Creating a Methodology
Chapter 1
Introduction to Statistics
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Statistics is the science of gathering, describing, and analyzing data.
Statistics is the numerical description of sample data.
Definitions:
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- Data – information, in particular, information prepared for a study.
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- Population – a particular group of interest.
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- Parameter – a numerical description of a particular population characteristic.
- Census – when data is collected from every member of the population.
Definitions:
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Sample – a subset of the population from which data is collected.
Sample Statistic – a numerical description of a particular sample characteristic.
Definitions:
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| Population | Sample |
| Whole group | Part of the group |
| Group I want to know about | Group I do know about |
| Characteristics are called parameters | Characteristics are called statistics |
| Parameters are generally unknown | Statistics are always known |
| Parameter is fixed | Statistics change with the sample |
- In a survey, 359 college students were asked if they had tried Vanilla Coke. 83 said yes.
Population = all college students
Sample = 359 college students
- A survey of 1125 households in the U.S. found that 65% subscribe to digital cable.
Population = all U.S. households
Sample = 1125 households
Identify the population and the sample.
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- The average grade on Test 1 in Ms. Shirley’s statistics class is an 87.
Parameter
- The average Math score for all high school graduates on the SAT was a 519.
Parameter
- In a survey of 135 college students, 52% of them said they plan to attend graduate school.
Statistic
Is the numerical value a parameter or a statistic?
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- Identify the population and sample.
Population = all families of the students at the school
Sample = 195 families
- Does the value “76%” represent a parameter or a statistic?
Statistic
The principal of a large K-12 school is considering adopting a dress code for the upcoming school year. Before going to the school board, he wants to know the percentage of parents who would favor a dress code. He randomly chooses 15 families from each grade to interview. Out of the 195 families surveyed, 76% favor a dress code.
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- Descriptive statistics – gathers, sorts, summarizes and displays the data; “just the facts”.
- Inferential statistics – uses descriptive statistics to estimate population parameters; an educated guess about the population based on the facts.
Branches of Statistics:
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In a survey of 100 students, 83.2% of students are happy with the food in the cafeteria.
Identify the descriptive statistic(s). What inferences can be made?
Descriptive statistic: 83.2% of the 100 students surveyed are happy with the food in the cafeteria.
Possible inferences: 83.2% of all students are happy with the food in the cafeteria.
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Qualitative
Quantitative
Descriptions and labels
Counts and measurements
Qualitative vs. Quantitative:
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1.2 Data Classifications
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- The weights of members of the football team.
Quantitative
- The flavors of Ben and Jerry’s Ice Cream.
Qualitative
- The jersey numbers of a women’s basketball team.
Qualitative
- Student ID numbers
Qualitative
Classify as Qualitative or Quantitative:
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Qualitative
Quantitative
Continuous
DISCRETE
Usually measurements
Usually counts of things
Continuous vs. Discrete:
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- The temperature in Fahrenheit of cities in North Mississippi.
Continuous
- The number of rooms in a house.
Discrete
- The number of peanuts in a jar.
Discrete
- The height of a door in inches.
Continuous
Classify as discrete or continuous:
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Levels of Measurement
Nominal
Names
Ordinal
Order
Interval
0 is a placeholder
Ratio
0 means the absence of something
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- Today’s high temperature (in Fahrenheit) for varying cities across the U.S.
Quantitative – Interval
- The colors contained in a box of crayons.
Qualitative – Nominal
- The boiling point (in Kelvin’s) for varying chemical compounds.
Quantitative – Ratio
- The individual page numbers at the bottom of each page in the statistics book.
Quantitative – Ordinal
Determine the level of measurement:
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Collect Data
Defines Population/Variables
Question
Calculate Statistic
Estimate Parameter
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1.3 Process of a Statistical Study
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- Observational Study – researcher observes data that already exists.
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- Experiment – researcher seeks to create data to identify cause and effect relationships.
Types of Studies:
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- A medical researcher wants to examine the effects of exercise on cardiovascular health.
Experimental
- A recording company is interested in knowing the percentage of teenagers that download music off of the internet.
Observational
- A chain of grocery stores wants to know how much the average family spends on produce each month.
Observational
Observational Study or Experimental Study?
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- Ask, “How will the data be gathered?”
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- Very Important:
- It is essential that a representative sample is chosen out of the population.
- A good sampling frame is the first step to choosing a representative sample. The sampling frame is a list of members of the population.
Observational Studies:
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- Census
- Random Sample
- Stratified Sample
- Cluster Sample
- Systematic Sample
- Convenience Sample
Sampling Techniques:
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Census:
Every member of the population is included.
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Random Sample:
Every member has an equal chance of being selected.
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Stratified Sample:
The population is divided into subgroups called strata and the
same number of subject are chosen from each strata.
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Cluster Sample:
The population is divided into subgroups, called clusters, that are
similar to the population and whole clusters are chosen at random.
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Systematic Sample:
Selecting every nth member of the population.
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Convenience Sample:
The sample is convenient for the researcher to select.
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- Chosen at random, 200 rural and 200 urban persons age 65 or older were asked about their health and experience with prescription drugs.
Stratified
- For quality assurance, every 12th engine part is selected from an assembly line and tested for durability.
Systematic
- A survey concerning the taste of a new soda flavor was performed at the local grocery store from 5:00 PM to 8:00 PM.
Convenience
Identify the sampling method:
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- To determine how a particular political candidate was going to fare in an upcoming election, different counties in the state were randomly selected and every eligible voter in the randomly selected counties was surveyed.
Cluster
- To determine who will win a $100,000 shopping spree at the local mall, the owner of the mall draws a name out of a box.
Random
Identify the sampling method:
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- Subjects – people, animals, or things being studied.
- Participants – term used when the subjects of a study are people.
- Treatment – characterizes an experiment; applied to some or all subjects.
- Treatment Group – a group in which researchers apply a treatment.
- Control Group – a group identical to the treatment group except that no treatment is applied.
Experiment:
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- Single-Masked – when the subjects do not know in which group they have been placed.
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- Double-Masked – when neither the subjects nor the people interacting with the subjects know to which group the subjects belong.
- Placebo – a substance that appears identical to the actual treatment.
Experiment:
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- Institutional Review Board (IRB)
- Informed consent
- Human or animal subjects
- Confidentiality
Ethical Concerns:
- Bias
- Researcher bias
- Sampling errors
- Non-sampling errors
Practical Concerns:
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Errors:
Sampling Errors
Non-Sampling Errors
Dropout – a participant who begins the study but fails to complete it.
Poor sampling frame
Participation bias – when there is a problem with either the participation, or lack thereof, of those chosen for the study.
Processing error – an error as simple as a typo.
Lying or faulty memory
Non-adheres – subjects who stray from the directions they were given.
Confounding variables – factors that influence the results of the study that the researchers did not, or could not, account for.
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Consider preparing a research proposal for the following question, “what percentage of 11 to 16 year olds smoke cigarettes?”
Something to Ponder:
What are some possible issues of getting informed consent, confidentiality, going to the IRB, dealing with human subjects, bias?
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CompuTech is a large computer company with hundreds of thousands of customers across the country. They are interested in knowing the percentage of customers that are satisfied enough with their purchases to continue buying CompuTech products in the future. The company hires an independent research firm to conduct the study. The firm randomly selects 50 customers from each of the following metropolitan areas: New York, Los Angeles, and Chicago. They find that 77% of the customers surveyed are satisfied with their CompuTech purchase and plan to continue buying CompuTech products in the future. Using statistical methods, the firm estimates that between 74% and 80% of all CompuTech customers will continue doing business with the company.
Identify the population.
All CompuTech customers
Identify the sample.
150 customers
Identify any statistics.
77% of the customers surveyed are satisfied
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CompuTech is a large computer company with hundreds of thousands of customers across the country. They are interested in knowing the percentage of customers that are satisfied enough with their purchases to continue buying CompuTech products in the future. The company hires an independent research firm to conduct the study. The firm randomly selects 50 customers from each of the following metropolitan areas: New York, Los Angeles, and Chicago. They find that 77% of the customers surveyed are satisfied with their CompuTech purchase and plan to continue buying CompuTech products in the future. Using statistical methods, the firm estimates that between 74% and 80% of all CompuTech customers will continue doing business with the company.
Identify the parameter.
Between 74% and 80% of all customers are satisfied
What sampling technique was used?
Stratified sampling
Is the study biased? If so, what type of bias occurred?
Sampling errors since the population of the U.S. was not represented
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Consider the following phrase, “the firm estimates that between 74% and 80% of all CompuTech customers will continue doing business with the company.”
Is this an example of descriptive or inferential statistics?
Inferential
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