Formulating Statistical Questions and Collecting Data

Alliance ClassSeptember 2011

GAISE: Instructional programs from Pre K-12 should enable all students to:1. Formulate questions that can be addressed

with data2. Collect, organize, and display data3. Analyze data4. Interpret results

Definition of Statistical Questions

Statistical questions specify populations and measurements of interest and anticipate answers based on data that vary.

Common Core State Standards

Statistics & Probability 6.SP Develop understanding of statistical variability.1. Recognize a statistical question as one that

anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.

Answers to statistical questions

• Address the variation in data

• Use probability statements

• Apply only to the population sampled

Non-Statistical questions may be very broad or very specific

• Research Question:• Does the pesticide Roundup harm ladybugs?

• Statistical Question:• What is the mortality rate in Coccinella

transversalis on hour after treatment with a 5% solution of Roundup?

• Research question:How has the WKCE math scores changed for our

school?

Statistical question:

Deterministic questions are very specific.

• They anticipate fixed answers• No randomness is involved

• Deterministic question: How tall is John?

• Statistical question: How tall are the students in my class?

• Deterministic question: How many words are there in this sentence?

• Statistical Question: How many words are there in the sentences in this book?

Activity

• For each question listed on the handout decide:

• Is it a statistical question or not?• If it is not give a reason why not and rewrite

so that it is a statistical question

Types of Statistical StudiesHow Data is Collected

GAISE Step TwoDesigning a plan to collect appropriate data

Types of VariablesExperimentsObservational StudiesSurveys

Do you know who my favorite horse is?

Not Seabiscuit

Not Trigger – the smartest horse in Hollywood

Not Mr. Ed

Clever Hans the Math Horse

In the late 1800’s, a German Math teacher named Wilhelm von Osten believed that humans had greatly underestimated the intelligence of animals. To test his hypothesis, he “tutored” his horse named Hans.

Hans learned to use his hoof to tap out numbers written on a blackboard. Wilhelm would write a “3” on the board and Hans would tap-tap-tap. Hans could repeat this for any number under 10

Encouraged by this success Wilhelm would write a basic arithmetic problem like 3 + 4 on the board and Hans would tap 7 times.

Wilhelm took Hans all over Germany. Large crowds came out and were not disappointed.

Hans success rate was 89%

Naturally there were skeptics. The German board of education assembled a team of scientists to test Hans without Wilhelm present.

Hans was successful – the board said Hans talents were real.

This still didn’t quiet the skeptics.

Another scientists decided to test Hans again but under a more controlled setting.

Hans did very well when the scientist posed the questions under normal situations but Hans failed when the scientist posed questions standing behind Hans.

The scientist discovered that Hans had no real grasp of math but was very receptive to the subtle, unconscious cues which the human questioners gave. Hans was sensitive to humans body language.

Researchers now have a term called “Clever Hans Effect” that describes the influence of a questioner’s subtle and unintentional cues given when asking questions.

Types of DataQuantitative Data

Takes numerical values for which arithmetic operations such as averaging make sense

ContinuousDecimals and fractionsHeight of a person

DiscreteWhole numbersNumber right on a test

Type of Data

Categorical or Qualitative DataPlaces an individual into one of several groups or categories

Favorite pizza toppingsWho you vote forEthnic background of your students

Clever Hans Variables

When the scientist tested Hans, what were some of the variables that were tested and not tested?

What type were these variables?

VocabularyPopulations vs Samples

• PopulationA population consists of all members of some

specified group.• SampleA sample is a subset of a population. It has the

same characteristics as the population.

Parameters vs Statistics

• ParametersA measure of a characteristic of an entire

population.• StatisticA measure of a characteristic of a sample.

Designs for Collecting Data

• Experiments

• Observational StudiesSurveys

Experiments

• The researchers deliberately impose some treatment on individuals and observe their responses.

• Causation is best established by an experiment

Examples of experiments

• Eating Chocolate• Breast Cancer• Velcro and Babies• McDonalds

Observational Studies

• Researchers observe individuals and measure variables of interest but do not attempt to influence the responses

• Association between variables may be observed but not causation.

Examples of Observational Studies

• Breast Feeding• Night Lights

Experiments vs Observational Studies

• Hormone Therapy Treatment Studies

Surveys

• An important type of observational study

• Surveys may be given to a sample from the population of interest

• Or they may be given to the entire population and referred to as a CENSUS

Activity

• For each study try and answer the following questions:

• What is the statistical question?• Is the study an experiment or observational

study?• What is the population of interest?• What is the result or conclusion of the study?

• Electrical Brain Simulation• Math Whizzes• Hands-on math• Three cell phone studies• Sleep apnea

Principles of Experimental Design

• RandomizationRandom assignment of treatment

• RepetitionRepeat the experiment to a “large” number of subjects

• ControlCompare two or more treatments to prevent

confoundingPlacebo

Randomized Comparative Design

Does taking Vitamin C reduce the occurrence of the flu?

808 student volunteers who had not gotten a flu shot were randomly assigned to one of two groups: a treatment group who received 1000 mg vitamin C daily and a control group who received a placebo. All the students where monitored daily to ensure they adhered to their assigned treatment. At the end of the school year all the student’s medical records were examined to determine if they had contracted the flu.

Cell Phone Study

Show the design of the Stewart Fist experiment

Tai Chi or Yoga?

Read the description of the study done to compare Tai Chi and Yoga.

Answer the questions