Chapter 1

Chapter 1

Getting Started

Understanding Basic Statistics Fifth Edition

By Brase and Brase Prepared by Jon Booze

© Cengage Learning. All rights reserved. 1 | 2

What is Statistics?

• Many definitions could apply. A few ideas about the subject:

- “The science of studying variation.”- “Description of and inference from data.”- The art of making decisions from data in

the face of error.”

What should be clear is that it’s all about data, analysis, and explaining and understanding variation.


What is Statistics?

• Collecting data• Organizing data• Analyzing data• Interpreting data

• Statistician’s Creed: “In God we trust….all others, bring data!”


Individuals and Variables

• Individuals are people or objects included in the study. (Also known as the “experimental units” or “subjects.”)

• Variables are characteristics of the individual to be measured or observed. They change from individual to individual…or over time.)


Variables

• Qualitative Variable – The variable describes an individual through grouping or categorization.

(e.g. hair color, religion, college major, birth city, etc.)

• Quantitative Variable – The variable is numerical, so operations such as adding and averaging make sense.(e.g. weight, height, temperature of liquid, length of time, etc.)


Data

• Population Data – The data are from every individual of interest.

• Sample Data – The data are from only some of the individuals of interest. That is, a sample is a subset of our population.


DataWhich of the following Venn diagrams shows the

relationship between population data and sample data?

a). b).

c). d).

S P

S

P S

P

P

S


Two VERY Important Terms

• Parameter – is a numerical measure that describes an aspect of a population

• Statistic – is a function of data from a sample.

• Remember the Mnemonic Device….

“P”: PARAMETER corresponds to POPULATION

“S”: STATISTIC corresponds to SAMPLE


Two VERY Important Terms

Just a quick note: With one exception that we will get later, we typically represent:

• PARAMETERS – using lowercase Greek characters (e.g. μ, σ, ρ, etc.)

• STATISTICS – using standard Arabic characters (e.g. s, s2, r, etc.)


Levels of Measurement

• Nominal Level – The data consists of names, labels, or categories.

• Ordinal Level – The data can be ordered, but the differences between data values are meaningless.



• Interval Level – The data can be ordered and the differences between data values are meaningful.

• Ratio Level – The data can be ordered, differences and ratios are meaningful, and there is a meaningful zero value.

NOIR: Nominal Ordinal Interval Ratio



Classify on our “NOIR” scale:1. Age of a person.2. Distance travelled from home to work.3. Grades recorded on an A,B,C,D,F scale.4. Undergraduate majors’ fields of study at EUP.5. Temperature of a liquid in degrees Fahrenheit. 6. Religious Affiliation of voters. 7. Rating of oral presentations on a 1,2,3,...,9

scale.8. Number of children in a family.



Classify on our “NOIR” scale:9. Response to a question on a Likert Scale

(Strongly Disagree, Disagree, Neutral, Agree, Strongly Agree).

10. Whether a person in a study is in the control group or the experimental group.



Solutions:

1. Ratio2. Ratio3. Ordinal4. Nominal5. Interval6. Nominal7. Ordinal

8. Ratio9. Ordinal10. Nominal


Two Approaches to Statistics

• Descriptive Statistics: Organizing, summarizing, and graphing information from samples.

• Inferential Statistics: Using information from a sample to draw conclusions about a population.


Sampling Techniques• Simple Random Sampling, Sample size = n

– Each member of the population has an equal chance of being selected.

– Each sample of size n has an equal chance of being selected.

• Stratified sampling Population

Subgroup 4

Subgroup 1Subgroup 2Subgroup 3

sample


Sampling Techniques • Cluster sampling

– Population is naturally divided into pre-existing segments.

– Make a random selection of clusters, then select all members of each cluster.

• Systematic sampling– Number every member of the population.– Select every kth member.

• Convenience sampling - Collect sample data from a readily-available population database.


Sampling Techniques Which of the five sampling designs is being

employed? (Simple Random, Stratified, Cluster, Systematic, or Convenience?)

1. A politician wants to survey his constituents. To do so, he polls 100 democrats in his district, 125 republicans, and 20 independents.

2. Wal-Mart would like to perform demographic analysis of its shoppers. So starting at 8:00am, the Wal-Mart greeter is asked to survey every 20th customer who enters the store.


Sampling Techniques 3. A doctor is assessing a new treatment

technique. She utilizes this treatment on all asthma patients she sees for a one month period.

4. A company wishes to survey its employees. There are 800 employees, an a random number is assigned to each. Fifty employees are selected using a random number table.

5. Residence life wants to examine student interests. Of the seven dorms, three dorms are randomly selected. Every student in the dorms selected is surveyed.


Sampling Techniques Solutions to Sampling Technique Problems.

1. Stratified2. Systematic (1-in-k)3. Convenience4. Simple Random Sample (SRS)5. Cluster


Census vs. Sample

• In a census, measurements or observations are obtained from the entire population (uncommon and often impractical).

• In a sample, measurements or observations are obtained from part of the population (common).


Observational Studies and Experiments

• Observational Study – Measurements are obtained in a way that does not change the response or the variable being measured. (No treatment is applied.)

• Experiment – A treatment is applied in order to observe its effect on the variable being measured. The research controls this primary variable.


Experiment

• Used to determine the effect of a treatment.

• Experimental design needs to control for other possible causes of the effect.

– Placebo effect. – Lurking variables.

• To minimize these confounds, create one or more control groups that receive no treatment.


Experiment Designs

• Randomization – A random process is used to assign individuals to a treatment group or to a control group.

• Double-Blinding – minimizes the unintentional transfer of bias between researcher and subject.


Surveys• Collecting data from respondents by asking them

questions.

Survey Pitfalls• Nonresponse → undercoverage of population.• Truthfulness – respondents sometimes lie.• Faulty recall of respondent• Hidden bias – due to poor question wording.• Vague wording – “sometimes”, “often”, “seldom”• Interviewer influence – who is asking the

questions and in what manner.• Voluntary response – relatively interested

individuals are more likely to participate.

Chapter 1

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