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Analyzing Quantitative Data: Key Concepts and Inferential Statistics in Research

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In this week's focus on quantitative data analysis, we explore critical concepts in inferential statistics. We'll discuss how to prepare your data, including coding and cleaning, and dive into the importance of making informed decisions in hypothesis testing. Key questions will evaluate the implications of rejecting null hypotheses, the differences between statistical and practical significance, and the dangers of Type I and Type II errors. As you prepare for next week’s reflections, consider how effectively you can analyze data to answer your research questions.

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Analyzing Quantitative Data: Key Concepts and Inferential Statistics in Research

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  1. EDUC 894 Week 11 Quantitative Data Analysis 2

  2. Plan for Today • Report # 3 In • Inferential Statistics • Big Ideas Discussion --------------------Dinner Break------------------- • Calculating and Interpreting Statistics • For next week: • Exhale, you’ve jut handed in Report #3! • Read Goddard & Feynman (we’ll spend time next class discussing the implications for your reports) • Start Research Reflection?

  3. Analyzing Quantitative Data – Key Concerns • #1 Concern: What are you trying to find out? What questions do you want to ask the data? • #2 Concern: How can a set of number used to represent some aspects of the world be organized to help you answer that question? • #3 Concern: Are there any issues with your data that might affect the validity of this answer?

  4. Analyzing Quantitative Data – Key Process Steps • Preparing Your Data • Coding & Cleaning • Descriptive Statistics • We’re making statements about the actual people you collected data from (your sample) • Inferential Statistics • We’re trying to claim that what we found for our sample is likely to be true for some larger population

  5. Inferential Statistics:Discussion Questions Question 1: The Big Decision • In hypothesis testing, what is the “big decision” that needs to be made? Why is this important and what does it mean? What are the dangers we worry about in making this decision?

  6. Inferential Statistics:Discussion Questions Question 1: The Big Decision • Do we always want to reject H0? • Are we always comparing 2 groups? • Is rejecting H0 the same as saying that HA is true? • How does effect size influence our decision on whether or not to reject H0 ? • How do you know when you make a Type I or Type II error?

  7. Inferential Statistics:Discussion Questions Type I and Type II Errors

  8. Inferential Statistics:Discussion Questions Question 2: Which way? (dir/non-dir hyp) • What is the difference between directional and non-directional hypotheses? How does this choice affect the statistics (conceptually?) Based on this, which is a better kind of hypothesis to use?

  9. Inferential Statistics:Discussion Questions Question 2: Which way? (dir/non-dir hyp) • How does the directionality of the hypothesis affect the p-value? • How does the directionality of the hypothesis affect the likelihood of making a Type I or Type II error? • If you only expect a treatment to make a small difference, should you use a one-tailed test?

  10. Inferential Statistics:Discussion Questions Question 3: Statistical vs. Practical Sig • What is the difference between statistical significance (think of a t-test) and practical significance (think of effect size)? What kinds of claims does each one let you make? Which one do you think is more important and why?

  11. Inferential Statistics:Discussion Questions Question 3: Statistical vs. Practical Sig • “Both are important - there is little point in getting excited by a large effect size when there is a high likelihood that chance plays a role in the difference, or that a study has high statistical significance, but a small effect size.” -M. Chu, 2008

  12. Inferential Statistics:Discussion Questions Question 3: Statistical vs. Practical Sig • Two stop-smoking treatments were each tested against a control group for the average # of cigarettes smoked by people in the group after the treatment. • ClearSkies produced a significant result at the .05 level (p<.05) • SmokeByeBye produced a significant result at the .01 level (p<.01) • Which treatment will help you stop smoking faster? • Can you have statistical significance without practical significance? • What about visa versa?

  13. Inferential Statistics:Language Issues • Things NOT to say • “statistical difference” • “insignificant” • “highly significant” • “approaching significance” • “p-test”

  14. Dinner Break

  15. Calculating and Interpreting Statistics – Key Process Steps • Preparing Your Data • Examining, Coding & Cleaning • Descriptive Statistics • Characterize the sample • Inferential Statistics • Looking for differences / relationships within the data

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