Descriptive Correlational Methods, Survey Methodology, and Statistical Correlations

The Survey Method in Descriptive Correlational Research

• Definition and Scope of Surveys:

  • A survey is a descriptive research method used to measure the prevalence of specific beliefs, attitudes, or behaviors within a given population.
  • Data collection is conducted through direct questions, administered either via written questionnaires or oral interviews.
  • Common survey questions include:
  • "Do you approve of the job the president is doing?"
  • "Should we get out and end the war in Iran?"
  • "What do you think of our product?"
  • Surveys are designed to assess internal, unobservable mental states, beliefs, and attitudes that cannot be measured through direct observation.

• Sampling Requirements:

  • Random or Representative Sample:
  • A sample is considered random when every individual in the relevant population has an equal probability of being selected as a participant.
  • Example: In a study examining the effects of marijuana on memory, every college student in the target population must have an equal chance of being selected for the study.
  • Challenges in Sampling:
  • It is difficult to construct and execute a perfectly random or representative sample.
  • Even when participants are properly selected, not every selected individual agrees to participate.
  • Generalizability:
  • The closer a study comes to obtaining a true random or representative sample, the higher the assurance that the findings apply to the entire target population, rather than strictly to the studied sample (e.g., concluding that marijuana impairs memory across all college students).

Key Problems and Methodological Challenges in Survey Research

• Sampling Bias and Non-Representative Samples:

  • A prominent historical case study of sampling bias is the $1936$ United States presidential election poll conducted by the Literary Digest.
  • Background and Methodology:
  • Goal: Predict whether Democratic candidate Franklin Delano Roosevelt or Republican candidate Alfred Landon would win the election.
  • Sample Selection: Distributed $10,000,000$ postcard questionnaires to individuals listed in telephone directories and automobile registration records.
  • Response Volume: Received $2,000,000$ completed postcard responses.
  • Outcome and Analysis:
  • Prediction: The survey predicted that Republican candidate Alfred Landon would win.
  • Actual Result: Franklin Delano Roosevelt won the presidency in a landslide victory.
  • Failure Analysis: In $1936$, during the Great Depression, only affluent individuals could afford telephone service or automobiles. Wealthier individuals were substantially more likely to vote Republican.
  • Illustrative Anecdote: Basketball player and announcer Charles Barkley once told his mother he was considering voting for George H.W. Bush. His mother stated, "Charles, don't you only know that rich people vote for Republicans?" to which Barkley replied, "Ma, I am rich."
  • Methodological Lesson: Sample size alone does not guarantee accuracy; a sample of $2,000,000$ respondents will yield invalid results if the sample is non-representative.

• Careless and Unthoughtful Responses:

  • Respondents often answer survey questions without careful reading or logical processing.
  • Case Study on Extraterrestrial Life:
  • In a survey question asking whether intelligent life exists on other planets, only $45\%$ of respondents agreed.
  • A subsequent question in the same survey asked if the government is hiding evidence of intelligent life on other planets, and $82\%$ of respondents answered affirmatively.
  • Logical Inconsistency: $37\%$ of respondents ($82\% - 45\% = 37\%$) reported believing that the government is concealing evidence of something they stated does not exist, demonstrating that participants did not thoroughly analyze the questions.

• Question Wording and Leading Questions:

  • Survey items must be framed neutrally to prevent bias.
  • Definition of Leading Question: A question phrased in a way that suggests or prompts a specific desired answer.

• Socially Desirable Responding:

  • Even in anonymous surveys, respondents frequently answer questions in a manner that presents themselves in a favorable light.
  • Examples:
  • Attendance at Religious Services: More individuals report attending religious services regularly than actually attend based on objective counts.
  • Voter Turnout: A higher percentage of people claim to have voted in recent presidential elections than the percentage of the population that actually cast ballots.

Fundamentals of Correlational Research and Correlation Coefficients

• Definition of Correlational Research:

  • Measures the direction and strength of the relationship between two or more variables without manipulating or controlling any of the variables.
  • Definition of Variable: Any measurable entity, characteristic, or condition that varies among individuals (e.g., educational attainment, income, number of vehicles, number of homes).

• Contrast with Experimental Methods:

  • Experimental methods require high levels of researcher control, including managing variable exposure (e.g., controlling which participants receive a brownie containing THC and which do not).
  • Correlational methods exercise zero control or manipulation over the variables being evaluated.

• Variations in Correlation Strength:

  • Different pairs of variables display varying degrees of association.
  • Example: The number of novels an individual reads per week has a significantly stronger correlation with vocabulary size than with knowledge of chemistry.

• Correlation Coefficient ($r$):

  • A statistical value that quantifies the strength and direction of the relationship between variables.
  • Range: Values are strictly bounded between $+1.0$ and $-1.0$.
  • Independence of Sign and Strength:
  • The plus ($+$) or minus ($-$) sign indicates direction only and does not denote the strength of the correlation.
  • A correlation of $-1.0$ reflects a relationship equal in strength to a correlation of $+1.0$.
  • A correlation of $-1.0$ is stronger than a correlation of $+0.9$.

Directionality and Types of Correlations

• Positive Correlation:

  • Occurs when two variables move in the same direction (both variables increase together, or both variables decrease together).
  • Examples:
  • Academic Performance: Higher high school GPA is associated with higher college GPA; lower high school GPA is associated with lower college GPA.
  • Health Factors: Age and the percentage of the population experiencing sleeping problems show a positive correlation, as both variables increase concurrently.

• Negative Correlation:

  • Occurs when two variables move in opposite directions (as one variable increases, the second variable decreases, and vice versa).
  • Example:
  • Class Absences: Class absences and exam scores show a negative correlation (a higher number of absences correlates with lower exam scores; a lower number of absences correlates with higher exam scores).

• Values and Graphical Representations ($r$):

  • Strong Correlation: An $r$ value of $r = 0.9$ indicates a strong correlation where observed data points cluster near a linear trend line.
  • Perfect Positive Correlation ($r = +1.0$): Data points fall on a straight line sloping upward.
  • Perfect Negative Correlation ($r = -1.0$): Data points fall on a straight line sloping downward.
  • Zero Correlation ($r = 0$): Indicates no statistical relationship between variables; as one variable changes, the second variable varies unpredictably.

Predictive Utility of Correlations

• Absence of Causation:

  • Correlational research cannot demonstrate causal relationships between variables.

• Value in Prediction:

  • If a strong correlation exists between two variables (whether positive or negative), knowing the value of one variable allows for the mathematical prediction of the unknown variable.