Formulating statistical questions and collecting data
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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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Formulating statistical questions and collecting data

Formulating Statistical Questions and Collecting Data

Alliance Class

September 2011


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 & Probability6.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?


Formulating statistical questions and collecting data

  • 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?


Formulating statistical questions and collecting data

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

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


Activity

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 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

Experiments

Observational Studies

Surveys


Do you know who my favorite horse is

Do you know who my favorite horse is?


Not seabiscuit

Not Seabiscuit


Not trigger the smartest horse in hollywood

Not Trigger – the smartest horse in Hollywood


Not mr ed

Not Mr. Ed


Clever hans the math horse

Clever Hans the Math Horse


Formulating statistical questions and collecting data

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


Formulating statistical questions and collecting data

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%


Formulating statistical questions and collecting data

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.


Formulating statistical questions and collecting data

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.


Formulating statistical questions and collecting data

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

Continuous

Decimals and fractions

Height of a person

Discrete

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

    Surveys


Experiments

Experiments

  • 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


Surveys

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


Activity1

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?


Formulating statistical questions and collecting data

  • 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

Placebo


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


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