Course: PSY 301 Understanding Statistics, East Texas A&M Source: Moore & Notz, Statistics: Concepts and Controversies, 10th ed., Chapters 1, 3, 8 Covers: Exam 1 material
Difficulty: Introductory Prerequisites: None. This is the foundation for everything else in the course.
Statistics is the science of collecting, organising, and drawing conclusions from data. Before you can do any analysis, you need to understand what data looks like, where it comes from, and whether you can trust it. Chapters 1, 3, and 8 lay that groundwork: what counts as data, how samples are drawn from populations, and how measurement quality (bias, reliability, validity) shapes every conclusion that follows. If you get these concepts wrong, nothing downstream will make sense.
Data are values collected on individuals. Good data come from well-designed samples that avoid bias. Any measurement you use needs to be both reliable (consistent) and valid (measuring the right thing), or your statistical conclusions fall apart.
Data
Systematically recorded information, usually organised in a table where rows are individuals and columns are variables. In simple terms, data is the raw material of statistics: the numbers, labels, or categories you collect before doing anything analytical.
Individuals (cases, subjects, units)
The objects or people described by a set of data. Think of it as: each row in your data table is one individual.
Variable
Any characteristic of an individual that can take different values. In simple terms, a variable is whatever you are measuring or recording about each person or thing in your study.
Categorical variable (qualitative variable)
A variable that places each individual into one of several groups or categories. Think of it as: labels, not numbers. Eye colour, political party, and yes/no responses are all categorical.
Quantitative variable (numerical variable)
A variable whose values are meaningful numbers on which arithmetic makes sense. In simple terms, if you can sensibly add or average the values, the variable is quantitative. Height, test scores, and reaction time are examples.
Population
The entire group of individuals you want information about. Think of it as: the full set, whether it is every university student in Texas or every manufactured widget in a factory.
Sample
A subset of the population that is actually examined or measured. In simple terms, because studying an entire population is usually impractical, you study a sample and use it to make inferences about the population.
Sampling frame
The list of individuals from which a sample is drawn. Think of it as: the practical version of the population. If your population is "all enrolled students" and you sample from a registration list, that list is your sampling frame.
Simple random sample (SRS)
A sample chosen so that every possible group of a given size has an equal chance of being selected. In simple terms, this is the gold standard of sampling: everyone gets a fair shot at being included, and no subgroup is systematically favoured.
Stratified random sample
A sample obtained by dividing the population into non-overlapping groups (strata) and then taking a separate random sample from each stratum. Think of it as: making sure key subgroups are represented before you randomise within them.
Cluster sample
A sample obtained by randomly selecting entire groups (clusters) and then measuring everyone within those clusters. In simple terms, instead of picking individuals, you pick whole classrooms, neighbourhoods, or clinics.
Convenience sample
A sample chosen because it is easy to reach, not because it is representative. Think of it as: surveying your flatmates because they happen to be there. Quick, but unreliable for generalising.
Voluntary response sample
A sample that consists of people who choose to participate on their own. In simple terms, this is what you get when you post a survey link and wait. The people who respond are usually those with strong opinions, so results skew.
Bias
A systematic tendency to over- or underestimate the true value of a characteristic in the population. Think of it as: a consistent lean in one direction. Bias is not random error; it is a pattern that repeats every time you use the same flawed method.
Selection bias (undercoverage)
Bias that occurs when some members of the population are systematically excluded from the sample. In simple terms, if your sampling frame misses a chunk of the population, your results cannot speak for those people.
Nonresponse bias
Bias that occurs when individuals selected for the sample do not participate, and they differ from those who do. Think of it as: the people who ignore your survey might have very different views from the people who complete it.
Response bias
Bias introduced by how questions are worded, who asks them, or the social desirability of certain answers. In simple terms, people sometimes lie or misremember, especially on sensitive topics, and question phrasing can push answers in a particular direction.
Reliability
The consistency or repeatability of a measurement. Think of it as: if you measure the same thing twice, do you get roughly the same answer? A reliable bathroom scale gives you similar readings each morning.
Validity
The extent to which a measurement captures what it is supposed to capture. In simple terms, a test is valid if it measures the concept you intend. A maths test given in a language the student does not speak might be reliable (consistent scores each time) but not a valid measure of maths ability.
Confounding variable (confound, lurking variable)
A variable that is associated with both the explanatory variable and the outcome, making it impossible to tell which is responsible for the observed effect. Think of it as: a hidden third factor muddying the relationship you are trying to study.
Explanatory variable (independent variable)
The variable you suspect causes or influences the outcome. In simple terms, this is the variable you manipulate or focus on to see its effect.
Response variable (dependent variable)
The variable you measure as the outcome. Think of it as: the result you are interested in explaining or predicting.
Statistics begins with data: values recorded on a set of individuals.
Every dataset has two components:
The individuals (who or what is being studied)
The variables (what is being measured about each individual)
Variables divide into categorical (group labels) and quantitative (meaningful numbers).
Asking "does the average make sense?" is a quick test. The average of jersey numbers is meaningless, so jersey number is categorical despite being a number.
A well-organised data table has one row per individual and one column per variable. This structure, sometimes called "tidy data," makes analysis possible.
The goal of sampling is to learn about a population by studying a manageable part of it.
A sample is only useful if it represents the population. Representation depends on how the sample is selected, not on its size alone.
Probability sampling methods (where chance determines who is included) are the foundation of trustworthy inference:
Simple random sample (SRS): Every subset of a given size is equally likely. Typically carried out with a random number table or software.
Stratified sample: Divide, then randomly sample within each stratum. Useful when you want guaranteed representation of subgroups (e.g., year of study).
Cluster sample: Randomly pick whole groups, study everyone in them. Practical when a full list of individuals is hard to get but a list of groups is available.
Non-probability methods to watch out for:
Convenience samples and voluntary response samples are both prone to heavy bias. They almost always attract individuals who are not typical of the population.
Larger samples reduce random variability, but no amount of size fixes a biased sampling method. A biased sample of 100,000 is still biased.
Measurement assigns values to variables. The quality of your measurement determines the quality of your data.
Bias in measurement means the method systematically misses the true value. A scale that reads 2 kg too heavy every time is biased. Collecting more data with the same scale will not fix the problem.
Reliability concerns consistency:
A measurement is reliable if repeating it under the same conditions gives similar results.
Reliability can be improved by standardising procedures, training observers, and using well-designed instruments.
Reliability is necessary but not sufficient: a broken thermometer can give the same wrong reading every time.
Validity concerns accuracy of meaning:
A measurement is valid if it captures the concept it is supposed to capture.
Validity is harder to establish than reliability. You cannot calculate it from a single formula; it requires evidence that the instrument behaves the way the underlying construct should.
A measurement can be reliable without being valid, but it cannot be valid without being reliable.
Confounding variables threaten the conclusions of observational studies. When two variables move together and a third variable is entangled with both, you cannot separate cause from effect.
Example: coffee drinkers may exercise less. If you find that coffee drinkers have higher blood pressure, the real cause might be sedentary behaviour, not coffee.
The distinction between explanatory and response variables is conceptual, not mathematical. The explanatory variable is what you think does the influencing; the response variable is what gets influenced.
No formulas are introduced in these chapters. The focus is conceptual. If you are looking for a reference, the key relationship to internalise is:
Validity requires reliability, but reliability does not guarantee validity.
A helpful mental diagram is a target:
Reliable and valid: shots clustered tightly at the centre.
Reliable but not valid: shots clustered tightly, but off-centre.
Neither reliable nor valid: shots scattered everywhere.
Polling organisations such as Gallup use stratified random sampling to predict election outcomes. When the sampling method is sound, a sample of roughly 1,000 people can estimate the preferences of an entire country within a few percentage points. When the method is flawed (voluntary response online polls, for instance), the results are meaningless regardless of how many people respond.
Psychological scales (e.g., depression inventories) are evaluated for both reliability (do they give consistent scores on retesting?) and validity (do they correspond with clinical diagnoses?). A scale that passes one test but not the other is not fit for use.
Students often think a large sample automatically means unbiased results. It does not. A large convenience sample is still a convenience sample, and the bias remains.
Students confuse "random" with "haphazard." A random sample uses a formal chance mechanism (tables, software). Standing outside a building and picking passers-by is haphazard, not random.
Students frequently mix up reliability and validity. Remember: reliability is about consistency, validity is about measuring the right thing. A clock that is always ten minutes fast is reliable but not valid for telling the correct time.
Students assume that correlation between two variables means one causes the other. Confounding variables can create an apparent relationship where no causal link exists.
⚠️ Know the difference between categorical and quantitative variables, and be able to classify examples of each.
⚠️ Be able to identify the type of sample (SRS, stratified, cluster, convenience, voluntary response) from a description.
⚠️ Expect questions that ask you to identify sources of bias (selection, nonresponse, response) in a given scenario.
⚠️ The reliability vs. validity distinction is heavily tested. Be ready to explain why one can exist without the other.
⚠️ Know what a confounding variable is and be able to identify one in a scenario. This concept returns in later chapters.
⚠️ Exams are cumulative, closed-book, and online. Material from these chapters reappears on every subsequent exam.
True or false: A voluntary response sample is a type of probability sample.
Fill in the blank: A measurement that consistently gives the same result is said to be __________.
True or false: A valid measurement is always reliable.
Fill in the blank: A variable that records group membership rather than a meaningful number is called a __________ variable.
True or false: Increasing sample size eliminates bias.
Answers: 1. False. 2. Reliable. 3. True. 4. Categorical. 5. False.
Q: A researcher surveys people who call in to a radio show about their political views. What type of sample is this, and what is the main concern?
A: This is a voluntary response sample. The main concern is bias: people who call in tend to hold stronger opinions than the general population, so the results will not represent the broader public.
Q: A psychology student creates a 20-item anxiety scale. Participants take it twice, one week apart, and their scores are nearly identical both times. However, experts agree the scale mainly measures general stress, not anxiety specifically. Is the scale reliable? Is it valid?
A: The scale is reliable (consistent scores across administrations) but not valid (it does not measure the intended construct of anxiety).
Q: Explain the difference between an explanatory variable and a confounding variable.
A: An explanatory variable is the factor you believe influences the outcome. A confounding variable is a third factor linked to both the explanatory and response variables that makes it impossible to determine which is driving the observed relationship.
Q: A university wants to survey student satisfaction. They email a questionnaire to all 30,000 students but only 1,200 respond. Name the bias most likely affecting this study.
A: Nonresponse bias. The 1,200 who responded may differ systematically from the 28,800 who did not (for example, students with strong positive or negative feelings may be more likely to respond).
Q: Give an example of a variable that is recorded as a number but is categorical.
A: Postcode (zip code). Although it is numeric, the digits label geographic areas rather than representing a meaningful quantity. Averaging postcodes is nonsensical.
This material connects to Chapters 10, 11, and 12 (Exam 2), where you begin to visualise and summarise data. Understanding what type of variable you have determines which graph or summary statistic is appropriate. It also connects to Chapter 22 (statistical significance), because the validity of a significance test depends entirely on how well the sample represents the population.
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