Learning Math: Data Analysis, Statistics, and Probability
Designing Experiments Homework
Conduct your own comparative study. It can be an observational study or an experimental study. The questions below should serve as guidelines as you proceed.
1. Ask a Question
a. What question would you like to answer with your study?
b. What population are you seeking to answer this question for? For example, the population might be teachers at your school, or boxes of Brand A raisins.
2. Collect Appriopriate Data
c. Come up with a design for your study, one that seeks to remove sources of potential bias. (See Design 5 of Problem C4 for a possible design strategy.) Remember that to answer your question, you will need two sets of data to compare. Make sure that you collect enough data to analyze; you should use at least 12 subjects (16, if possible).
d. If you’ve chosen an experimental study, what treatment will you be investigating? Remember that the goal of an experimental study is to judge the effectiveness of a particular treatment.
3. Analyze the Data
e. Determine Five-Number Summaries and box plots for each set of data you collect, and compare the box plots side by side.
4. Interpret the Results
f. Does your data answer the original question? Do your results suggest any new questions? If the data you collected did not answer the question, how might you modify the study to answer the question more thoroughly?
Noether, Gottfried (1994). Mental Random Numbers: Perceived and Real Randomness. In Teaching Statistics at Its Best (pp. 40-41). University of Sheffield, England: Teaching Statistics Trust.
This article first appeared in Teaching Statistics <http://science.ntu.ac.uk/rsscse/ts/> and is used with permission.
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Mental Random Numbers: Perceivedand Real Randomness
Solution: Problem H1
Answers will vary.
Session 1 Statistics As Problem Solving
Consider statistics as a problem-solving process and examine its four components: asking questions, collecting appropriate data, analyzing the data, and interpreting the results. This session investigates the nature of data and its potential sources of variation. Variables, bias, and random sampling are introduced.
Session 2 Data Organization and Representation
Explore different ways of representing, analyzing, and interpreting data, including line plots, frequency tables, cumulative and relative frequency tables, and bar graphs. Learn how to use intervals to describe variation in data. Learn how to determine and understand the median.
Session 3 Describing Distributions
Continue learning about organizing and grouping data in different graphs and tables. Learn how to analyze and interpret variation in data by using stem and leaf plots and histograms. Learn about relative and cumulative frequency.
Session 4 Min, Max and the Five-Number Summary
Investigate various approaches for summarizing variation in data, and learn how dividing data into groups can help provide other types of answers to statistical questions. Understand numerical and graphic representations of the minimum, the maximum, the median, and quartiles. Learn how to create a box plot.
Session 5 Variation About the Mean
Explore the concept of the mean and how variation in data can be described relative to the mean. Concepts include fair and unfair allocations, and how to measure variation about the mean.
Session 6 Designing Experiments
Examine how to collect and compare data from observational and experimental studies, and learn how to set up your own experimental studies.
Session 7 Bivariate Data and Analysis
Analyze bivariate data and understand the concepts of association and co-variation between two quantitative variables. Explore scatter plots, the least squares line, and modeling linear relationships.
Session 8 Probability
Investigate some basic concepts of probability and the relationship between statistics and probability. Learn about random events, games of chance, mathematical and experimental probability, tree diagrams, and the binomial probability model.
Session 9 Random Sampling and Estimation
Learn how to select a random sample and use it to estimate characteristics of an entire population. Learn how to describe variation in estimates, and the effect of sample size on an estimate's accuracy.
Session 10 Classroom Case Studies, Grades K-2
Explore how the concepts developed in this course can be applied through a case study of a K-2 teacher, Ellen Sabanosh, a former course participant who has adapted her new knowledge to her classroom.
Session 11 Classroom Case Studies, Grades 3-5
Explore how the concepts developed in this course can be applied through case studies of a grade 3-5 teacher, Suzanne L'Esperance and grade 6-8 teacher, Paul Snowden, both former course participants who have adapted their new knowledge to their classrooms.