Probability and Statistics Terminology, Experimental Design, and Ethics

�Random Variables

A Random Variable is a variable whose value depends on the outcome of a random experiment

• The number of pips on the top face of a die after it is rolled
• The distance of a golf ball hit off of a tee
• The height of an individual on their 18^th birthday
• The color of a car passing through a lane at a highway toll

A random variable is considered Categorical (or Qualitative) if the values it takes on are categories or groups

A random variable is considered Numerical (or Quantitative) if it is meaningful to average a set of observed outcomes together

• A numerical variable is discrete if its observed values can be counted, while it is continuous if [theoretically] any numeric value could be observed

�Samples versus Populations

Population

• The entire group we are interested in studying
• Impractical to collect data from
• Too large
• Too fluid

Sample

• A subset of the population from which we collect data
• If representative of the population, gives insight into population characteristics
• Insights aren’t perfect because they are sample-dependent

�Describing Samples versus Describing Populations

Populations (Inferential Statistics)

• Population parameters
• Population mean, μ
• Population standard deviation, σ
• Population proportion,  ρ 
• Want to find or describe these parameters, but we can’t do it directly

Samples (Descriptive Statistics)

• Sample statistics
• Sample mean, x̄
• Sample standard deviation, s
• Sample proportion, p or p̂
• Can find these statistics directly and, under certain conditions, use them to approximate population parameters

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�Sampling Methods

Samples must be representative of our target population if we want inferences to be valid

• Census (generally infeasible)
• Simple random sample
• Stratified sample
• Cluster sampling
• Multistage sampling
• Systematic sampling
• Convenience sampling (for exploratory purposes only)

�Sampling Error, Non-Sampling Error, and Sampling Bias

The difference between a sample statistic and the corresponding population parameter is called the sampling error

• Sampling error is unavoidable
• Different samples result in different sample statistics
• Sampling error is a random variable

Non-sampling error is error not due to the sampling process (for example, measurement errors due to faulty equipment)

Sampling bias is present when not every element of the population has equal likelihood of being included in the sample (results in non-representative sample and invalid conclusions)

�Basics of Experimental Design

• The response variable is the primary variable being studied – it is the “outcome”
• The response variable is sometimes called a dependent variable, and is usually graphed along the vertical (y-axis)
• Explanatory variables are variables which we think might influence the response
• Explanatory variables are often referred to as independent variables and are typically graphed along the horizontal (x-axis)
• Lurking or confounding variables influence both the response and at least one explanatory variable
• These variables make it difficult to isolate associations between the explanatory variable and response

Randomized Experiments and �Observational Studies

• Randomized Experiments (or Randomized Control Trials, RCTs), researchers manipulate values of an explanatory variable (a treatment) for experimental units
• Random assignment between control or treatment groups distribute confounders or lurking variables proportionally
• Can use blocking variables to force proportionality across groups
• Since the only difference between groups is the treatment, randomized experiments permit causal (cause and effect) interpretations
• Observational studies lack random assignment and only permit interpreting ”associations”

�Additional Strategies in RCTs

• The belief that an individual is receiving a beneficial treatment can result in observed improvements in a response variable, called the placebo effect
• In RCTs, groups are nearly always blinded so that participants do not know whether they are in a treatment or control group
• Individuals facilitating an RCT can treat participants differently if they know whether the participant belongs to a control or treatment group
• Studies use double-blinding to ensure that neither participants or facilitators are aware of what group a participant belongs to

�Ethics in Experiments and Analysis

• Sometimes running an RCT is impossible due to ethical implications
• For example, in a hypothetical study on the effects of opioid use during pregnancy, it would be unethical to create a treatment group of expectant mothers and have them take opioids throughout their pregnancies
• Publication bias has also encouraged bad behaviors in research
• Brian Wansink had over 15 papers retracted after complaining on a blog that a graduate student refused to “p-hack” (a phenomena we’ll discuss later)
• Diederik Stapel lost his job and reputation for falsifying data
• Check out the Retraction Watch blog for more

�Ethics Guardrails

Because of ethical issues in experimentation and data analysis, guidelines and laws have been put in place to protect participants in studies

• The American Statistical Association (ASA) has published ethical research expectations
• The US Department of Heath and Human Services provides guidelines and laws around ethical research
• Universities have Internal Review Boards (IRB) to get approval to run experiments
• Many communities recommend (or demand) pre-registration of hypotheses

Exit Ticket

Navigate to our MAT240 Exit Ticket Form, answer the questions, and complete the task below.

Note. Today’s discussion is listed as 2. Intro to Data

Task: Describe a study that you might be interested in conducting. Identify the response (outcome) variable and any explanatory variables you might be interested in. Are there any ethical concerns around your study that you should be aware of?

�Next Time…

• What we’ll be doing…
• Unlocking Excel: An Overview of Excel for Data Analysis
• Software setup…
• Make sure that you can access Excel via Office 365
• Bring your computer to class with you

Homework: Complete the Topic 2 – An Introduction to Spreadsheets interactive prep-work activity and submit the hash code using the Google Form from this week’s BrightSpace Announcement.