1.5: Exploring Statistical Questions
- Page ID
- 58857
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Thinking Like a Statistician – A Guided Experience
Now that you've seen the building blocks of a statistical investigation including data types, sampling, randomness, and bias, it's time to bring it all together. In this section, you'll engage with a real question and work through the full cycle of a statistical study.
This will give you practice using the language and structure you’ve learned so far, and prepare you for more complex analyses in future chapters.
Step-by-Step: The Statistical Process
Six major steps that can guide statistical thinking:
- Ask a question that can be answered with data
- Collect accurate and relevant data
- Organize and summarize the data to understand its structure
- Analyze the data to find patterns or test relationships
- Interpret the results in context
- Communicate your findings clearly and effectively
Below are five sample statistical questions representing different real-world domains. Choose one that interests you most, and walk through the six steps, using the guiding prompts provided.
Choose One Question from the List Below
- Education: Do students who participate in after-school tutoring programs perform better on standardized math tests?
- Environment: Is there a relationship between air quality and asthma-related hospital visits in major cities?
- Health: How does average daily screen time differ between high school students who sleep 6 or fewer hours and those who sleep 8 or more?
- Business: Does the size of a restaurant’s menu affect the average customer rating on review platforms?
- Sports: Are baseball players with higher batting averages more likely to have higher on-base percentages?
Work Through the Process
Take your chosen question and apply the steps below. Use your notebook, a worksheet, or small group discussion to organize your thinking. Some of the ideas, vocab or concepts below may be unfamiliar, but take some time thinking about each of the steps as well as the process as a whole. Throughout the book we will reflect back on these steps with the goal of filling in all the concepts and details.
1. Ask a Clear Question
Rephrase the topic into a well-formed statistical question.
- Does your question involve variability?
- Can it be answered by collecting real data (not just opinions)?
- What exactly are you comparing or examining?
2. Collect Accurate and Relevant Data
Imagine or sketch out a plan to collect meaningful data.
- Who or what will you study (your population)?
- Will you take a sample, and if so, how will you select it?
- Where will the data come from? A survey, experiment, database, or sensors?
- Could any forms of bias affect your results?
3. Organize and Summarize the Data
Think about how to make sense of what you collect.
- Would tables, averages, or percentages be useful?
- What types of graphs or displays might help explain the data?
- How will you account for trends, groups, or outliers?
4. Analyze the Data
What relationship or pattern are you looking for?
- Are you comparing two groups? Looking for a correlation?
- Will you be calculating differences, percent changes, or association measures?
- Would a statistical test or confidence interval help support your findings later?
5. Interpret the Results in Context
What do your calculations and patterns actually mean?
- What is your overall takeaway?
- How confident are you in your result? What limitations exist?
- Could there be alternative explanations?
6. Communicate Clearly and Effectively
Imagine explaining this to someone unfamiliar with the data.
- How would you explain your findings in plain English?
- What visuals or summaries would support your answer?
- What key information must be included to avoid misinterpretation?
Looking Ahead: Designing a Statistical Study
Next we will look at how to synthesis ideas of questions, sampling, and data collection into the framework of a statistical study.