1.1.2 - Explanatory & Response Variables | STAT 200

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1.1.2 - Explanatory & Response Variables

In some research studies one variable is used to predict or explain differences in another variable. In those cases, the explanatory variable is used to predict or explain differences in the response variable. In an experimental study, the explanatory variable is the variable that is manipulated by the researcher.

Explanatory Variable

Also known as the independent or predictor variable, it explains variations in the response variable; in an experimental study, it is manipulated by the researcher

Response Variable

Also known as the dependent or outcome variable, its value is predicted or its variation is explained by the explanatory variable; in an experimental study, this is the outcome that is measured following manipulation of the explanatory variable

Example: Panda Fertility Treatments Section

A team of veterinarians wants to compare the effectiveness of two fertility treatments for pandas in captivity. The two treatments are in-vitro fertilization and male fertility medications. This experiment has one explanatory variable: type of fertility treatment. The response variable is a measure of fertility rate.

Example: Public Speaking Approaches Section

A public speaking teacher has developed a new lesson that she believes decreases student anxiety in public speaking situations more than the old lesson. She designs an experiment to test if her new lesson works better than the old lesson. Public speaking students are randomly assigned to receive either the new or old lesson; their anxiety levels during a variety of public speaking experiences are measured. This experiment has one explanatory variable: the lesson received. The response variable is anxiety level.

Example: Coffee Bean Origin Section

A researcher believes that the origin of the beans used to make a cup of coffee affects hyperactivity. He wants to compare coffee from three different regions: Africa, South America, and Mexico. The explanatory variable is the origin of coffee bean; this has three levels: Africa, South America, and Mexico. The response variable is hyperactivity level.

Example: Height & Age Section

A group of middle school students wants to know if they can use height to predict age. They take a random sample of 50 people at their school, both students and teachers, and record each individual's height and age. This is an observational study. The students want to use height to predict age so the explanatory variable is height and the response variable is age.

Example: Grade & Height Section

Research question: Do fourth graders tend to be taller than third graders?

This is an observational study. The researcher wants to use grade level to explain differences in height. The explanatory variable is grade level. The response variable is height.

  • Previous1.1.1 - Categorical & Quantitative Variables
  • Next1.2 - Samples & Populations

Lessons

  • Welcome to STAT 200!
  • 0: Prerequisite Skills
    • 0.1 - Review of Algebra
      • 0.1.1 - Order of Operations
      • 0.1.2 - Summations
      • 0.1.3 - Basic Linear Equations
    • 0.2 - Introduction to Minitab
    • 0.3 - Word's Equation Editor
    • 0.4 - Canvas' Equation Editor
  • 1: Collecting Data
    • 1.1 - Cases & Variables
      • 1.1.1 - Categorical & Quantitative Variables
      • 1.1.2 - Explanatory & Response Variables
    • 1.2 - Samples & Populations
      • 1.2.1 - Sampling Bias
      • 1.2.2 - Sampling Methods
        • 1.2.2.1 - Minitab: Simple Random Sampling
    • 1.3 - Other Sources of Bias
    • 1.4 - Research Study Design
      • 1.4.1 - Confounding Variables
      • 1.4.2 - Causal Conclusions
      • 1.4.3 - Independent and Paired Samples
      • 1.4.4 - Control and Placebo Groups
      • 1.4.5 - Blinding
    • 1.5 - Lesson 1 Summary
  • 2: Describing Data, Part 1
    • 2.1 - Categorical Variables
      • 2.1.1 - One Categorical Variable
        • 2.1.1.1 - Risk and Odds
        • 2.1.1.2 - Visual Representations
          • 2.1.1.2.1 - Minitab: Frequency Tables
          • 2.1.1.2.2 - Minitab: Pie Charts
          • 2.1.1.2.3 - Minitab: Bar Charts
      • 2.1.2 - Two Categorical Variables
        • 2.1.2.1 - Minitab: Two-Way Contingency Table
        • 2.1.2.2 - Minitab: Clustered Bar Chart
        • 2.1.2.3 - Minitab: Stacked Bar Chart
      • 2.1.3 - Probability Rules
        • 2.1.3.1 - Range of Probabilities
        • 2.1.3.2 - Combinations of Events
          • 2.1.3.2.1 - Disjoint & Independent Events
          • 2.1.3.2.2 - Intersections
          • 2.1.3.2.3 - Unions
          • 2.1.3.2.4 - Complements
          • 2.1.3.2.5 - Conditional Probability
            • 2.1.3.2.5.1 - Advanced Conditional Probability Applications
    • 2.2 - One Quantitative Variable
      • 2.2.1 - Graphs: Dotplots and Histograms
      • 2.2.2 - Outliers
      • 2.2.3 - Shape
      • 2.2.4 - Measures of Central Tendency
        • 2.2.4.1 - Skewness & Central Tendency
      • 2.2.5 - Measures of Spread
      • 2.2.6 - Minitab: Central Tendency & Variability
      • 2.2.7 - The Empirical Rule
      • 2.2.8 - z-scores
      • 2.2.9 - Percentiles
      • 2.2.10 - Five Number Summary
    • 2.3 - Lesson 2 Summary
  • 3: Describing Data, Part 2
    • 3.1 - Single Boxplot
    • 3.2 - Identifying Outliers: IQR Method
    • 3.3 - One Quantitative and One Categorical Variable
    • 3.4 - Two Quantitative Variables
      • 3.4.1 - Scatterplots
        • 3.4.1.1 - Minitab: Simple Scatterplot
      • 3.4.2 - Correlation
        • 3.4.2.1 - Formulas for Computing Pearson's r
        • 3.4.2.2 - Example of Computing r by Hand (Optional)
        • 3.4.2.3 - Minitab: Compute Pearson's r
      • 3.4.3 - Simple Linear Regression
        • 3.4.3.1 - Minitab: SLR
        • 3.4.3.2 - Example: Interpreting Output
    • 3.5 - Relations between Multiple Variables
      • 3.5.1 - Scatterplot with Groups
      • 3.5.2 - Bubble Plots
      • 3.5.3 - Time Series Plot
    • 3.6 - Lesson 3 Summary
  • 4: Confidence Intervals
    • 4.1 - Sampling Distributions
      • 4.1.1 - StatKey Examples
        • 4.1.1.1 - NFL Salaries (One Mean)
        • 4.1.1.2 - Coin Flipping (One Proportion)
      • 4.1.2 - Copying Data into StatKey
      • 4.1.3 - Impact of Sample Size
    • 4.2 - Introduction to Confidence Intervals
      • 4.2.1 - Interpreting Confidence Intervals
      • 4.2.2 - Applying Confidence Intervals
    • 4.3 - Introduction to Bootstrapping
      • 4.3.1 - Example: Bootstrap Distribution for Proportion of Peanuts
      • 4.3.2 - Example: Bootstrap Distribution for Difference in Mean Exercise
    • 4.4 - Bootstrap Confidence Interval
      • 4.4.1 - StatKey: Standard Error Method
        • 4.4.1.1 - Example: Proportion of Lactose Intolerant German Adults
        • 4.4.1.2 - Example: Difference in Mean Commute Times
      • 4.4.2 - StatKey: Percentile Method
        • 4.4.2.1 - Example: Correlation Between Quiz & Exam Scores
        • 4.4.2.2 - Example: Difference in Dieting by Biological Sex
        • 4.4.2.3 - Example: One sample mean sodium content
    • 4.5 - Paired Samples
    • 4.6 - Impact of Sample Size on Confidence Intervals
    • 4.7 - Lesson 4 Summary
  • 5: Hypothesis Testing, Part 1
    • 5.1 - Introduction to Hypothesis Testing
    • 5.2 - Writing Hypotheses
      • 5.2.1 - Examples
    • 5.3 - Randomization Procedures
      • 5.3.1 - StatKey Randomization Methods (Optional)
    • 5.4 - p-values
    • 5.5 - Randomization Test Examples in StatKey
      • 5.5.1 - Single Proportion Example: PA Residency
      • 5.5.2 - Paired Means Example: Age
      • 5.5.3 - Difference in Means Example: Exercise by Biological Sex
      • 5.5.4 - Correlation Example: Quiz & Exam Scores
    • 5.6 - Lesson 5 Summary
  • 6: Hypothesis Testing, Part 2
    • 6.1 - Type I and Type II Errors
    • 6.2 - Significance Levels
    • 6.3 - Issues with Multiple Testing
    • 6.4 - Practical Significance
    • 6.5 - Power
    • 6.6 - Confidence Intervals & Hypothesis Testing
    • 6.7 - Lesson 6 Summary
  • 7: Normal Distributions
    • 7.1 - Standard Normal Distribution
    • 7.2 - Minitab: Finding Proportions Under a Normal Distribution
      • 7.2.1 - Proportion 'Less Than'
        • 7.2.1.1 - Example: P(Z<-1)
        • 7.2.1.2 - Example: P(SATM<540)
      • 7.2.2 - Proportion 'Greater Than'
        • 7.2.2.1 - Example: P(Z>0.5)
      • 7.2.3 - Proportion 'In between'
        • 7.2.3.1 - Example: Proportion Between z -2 and +2
      • 7.2.4 - Proportion 'More Extreme Than'
    • 7.3 - Minitab: Finding Values Given Proportions
      • 7.3.1 - Top X%
      • 7.3.2 - Bottom X%
      • 7.3.3 - Middle X%
    • 7.4 - Central Limit Theorem
      • 7.4.1 - Hypothesis Testing
        • 7.4.1.1 - Video Example: Mean Body Temperature
        • 7.4.1.2 - Video Example: Correlation Between Printer Price and PPM
        • 7.4.1.3 - Example: Proportion NFL Coin Toss Wins
        • 7.4.1.4 - Example: Proportion of Women Students
        • 7.4.1.5 - Example: Mean Quiz Score
        • 7.4.1.6 - Example: Difference in Mean Commute Times
      • 7.4.2 - Confidence Intervals
        • 7.4.2.1 - Video Example: 98% CI for Mean Atlanta Commute Time
        • 7.4.2.2 - Video Example: 90% CI for the Correlation between Height and Weight
        • 7.4.2.3 - Example: 99% CI for Proportion of Women Students
    • 7.5 - Lesson 7 Summary
  • 8: Inference for One Sample
    • 8.1 - One Sample Proportion
      • 8.1.1 - Confidence Intervals
        • 8.1.1.1 - Normal Approximation Formulas
          • 8.1.1.1.1 - Video Example: PA Residency
          • 8.1.1.1.2 - Video Example: Dog Ownership
          • 8.1.1.1.3 - Video Example: Books
          • 8.1.1.1.4 - Example: Retirement
        • 8.1.1.2 - Minitab: Confidence Interval for a Proportion
          • 8.1.1.2.1 - Example with Summarized Data
          • 8.1.1.2.2 - Example with Summarized Data
        • 8.1.1.3 - Computing Necessary Sample Size
      • 8.1.2 - Hypothesis Testing
        • 8.1.2.1 - Normal Approximation Method Formulas
          • 8.1.2.1.1 - Video Example: Male Babies
          • 8.1.2.1.2 - Example: Handedness
          • 8.1.2.1.3 - Example: Ice Cream
          • 8.1.2.1.4 - Example: Overweight Citizens
        • 8.1.2.2 - Minitab: Hypothesis Tests for One Proportion
          • 8.1.2.2.1 - Minitab: 1 Proportion z Test, Raw Data
          • 8.1.2.2.2 - Minitab: 1 Sample Proportion z test, Summary Data
            • 8.1.2.2.2.1 - Minitab Example: Normal Approx. Method
    • 8.2 - One Sample Mean
      • 8.2.1 - t Distribution
      • 8.2.2 - Confidence Intervals
        • 8.2.2.1 - Formulas
          • 8.2.2.1.1 - Example: MLB Age
          • 8.2.2.1.2- Example: Sleep Deprivation
          • 8.2.2.1.3 - Example: Milk
        • 8.2.2.2 - Minitab: Confidence Interval of a Mean
          • 8.2.2.2.1 - Example: Age of Pitchers (Summarized Data)
          • 8.2.2.2.2 - Example: Coffee Sales (Data in Column)
        • 8.2.2.3 - Computing Necessary Sample Size
          • 8.2.2.3.1 - Example: Estimating IQ
          • 8.2.2.3.2 - Video Example: Age
          • 8.2.2.3.3 - Video Example: Cookie Weights
      • 8.2.3 - Hypothesis Testing
        • 8.2.3.1 - One Sample Mean t Test, Formulas
          • 8.2.3.1.1 - Video Example: Book Costs
          • 8.2.3.1.2 : Example: Pulse Rate
          • 8.2.3.1.3 - Example: Coffee
          • 8.2.3.1.4 - Example: Transportation Costs
        • 8.2.3.2 - Minitab: One Sample Mean t Tests
          • 8.2.3.2.1 - Minitab: 1 Sample Mean t Test, Raw Data
          • 8.2.3.2.2 - Minitab: 1 Sample Mean t Test, Summarized Data
        • 8.2.3.3 - One Sample Mean z Test (Optional)
    • 8.3 - Paired Means
      • 8.3.1 - Confidence Intervals
        • 8.3.1.1. - Example: Change in Knowledge
        • 8.3.1.2 - Video Example: Difference in Exam Scores
      • 8.3.2 - Hypothesis Testing
        • 8.3.2.1 - Example: Quiz Scores
      • 8.3.3 - Minitab: Paired Means Test
        • 8.3.3.1 - Example: SAT Scores
        • 8.3.3.2 - Example: Marriage Age (Summarized Data)
    • 8.4 - Lesson 8 Summary
  • 9: Inference for Two Samples
    • 9.1 - Two Independent Proportions
      • 9.1.1 - Confidence Intervals
        • 9.1.1.1 - Minitab: Confidence Interval for 2 Proportions
      • 9.1.2 - Hypothesis Testing
        • 9.1.2.1 - Normal Approximation Method Formulas
          • 9.1.2.1.1 – Example: Ice Cream
          • 9.1.2.1.2 – Example: Same Sex Marriage
        • 9.1.2.2 - Minitab: Difference Between 2 Independent Proportions
          • 9.1.2.2.1 - Example: Dating
    • 9.2 - Two Independent Means
      • 9.2.1 - Confidence Intervals
        • 9.2.1.1 - Minitab: Confidence Interval Between 2 Independent Means
          • 9.2.1.1.1 - Video Example: Mean Difference in Exam Scores, Summarized Data
      • 9.2.2 - Hypothesis Testing
        • 9.2.2.1 - Minitab: Independent Means t Test
          • 9.2.2.1.1 - Example: Summarized Data
          • 9.2.2.1.3 - Example: Height by Sex
    • 9.3 - Lesson 9 Summary
  • 10: One-Way ANOVA
    • 10.1 - Introduction to the F Distribution
    • 10.2 - Hypothesis Testing
    • 10.3 - Pairwise Comparisons
    • 10.4 - Minitab: One-Way ANOVA
    • 10.5 - Example: SAT-Math Scores by Award Preference
    • 10.6 - Example: Exam Grade by Professor
    • 10.7 - Lesson 10 Summary
  • 11: Chi-Square Tests
    • 11.1 - Reviews
      • 11.1.1 - Frequency Table
      • 11.1.2 - Two-Way Contingency Table
      • 11.1.3 - Probability Distribution Plots
      • 11.1.4 - Conditional Probabilities and Independence
    • 11.2 - Goodness of Fit Test
      • 11.2.1 - Five Step Hypothesis Testing Procedure
        • 11.2.1.1 - Video: Cupcakes (Equal Proportions)
        • 11.2.1.2- Cards (Equal Proportions)
        • 11.2.1.3 - Roulette Wheel (Different Proportions)
      • 11.2.2 - Minitab: Goodness-of-Fit Test
        • 11.2.2.1 - Example: Summarized Data, Equal Proportions
        • 11.2.2.2 - Example: Summarized Data, Different Proportions
    • 11.3 - Chi-Square Test of Independence
      • 11.3.1 - Example: Gender and Online Learning
      • 11.3.2 - Minitab: Test of Independence
        • 11.3.2.1 - Example: Raw Data
        • 11.3.2.2 - Example: Summarized Data
      • 11.3.3 - Relative Risk
    • 11.4 - Lesson 11 Summary
  • 12: Correlation & Simple Linear Regression
    • 12.1 - Review: Scatterplots
    • 12.2 - Correlation
      • 12.2.1 - Hypothesis Testing
        • 12.2.1.1 - Example: Quiz & Exam Scores
        • 12.2.1.2 - Example: Age & Height
        • 12.2.1.3 - Example: Temperature & Coffee Sales
      • 12.2.2 - Correlation Matrix
        • 12.2.2.1 - Example: Student Survey
        • 12.2.2.2 - Example: Body Correlation Matrix
    • 12.3 - Simple Linear Regression
      • 12.3.1 - Formulas
      • 12.3.2 - Assumptions
      • 12.3.3 - Minitab - Simple Linear Regression
      • 12.3.4 - Hypothesis Testing for Slope
        • 12.3.4.1 - Example: Quiz and exam scores
        • 12.3.4.2 - Example: Business Decisions
      • 12.3.5 - Confidence Interval for Slope
        • 12.3.5.1 - Example: Quiz and exam scores
    • 12.4 - Coefficient of Determination
    • 12.5 - Cautions
    • 12.6 - Correlation & Regression Example
    • 12.7 - Lesson 12 Summary

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