Exam 1 Study Guide

Observational vs. experimental: how to decide

Ask: did the researchers ASSIGN the treatment? If they assigned it (ideally randomly) it's an experiment. If they only recorded what already happened, it's observational.

Why an observational study can't prove causation

Subjects chose their own groups, so other differences between the groups (confounders) could explain the result.

Population

The entire group the study wants to draw conclusions about.

Sample

The subset of the population that data is actually collected from.

Explanatory variable

The variable suspected of affecting the outcome (the 'cause' side, x). Ex: whether a county was in the campaign.

Response variable

The outcome being measured (the 'effect' side, y). Ex: degree earned, salary.

Confounding variable

A third variable related to BOTH the explanatory and the response variable, so it could be the real reason for an apparent relationship. Ex: county wealth, local job market, nearby universities.

How to name a confounder (exam tip)

Pick something that differs between the groups being compared AND affects the outcome, then say how it could create a false conclusion.

Simple random sample

Every individual in the population has an equal chance of being picked; no grouping first.

Stratified sample

Split the population into similar groups (strata), then randomly sample from EVERY stratum.

Cluster sample

Randomly pick a few groups (clusters), then include EVERYONE in the chosen clusters.

Multistage sample

Randomly pick some clusters, then randomly sample individuals WITHIN each chosen cluster (two rounds of randomness).

Cluster vs. multistage vs. stratified (quick test)

Take everyone in the chosen groups = cluster. Randomly pick groups, then randomly pick people inside them = multistage. Sample from every group = stratified.

Census

Collecting data from the ENTIRE population instead of a sample.

Index (identifier) variable

A variable that only labels or identifies each case and has no analytical meaning. Ex: name, student ID.

Binary variable

Categorical variable with exactly two outcomes. Ex: Yes/No, M/F.

Nominal categorical variable

Categories with no natural order. Ex: degree major.

Ordinal categorical variable

Categories with a natural order but uneven/unknown gaps. Ex: class standing, satisfaction rating.

Count variable

Numerical variable made of whole-number counts (discrete). Ex: number of children, number of tickets closed.

Continuous variable

Numerical variable that can take any value in a range. Ex: salary, weight, time.

4 things to describe in a histogram

Modality (number of peaks), skewness (shape), center, and spread; also note outliers or other unusual patterns.

Mode

The most common value, or the location of the tallest bar/peak in a histogram.

Estimating the median from a histogram

Find the value that splits the total area (all the bars) into two equal halves.

Estimating the mean from a histogram

The balance point of the histogram; it gets pulled toward the long tail.

Order of mode, median, mean by shape

Symmetric: all about equal. Right skewed: mode < median < mean. Left skewed: mean < median < mode.

Five-number summary

Min, Q1, Median, Q3, Max.

Finding the median

Put the data IN ORDER first. Odd n: the middle value. Even n: average of the two middle values.

Outlier rule (1.5 × IQR)

Lower fence = Q1 − 1.5 × IQR. Upper fence = Q3 + 1.5 × IQR. Any value outside the fences is a potential outlier.

Most common mistake on five-number summary problems

Forgetting to sort the numbers before finding the median and quartiles.

Two-way (contingency) table

A table that counts cases by two categorical variables at once. Ex: hospital × thrombosis status.

Proportion within a group (row proportion)

Count with the outcome in that row ÷ that ROW's total (not the grand total). Ex: thrombosis at Hospital A ÷ all patients at Hospital A.

Does a difference look 'significant'? (before formal tests)

Compare proportions: a large gap suggests a real difference; a small gap could just be natural random variation. A formal test (2 Proportion Z test) would confirm it later.

Side-by-side boxplots

Boxplots of one numerical variable drawn for each level of a categorical variable, used to compare groups. Ex: gas mileage by number of cylinders.

Reading Q1 and Q3 off a boxplot

Q1 = bottom (or left) edge of the box. Q3 = top (or right) edge of the box. Median = line inside the box.

Reading skew from a boxplot

Median near the center of the box and similar whiskers = symmetric. Longer upper whisker / median near the bottom of box = right skewed. Longer lower whisker / median near the top = left skewed.

Outliers on a boxplot

Points drawn as individual dots beyond the whiskers.

Describing a relationship from side-by-side boxplots

State the direction (as the category goes up, does the response go up or down?), compare centers (medians), compare spreads, and note overlap and outliers. Association only, not causation.