Statistics

The science of collecting, analyzing, and interpreting data.

The Statistical Problem Solving Process:

1. Ask a question of interest

2. Produce or collect some data

3. Analyze, graph and describe the data

4. Make a conclusion, answering the question of interest

Individuals & Variables• Individuals are the objects described by a set of

data.– People, animals, or things

• A Variable is any characteristic of an individual. Variables can take different values for different individuals.– Categorical Variables: places an individual into one of

several categories (Job type, gender, race)– Quantitative Variables: takes numerical values for

which ordering and averaging make sense (age, weight, salary)

Example: a few lines from a teacher's gradebook

Name           Gender         Grade level        Calc No.       Test 1

Hsu, Danny        M                   12                 B319              81

Iris, Francine       F                   12                 B298              92

Ruiz, Ricardo      M                  11                 B304              87

• What individuals does this data describe?

• What variables does this data describe?

– Which of these are categorical?– Which are quantitative?

Danny, Francine, and Ricardo

Gender, grade level, calc no, and test grade

Gender, calc noGrade level, test grade

Populations & Samples• The population of interest in a statistical

study is the entire group of individuals about which we want information– A parameter is a number that describes the

population

• A sample is a part of the population from which we actually collect

information.– A statistic is a number that describes the sample

• Sample data is used to draw conclusions about the population as a whole.– A statistic helps to estimate a parameter

Example: TV ratingshttp://www.nielsen.com/us/en/nielsen-solutions/nielsen-measurement/nielsen-tv-measurement.html• Market research is designed to discover what consumers

want and what products they use. One example of product research is the television rating service of Nielsen Media Research. The Nielsen ratings influence how much advertisers will pay to sponsor a program and whether or not the program stays on the air.

• Based on a 2010 study from 11,000 household people meters, Nielsen found that the average household has 2.5 TV's, 31% of the households own 4 or more TVs, and the average American watches 35.6 hours of TV a week.

• For this study:– What is the population?– What is the sample?– What are the individuals?– What variables were measured? (C or Q?)– Are the numbers given (2.5, 31%, and 35.6) parameters or

statistics?

American households11,000 households

Each household# of TVs (Q/C), hrs watched (Q)

statistics

Censushttp://www.census.gov/multimedia/www/videos/stats_in_action.php?intcmp=sldr4

• A study that attempts to include the entire population in the sample.

• Censuses are often too costly and timely to conduct so we take samples instead.

• The Bureau of Labor and Statistics and Census Bureau conduct a census of the US every 10 years and sample surveys much more frequently . – The Current Population Survey (CPS) interviews about

60,000 monthly.– The American Community Survey (ACS) interviews

about 3,000,000 households each year.– http://www.census.gov/people/laborforce/publications/ACS-CPS_Comparison_Report.pdf

2 Types of StudiesObservational Study

Experimental Study

Observational Study

An observational study observes individuals and measures variable(s) of interest but does not attempt to influence the responses.

The purpose of an observational study is to describe some group or situation.

Experiments

• An experiment deliberately imposes treatments on individuals in order to observe their responses.

• The purpose of an experiment is to study whether the treatment causes a change in the response.

The Beauty of Well Designed Experiments

• Everyone randomly chooses a red or blue chip out of a bag. The red group is assigned to do jumping jacks for two minutes and the blue group is assigned to meditate for two minutes. After the two minutes, their heart rate is measured. Does the treatment cause the difference in heart rate?

• Since well designed experiments have an element of control, they can be used to imply causation (cause/effect) between the variables.

Observational Study or Experiment?• A business is studying the relationship between physical

fitness and productivity. They divide the employee volunteers into two groups (low and high fitness) and then compare their productivity once the fitness program has been completed.

• You want to determine what the most popular cars on campus are. To do this, you go to the parking lot and record the types of cars for several samples from different areas of the lot.

• A insurance company wants to research if there is a difference in the number of children elementary and secondary teachers have. They submit a questionnaire to a random sample of teachers asking them to categorize themselves as elementary or secondary and how many children they have.

The Statistical Problem Solving Process - APAC

• A – Ask a question of interest• P – Produce data• A – Analyze and describe/graph the data • C – Conclusion, answering the question

Using APAChttp://www.usatoday.com/

• Which element of APAC is shown here?

• What is a reasonable question of interest?

• How do you think the data were produced?– Observational or

experimental?– What are the individuals?– What is the variable?– Is it quantitative or

categorical?• What can be concluded?

Additional example

• According to the National Institute on Media and the Family, a preschooler’s risk of obesity jumps 6% for every hour of television watched per day. The risk increases by 31% if the TV is in their bedroom.– 1.What element of APAC is given here?– 2. What is a reasonable question of interest in this case?– 3. The actual study that produced these results involved 2761 low-

income adults in New York with children aged 1 to 4 years. Who are the individuals in this study?

• Do you think this was done with an observational study or an experimental study?

– 4. What variable(s) were measured?