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Formulating Statistical Questions and Collecting Data. Alliance Class September 2011. GAISE: Instructional programs from Pre K-12 should enable all students to:. Formulate questions that can be addressed with data Collect , organize, and display data Analyze data 4. Interpret results.

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gaise instructional programs from pre k 12 should enable all students to
GAISE: Instructional programs from Pre K-12 should enable all students to:
  • Formulate questions that can be addressed with data
  • Collect, organize, and display data
  • Analyze data

4. Interpret results

definition of statistical questions
Definition of Statistical Questions

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

common core state standards
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
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
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
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?
  • 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 studies how data is collected
Types of Statistical StudiesHow Data is Collected

GAISE Step Two

Designing a plan to collect appropriate data

Types of Variables


Observational Studies



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 data
Types of Data

Quantitative Data

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


Decimals and fractions

Height of a person


Whole numbers

Number right on a test

type of data
Type of Data

Categorical or Qualitative Data

Places an individual into one of several groups or categories

Favorite pizza toppings

Who you vote for

Ethnic background of your students

clever hans variables
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?

vocabulary populations vs samples
VocabularyPopulations vs Samples
  • Population

A population consists of all members of some specified group.

  • Sample

A sample is a subset of a population. It has the same characteristics as the population.

parameters vs statistics
Parameters vs Statistics
  • Parameters

A measure of a characteristic of an entire population.

  • Statistic

A measure of a characteristic of a sample.

designs for collecting data
Designs for Collecting Data
  • Experiments

• Observational Studies


  • The researchers deliberately impose some treatment on individuals and observe their responses.
  • Causation is best established by an experiment
examples of experiments
Examples of experiments
  • Eating Chocolate
  • Breast Cancer
  • Velcro and Babies
  • McDonalds
observational studies
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
Examples of Observational Studies
  • Breast Feeding
  • Night Lights
experiments vs observational studies
Experiments vs Observational Studies
  • Hormone Therapy Treatment Studies
  • 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
  • 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
Principles of Experimental Design

• Randomization

Random assignment of treatment

• Repetition

Repeat the experiment to a “large” number of subjects

• Control

Compare two or more treatments to prevent confounding


randomized comparative design
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
Cell Phone Study

Show the design of the Stewart Fist experiment

tai chi or yoga
Tai Chi or Yoga?

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

Answer the questions