📊AP Statistics Unit 3 – Collecting Data

Key Concepts

• Population refers to the entire group of individuals, objects, or events that a researcher is interested in studying
• Sample is a subset of the population that is selected for study and is used to make inferences about the population
• Parameter is a numerical summary that describes a characteristic of a population (mean, standard deviation)
• Statistic is a numerical summary that describes a characteristic of a sample (sample mean, sample standard deviation)
• Variables are characteristics or attributes that can be measured or observed and vary among individuals in a population
  • Quantitative variables have numerical values and can be discrete (whole numbers) or continuous (any value within a range)
  • Qualitative variables are categorical and can be nominal (no inherent order) or ordinal (natural order)
• Sampling bias occurs when some members of the population are more likely to be selected for the sample than others, leading to a sample that is not representative of the population
• Nonresponse bias happens when individuals who respond to a survey differ systematically from those who do not respond

Types of Data

• Categorical data consists of observations that can be classified into distinct categories or groups (gender, race, political affiliation)
• Numerical data involves observations that are measured on a numerical scale and can be either discrete or continuous
  • Discrete data can only take on certain values, often whole numbers (number of siblings, number of cars owned)
  • Continuous data can take on any value within a specified range (height, weight, temperature)
• Cross-sectional data is collected at a single point in time from different individuals or groups
• Time series data is collected over a period of time, typically at regular intervals, from the same individual or group
• Observational data is collected by observing and recording information without manipulating any variables
• Experimental data is collected by deliberately manipulating one or more variables while controlling other factors and measuring the effect on the response variable

Sampling Methods

• Simple random sampling ensures that each member of the population has an equal chance of being selected for the sample
  • Requires a complete list of all members of the population (sampling frame)
  • Can be done with or without replacement (member can be selected more than once)
• Stratified random sampling divides the population into distinct subgroups (strata) based on a specific characteristic and then randomly samples from each stratum
  • Ensures that each subgroup is represented in the sample in proportion to its size in the population
• Cluster sampling involves dividing the population into clusters (naturally occurring groups) and then randomly selecting entire clusters to include in the sample
  • Useful when a complete list of all members of the population is not available or when the population is geographically dispersed
• Systematic sampling selects every kth member from a list of the population, starting with a randomly chosen member
  • Requires a complete list of all members of the population in a specific order
• Convenience sampling selects members of the population who are easily accessible or readily available (mall intercept, online surveys)
  • Not a probability sampling method and may lead to biased results

Data Collection Techniques

• Surveys involve asking a sample of individuals a set of questions to gather information about their opinions, behaviors, or characteristics
  • Can be conducted through various modes (face-to-face, telephone, mail, online)
  • Require careful design to ensure that questions are clear, unbiased, and elicit accurate responses
• Interviews are a more in-depth form of data collection that involves asking open-ended questions to gather detailed information from respondents
  • Can be structured (fixed set of questions), semi-structured (mix of fixed and open-ended questions), or unstructured (no fixed questions)
• Observations involve collecting data by watching and recording the behavior of individuals or groups in a natural setting
  • Can be participant (researcher is part of the group being observed) or non-participant (researcher is not part of the group)
• Experiments involve deliberately manipulating one or more variables (independent variables) while controlling other factors and measuring the effect on the response variable (dependent variable)
  • Require random assignment of subjects to treatment and control groups to ensure that any differences in the response variable are due to the manipulation of the independent variable(s)
• Secondary data analysis involves using data that has already been collected by someone else for a different purpose
  • Requires careful evaluation of the quality and appropriateness of the data for the current research question

Survey Design

• Clearly define the research question and target population before designing the survey
• Use simple, clear, and unbiased language in the questions to ensure that respondents understand what is being asked
• Avoid leading questions that suggest a particular answer or double-barreled questions that ask about more than one thing at a time
• Use closed-ended questions with a fixed set of response options for easier data analysis and open-ended questions to gather more detailed information
• Consider the order of the questions and group related questions together to improve the flow of the survey
• Pretest the survey with a small sample of the target population to identify any problems with the questions or response options
• Include clear instructions and definitions for any technical terms or concepts used in the survey
• Offer incentives for participation, if appropriate, to increase response rates

Experimental Design

• Clearly define the research question and hypotheses before designing the experiment
• Identify the independent variable(s) (factors that will be manipulated) and the dependent variable (outcome that will be measured)
• Use a control group that does not receive the treatment to serve as a basis for comparison
• Randomly assign subjects to treatment and control groups to ensure that any differences in the dependent variable are due to the manipulation of the independent variable(s)
• Control for extraneous variables (factors that could affect the dependent variable but are not of interest) by holding them constant or using blocking
• Use blinding (single or double) to prevent bias in the measurement of the dependent variable
• Determine the appropriate sample size and power to detect a meaningful difference between the treatment and control groups
• Use appropriate statistical methods to analyze the data and draw conclusions about the effect of the independent variable(s) on the dependent variable

Potential Biases and Errors

• Selection bias occurs when the sample is not representative of the population due to the way in which subjects are selected
  • Can be reduced by using probability sampling methods and ensuring that the sampling frame is complete and up-to-date
• Response bias occurs when respondents do not answer questions truthfully or accurately due to social desirability, acquiescence, or other factors
  • Can be reduced by using neutral language in questions, offering anonymity or confidentiality, and using multiple methods to measure the same construct
• Nonresponse bias occurs when those who do not respond to a survey differ systematically from those who do respond
  • Can be reduced by using follow-up procedures to increase response rates and comparing the characteristics of respondents and nonrespondents
• Measurement error occurs when the instruments or methods used to collect data are not reliable or valid
  • Can be reduced by using established and validated measures, pretesting instruments, and using multiple methods to measure the same construct
• Sampling error occurs when the sample statistics differ from the population parameters due to chance variation in the sampling process
  • Can be reduced by increasing the sample size and using stratified or cluster sampling to ensure that subgroups are adequately represented

Ethical Considerations

• Obtain informed consent from participants by providing them with information about the purpose, procedures, risks, and benefits of the study and ensuring that they understand their rights as participants
• Protect the privacy and confidentiality of participants by using secure data storage and reporting methods and not disclosing identifying information without permission
• Avoid deception by being truthful about the purpose and procedures of the study and debriefing participants afterwards if deception was necessary
• Minimize harm to participants by carefully weighing the risks and benefits of the study and taking steps to prevent or mitigate any potential harm
• Respect the autonomy of participants by allowing them to make their own decisions about whether to participate and to withdraw from the study at any time without penalty
• Ensure that the study is justified by the potential benefits to society and that the risks to participants are reasonable in relation to the anticipated benefits
• Report the results of the study accurately and honestly, including any limitations or negative findings, and make the data available for replication by other researchers