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
4. Interpret results
Statistical questions specify populations and measurements of interest and anticipate answers based on data that vary.
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.
How has the WKCE math scores changed for our school?
GAISE Step Two
Designing a plan to collect appropriate data
Types of Variables
Do you know who my favorite horse is?
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.
Takes numerical values for which arithmetic operations such as averaging make sense
Decimals and fractions
Height of a person
Number right on a test
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
When the scientist tested Hans, what were some of the variables that were tested and not tested?
What type were these variables?
A population consists of all members of some specified group.
A sample is a subset of a population. It has the same characteristics as the population.
A measure of a characteristic of an entire population.
A measure of a characteristic of a sample.
• Observational Studies
Random assignment of treatment
Repeat the experiment to a “large” number of subjects
Compare two or more treatments to prevent confounding
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.
Show the design of the Stewart Fist experiment
Read the description of the study done to compare Tai Chi and Yoga.
Answer the questions