Frame For Population With 850

ItemsItem Name Item #Bev R. 001Ulan X. 002. .. .. .. .Joann P. 849Paul F. 850

Portion Of A Random Number Table49280 88924 35779 00283 81163 0727511100 02340 12860 74697 96644 8943909893 23997 20048 49420 88872 08401

The First 5 Items in a simple random sample

Item # 492Item # 808Item # 892 -- does not exist so ignoreItem # 435Item # 779Item # 002

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Decide on sample size: n Divide frame of N individuals into groups of k

individuals: k=N/n Randomly select one individual from the 1st

group Select every kth individual thereafter

Probability Sample:Systematic Sample

N = 40n = 4k = 10

First Group

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Probability Sample:Stratified Sample

Divide population into two or more subgroups (called strata) according to some common characteristic.

A simple random sample is selected from each subgroup, with sample sizes proportional to strata sizes.

Samples from subgroups are combined into one. This is a common technique when sampling population of

voters, stratifying across racial or socio-economic lines.

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Probability SampleCluster Sample

Population is divided into several “clusters,” each representative of the population.

A simple random sample of clusters is selected.

All items in the selected clusters can be used, or items can be chosen from a cluster using another probability sampling technique.

A common application of cluster sampling involves election exit polls, where certain election districts are selected and sampled.

Population divided into 16 clusters. Randomly selected

clusters for sample

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Probability Sample:Comparing Sampling Methods

Simple random sample and Systematic sample: Simple to use. May not be a good representation of the population’s

underlying characteristics. Stratified sample:

Ensures representation of individuals across the entire population.

Cluster sample: More cost effective. Less efficient (need larger sample to acquire the

same level of precision).

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The registrar of a university with a population of N = 4,000full-time students is asked by the president to conduct a survey to measure satisfaction with the quality of life on campus. The following table contains a breakdown of the 4,000 registered full-time students, by gender and class designation:

The registrar intends to take a probability sample of n = 200students and project the results from the sample to the entirepopulation of full-time students.a. If the frame available from the registrar’s files is an alphabetical listing of the names of all N = 4,000 registered full-timestudents, what type of sample could you take? Discuss.


b. What is the advantage of selecting a simple random samplein (a)?c. What is the advantage of selecting a systematic sample in (a)?d. If the frame available from the registrar’s files is a list of thenames of all N = 4,000 registered full-time students compiledfrom eight separate alphabetical lists, based on the gender andclass designation breakdowns shown in the class designationtable, what type of sample should you take? Discuss. e. Suppose that each of the N = 4,000 registered full-time students lived in one of the 10 campus dormitories. Each dormitoryaccommodates 400 students. It is college policy to fully integratestudents by gender and class designation in each dormitory. Ifthe registrar is able to compile a listing of all students by dormitory, explain how you could take a cluster sample.


Data Cleaning Is An Important Data Preprocessing Task Prior To Analysis

Data cleaning corrects irregularities in the data: Invalid variable values, including:

Non-numerical data for numerical variable. Invalid categorical values for a categorical variable. Numeric values outside a defined range.

Coding errors, including: Inconsistent categorical values. Inconsistent case for categorical values. Extraneous characters.

Data integration errors, including: Redundant columns. Duplicated rows. Differing column lengths. Different units of measure or scale for numerical variables.

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Examples Of Coding Errors

Copy-and-paste or data import can result in poor recording or entry of data.

Categorical variable: Gender, Correct coding: F or M Correctable error: Female. Invalid data: New York. Correctable or software tolerated: m. Extraneous and nonprintable characters:

Leading or trailing space(s): _F or F_. Other nonprintable characters may also be leading or trailing

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Data Integration Errors From Combining Two Different Computerized Data Sources

Data integration errors often requires time-consuming manual effort.

Some examples: Variable names or definitions may differ.

Duplicated rows (observations) may also occur.

Different units of measurement (or scale) may not be obvious without human interpretation.

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Stacked vs Unstacked Data For unstacked data you create separate

numerical variables for different groups (i.e. genders, locations, etc.)

For stacked data you create a single column for the variable of interest and create additional columns for the potential grouping variables.

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An amusement park company owns three hotels on an adjoining site. A guest relations manager wants to study the time it takesfor shuttle buses to travel from each of the hotels to the amusement park entrance. Data were collected on a particular day that recorded the travel times in minutes.a. Explain how the data could be organized in an unstacked format.b. Explain how the data could be organized in a stacked format


A hotel management company runs 10 hotels in a resort area. The hotels have a mix of pricing—some hotels have budget priced rooms, some have moderate-priced rooms, and some have deluxe-priced rooms. Data are collected that indicate the number of rooms that are occupied at each hotel on each day of a month.Explain how the 10 hotels can be recoded into these three pricecategories.


Evaluating Survey Worthiness

What is the purpose of the survey?

Is the survey based on a probability sample?

Coverage error – appropriate frame?

Nonresponse error – follow up.

Measurement error – good questions elicit good responses.

Sampling error – always exists.

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Types of Survey Errors Coverage error or selection bias:

Exists if some groups are excluded from the frame and have no chance of being selected.

Nonresponse error or bias: People who do not respond may be different from those who

do respond.

Sampling error: Variation from sample to sample will always exist.

Measurement error: Due to weaknesses in question design and / or respondent

error.

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Types of Survey Errors

Coverage error

Nonresponse error

Sampling error

Measurement error

Excluded from frame

Follow up on nonresponses

Random differences from sample to sample

Bad or leading question

(continued)

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Nonresponse ErrorNot everyone is willing to respond to a survey. Nonresponse error arises from failure to collect data on all items in the sample and results in a nonresponse bias.


Ethical Issues About Surveys Coverage error and nonresponse error can be

leveraged by survey designers to purposely bias survey results.

Sampling error can be an ethical issue if the findings are purposely not reported with the associated margin of error.

Measurement error can be an ethical issue: Survey sponsor chooses leading questions. Interviewer purposely leads respondents in a

particular direction. Respondent(s) willfully provide false information.

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Chapter SummaryIn this chapter we have discussed: Understanding issues that arise when defining

variables. How to define variables. Understanding the different measurement scales. How to collect data. Identifying different ways to collect a sample. Understanding the issues involved in data

preparation. Understanding the types of survey errors.


1. What is the difference between a sample and a population?2. What is the difference between a statistic and a parameter?3. What is the difference between a categorical variable and anumerical variable?4. What is the difference between a discrete numerical variableand a continuous numerical variable?5. What is the difference between a nominal scaled variable andan ordinal scaled variable?6. What is the difference between an interval scaled variable anda ratio scaled variable?7. What is the difference between probability sampling and nonprobability sampling?8. What is the difference between a missing value and an outlier?9. What is the difference between unstack and stacked variables?10. What is the difference between coverage error and nonresponse error?11. What is the difference between sampling error and measurement error?


1. Results of a 2017 Computer Services, Inc. (CSI) survey of a sample of 163 bank executives reveal insights on banking priorities among financial institutions (goo.gl/mniYMM). As financial institutions begin planning for a new year, of utmost importance is boosting profitability and identifying growth areas.The results show that 55% of bank institutions note customer experience initiatives as an area in which spending is expected to increase. Implementing a customer relationship management (CRM) solution was ranked as the top most important omnichannel strategy to pursue with 41% of institutions citing digital banking enhancements as the greatest anticipated strategy to enhance the customer experience.a. Describe the population of interest.b. Describe the sample that was collected.c. Describe a parameter of interest.d. Describe the statistic used to estimate the parameter in (c)


2. Three professors examined awareness of four widely disseminated retirement rules among employees at the Universityof Utah. These rules provide simple answers to questions aboutretirement planning (R. N. Mayer, C. D. Zick, and M. Glaittle,“Public Awareness of Retirement Planning Rules of Thumb,”Journal of Personal Finance, 2011 10(1), 12–35). At the time of the investigation, there were approximately 10,000 benefited employees, and 3,095 participated in the study. Demographic data collected on these 3,095 employees included gender, age (years), education level (years completed), marital status, household income ($), and employment category.a. Describe the population of interest.b. Describe the sample that was collected.c. Indicate whether each of the demographic variables mentionedis categorical or numerical.


3. IBM Survey The computer giant IBM has 329,373 employees and 637,133 stockholders. A vice president plans to conduct a survey to study the numbers of shares held by individual stockholders.a. Are the numbers of shares held by stockholders discrete or continuous?b. Identify the level of measurement (nominal, ordinal, interval, ratio) for the numbers of shares held by stockholders.c. If the survey is conducted by telephoning 20 randomly selected stockholders in each of the 50 United States, what type of sampling (random, systematic, convenience, stratified, cluster) is being used?d. If a sample of 1000 stockholders is obtained, and the average (mean) number of shares is calculated for this sample, is the result a statistic or a parameter?e. What is wrong with gauging stockholder views about employee benefits by mailing a questionnaire that IBM stockholders could complete and mail back?


4. IBM Survey Identify the type of sampling (random, systematic, convenience, stratified, cluster) used when a sample of the 637,133 stockholders is obtained as described. Then determine whether the sampling scheme is likely to result in a sample that is representative of the population of all 637,133 stockholders.a. A complete list of all stockholders is compiled and every 500th name is selected.b. At the annual stockholders’ meeting, a survey is conducted of all who attend.c. Fifty different stockbrokers are randomly selected, and a survey is made of all their clients who own shares of IBM.d. A computer file of all IBM stockholders is compiled so that they are all numbered consecutively, then random numbers generated by computer are used to select the sample of stockholders.e. All of the stockholder zip codes are collected, and 5 stockholders are randomly selected from each zip code.

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Basic Business Statistics Concepts and Applications 14th Ediition - MAS202 chap1