Understanding Statistics Eighth Edition By Brase and Brase Prepared by: Joe Kupresanin Ohio State...

Understanding StatisticsEighth Edition

By Brase and BrasePrepared by: Joe Kupresanin

Ohio State University

Chapter One

Getting Started

Copyright © Houghton Mifflin Company. All rights reserved. 1 | 2

What is Statistics?

• Collecting data

• Organizing data

• Analyzing data

• Interpreting data


Individuals and Variables

• Individuals are people or objects included in the study.

• Variables are characteristics of the individual to be measured or observed.


Quantitative Variables

• The variable is numerical, so operations such as adding and averaging make sense.


Qualitative Variables

• The variable describes an individual through grouping or categorization.

– Beware: Qualitative variables may be numerical, but mathematical operations won’t make sense.


Examples

• Purchase price of an MP3 player, say $299.99, is

• Model number of an MP3 player, say model 21883, is

• Gender, religious affiliation, zip code, and political party are all

quantitative.

qualitative.

qualitative.


Population Data

• The variable is part of every individual of interest.– Example: The selling price of all the MP3

players at Wal-Mart.


Sample Data

• The variable is part of only some of the individuals of interest, i.e. of just a part of the population.– Example: The selling prices of MP3

players for Wal-Mart stores in Ohio only.


Levels of Measurement: Nominal

• The data that consist of names, labels, or categories.– Examples:

• Gender• Eye color• City


Levels of Measurement: Ordinal

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

• Class rank• Rating scales

(Poor, Fair, Average, Good, Excellent)


Levels of Measurement: Interval

• The data can be ordered and the differences between data values are meaningful.– Examples:

• Year• Degrees Fahrenheit


Levels of Measurement: Ratio

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

• Weight (lbs) of college freshmen• Pressure (PSI) in SUV tires


Two Branches of Statistics

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

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


1.2Sampling From a Population

• Simple Random Sample of 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.


Simple Random Sampling Techniques

• Use a computer program.

• Use a random-number table.

• “Pick names out of a hat.”


NOT Simple Random Sampling Techniques

• Asking patrons in a mall to participate in a survey.

• Soliciting volunteers in a newspaper ad to taste test a new snack food.

• Polling the members of this class on their majors.


Stratified Sampling

• First, break the population into strata in which all the occupants share a characteristic.– Split the residents of California into urban,

suburban, and rural residents.

• Then, randomly sample from each strata.– 1000 urban dwellers, 800 suburbanites, and 200

rural folks are randomly selected and asked for their opinion on whether the amount of public art should be increased.


Systematic Sampling

• Members of the population are sequentially numbered.

• Pick a starting point, and then select every kth member for the sample.– Example: At the University of Maine, give

each faculty member a number, and select every 13th faculty member to answer questions about the salary structure.


Cluster Sampling

• First, divide the population into clusters. The clusters should be similar to each other.– Split a high-rise male-only dormitory into floors

(each floor should be no different)

• Then, randomly select clusters and sample all members of the cluster.– After floors 2, 5, 14 are selected, ask every

resident on those floors his opinion on the cost of room & board.


Convenience Sampling

• Members of the sample are chosen by being available and willing to participate.– Customers at a cell phone store who will

fill out a comment card– Students walking on campus who will

participate in a short survey


1.3Guidelines For Planning a Statistical Study

1. Identify individuals or objects of interest.

2. Specify the variables.3. Determine if you will use the entire

population. If not, determine an appropriate sampling method

4. Determine a data collection plan, addressing privacy, ethics, and confidentiality if necessary.


Guidelines For Planning a Statistical Study

5. Collect data.

6. Analyze the data using appropriate statistical methods.

7. Note any concerns about the data and recommend any remedies for further studies.


Census vs. Sample

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

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


Observational Study

• Measurements and observations are obtained in a way that does not change the response or variable being measured.


Designed Experiments

• A treatment is applied to the individuals in the experiment in order to observe a potential effect on the variable being measured

• Designed experiments are used to pin down a cause-and-effect relationship.



• To measure the effect of a treatment, statisticians may break the individuals into two groups:– Treatment group: Members have the

treatment applied and the variable is measured.

– Control group: Members receive a dummy treatment, or no treatment, and the variable is measured.



• Placebo Effect– A measurable change in the variable due

to recipients thinking that they received a treatment, when they actually did not.

• Example: A patient feels better after taking a sugar pill.



• Lurking Variable– Unknown variable that might be an underlying

cause for the change in the measurement• Blocking

– Splitting the individuals into similar groups before applying different treatments

• Before applying one of two exercise programs, block the individuals into weight categories.

• Randomization– Placing individuals in the control/treatment group

randomly is required to prevent bias in the measurement.



• Blind Experiments– The participants in the study do not know

which treatment they are receiving.

• Double-Blind Experiments– Both the participants and those

administering the treatment do not know which treatment is being applied.


Surveys

• The art of collecting data from respondents through interviews, phone conversations, internet polls, mail polls, etc…


Survey Definitions

• Non-response: Respondents cannot be contacted or refuse to answer.

• Voluntary response surveys: Method may produce biased results due to strong opinions held by those willing to participate.

• Survey results usually cannot pin down a cause-and-effect relationship.

Understanding Statistics Eighth Edition By Brase and Brase Prepared by: Joe Kupresanin Ohio State...

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