3: Controlled Comparisons Flashcards
(21 cards)
def confounder
A confounder is a variable that:
-Occurs before IV has its effect on DV (is pretreatment).
-Is related to both the independent variable (IV) and the dependent variable (DV).
Example: Wealth might be a confounder in studying the relationship between education and political participation. It affects both.
what is a controlled variable
A variable other than the independent variable (IV) that could explain the changes in the dependent variable (DV) a rival variable that you controll becomes a controlled variable
-> ex: You’re studying whether hours spent studying (X) affects exam scores (Y).
But someone suggests:
“What if students who study more also get more sleep (Z), and it’s really sleep that improves exam scores?”
In this case, sleep is a rival variable — it offers a different explanation for why exam scores are high.
-> so you have to hold it constant to better understand the true relationship between an independent variable (X) and a dependent variable (Y).
-> so we isolate the 3rd variable (Z) to understand the real effect of X on Y
->partial effect= the relationship between X and Y after controlling for Z.
diff btwn confounder and controlled variable
A third variable that distorts the relationship between X and Y
vS A variable that the researcher adjusts for to clarify the relationship between X and Y
what are controlled comparisons
A controlled comparison lets us examine the effect of the independent variable (X) on the dependent variable (Y), while holding constant a potential confounder (Z).
Confounder structure:
X ← Z → Y
Example:
Shoe size ← Age → Reading ability
Bigger shoe size doesn’t cause better reading—it’s age that explains both.
Solution: Compare only within one value of Z (e.g. only seven-year-olds) → this removes the confounding effect.what
Two methods:
1; Random assignment (used in experiments).
2; Statistical controls / controlled comparisons (used in observational studies).
-> result of a controlled comparison: Z is/ is not a confounder
what are the 3 patterns of relationship in comparing IV and DV after controlling Z
When you compare the zero-order relationship (simple comparison without controls) to a controlled relationship (comparison with confounder held constant), you can observe:
1; Spurious relationship (false or misleading correlation between two variables that appears to exist only because of a third variable):
-The apparent relationship between IV and DV disappears after controlling.
-The relationship was due to a confounder.
-> ex of crimes and ice cream
- Additive relationship:
-The relationship between IV and DV remains, but a confounder also independently affects DV.
-> ex: Both education and income affect the support for democracy, but independently of each other. - Interaction effect (interactive relationship or specification) (Z is called the moderator bcs controls the strenghts and direction):
-The strength or direction of the relationship between IV and DV changes depending on the level of the third variable.
-> ex: = Political ads exposure
Y = Likelihood to vote
Z = Political interest
-For people with high political interest, ads have little effect (they already plan to vote).
-For people with low interest, political ads increase their likelihood to vote.
-> see graphs!!!!!
what are zero-order relationships
These are simple, uncontrolled comparisons.
Example: Saying “on average, richer countries have higher voter turnout” is a zero-order relationship.
Always leads to the “how else” question—what other differences (confounders) might explain this?
what are the 2 causal pathways?
IV → Mediator → DV = Indirect path (a real, causal relationship that runs through an intermediate step)
-> So the effect of the IV on the DV is indirect — it goes through the mediator.
IV ← Confounder → DV = Spurious link (confounding)
what is random treatment/ assignment and why is it useful
*def:
process of assigning units (like people, countries, or groups) to different conditions or treatments purely by chance.
This ensures that every group is similar in all respects except for the treatment, so any difference in the outcome (dependent variable) can be attributed to the treatment (independent variable), not to other hidden factors.
*Why it matters:
Only random assignment can eliminate compositional differences between groups (i.e. other ways the groups might differ besides the IV).
→ This ensures causality is easier to establish.
Without random assignment:
You must ask the “How else?” question:
“How else, other than the independent variable, are the groups I’m comparing different?”
*example:
Research Question: Does foreign aid increase support for the government?
Random Treatment Example:
You randomly divide 200 villages into two groups:
Group A receives a new foreign aid-funded school.
Group B receives nothing.
After six months, you compare how positively residents in each group view their government.
Because the assignment was random, any observed difference in political support is likely caused by the aid, not by pre-existing factors like income, ethnicity, or education.
when is comparison table used; and when is a box plot used
When the dependent variable is measured at the interval level,
boxplot: to visualize mean comparison
what is causal Hurdles Scorecard
tool helps in evaluating how convincingly a research design supports a causal inference. It includes the following steps (or “hurdles”):
Is there a credible causal mechanism?
Can we rule out reverse causality?
Is there a covariation between X and Y?
Have we controlled for confounding variables?
what are the 2 strategies to make controlled comparisons
*Cross-Tabulation
-basic method of displaying the relationship between two categorical variables in a matrix format.
-To control for a third variable (Z), separate cross-tabs can be created for each value of Z.
-Example: Examining the relationship between education level (X) and political participation (Y), while controlling for income (Z).
*Mean Comparisons
-involves comparing the average values of the dependent variable for different groups of the independent variable.
-Similar to cross-tabulation, but used when Y is continuous.
-Controlled comparisons are made by calculating means within subgroups of a control variable.
randomization vS control
In experimental research, random assignment achieves control by ensuring that confounders are evenly distributed across groups.
In nonexperimental research, researchers must explicitly measure and control for these variables using statistical or analytical techniques.
what are the limitations of the controlled comparisons
Omitted Variable Bias: If a confounding variable is not included, results may still be biased.
Measurement Error: If control variables are poorly measured, their ability to “control” is limited.
Multicollinearity: If X and control variables are highly correlated, it becomes difficult to isolate the effect of X.
def compositional difference
a difference between groups that exists because of some other characteristics, not the independent variable (IV) you’re studying.
ex: Imagine you’re studying the effect of gender (IV) on political opinion.
But maybe men and women also differ in education level, income, or age.
These other characteristics are compositional differences
-> associated with the qu°how else: If you’re not randomly assigning people to groups (like male/female or rich/poor), then “how else” do these groups differ?
what does a controlled variable reveals?
- Controlled Effect
👉 “What’s the effect of x on y when z is held constant?”
(x → y, but only for one specific value of z). - Effect of the Control Variable
👉 “What’s the effect of z on y when x is held constant?”
You’re looking at z → y, but only for one specific value of x.
what are controlled comparaison tables
Presents a cross-tabulation between an IV and DV for each value of the control
variable
- Makes no sense to talk about negative or positive relationships for nominal
variables
synonyme rival variable
controlled variable
what is the partial effect?
true effect of your main independent variable (X) on the dependent variable (Y), once you control for a third variable (Z) that might influence both.
how is a partial effect found (2 ways)
Fixed variable comparison (Controlled Comparison):
You hold the rival variable constant by splitting the data into groups based on the control variable (Z).
Then you compare the effect of X on Y within each group.
📌 Example: If Z = gender, you look at the effect of X on Y among men only, then among women only.
- Percentages or means (Controlled Mean Comparison):
You use a three-variable table (also called a cross-tab with control).
You analyze:
Down each column: effect of X on Y when Z is fixed.
Across each row: effect of Z on Y when X is fixed.
Margins (“totals”): overall effects.
diff btwn controlled and controlled mean comparisons
-Data type: Percentages or categorical data vS Numerical/interval data (means) -What you compare: % or proportions across groups vS Average scores across groups
-Goal: See how relationship changes across levels of a control variable vS See how average values change across levels of variables
-Reading: Often focuses on % differences vS Involves reading means across rows/columns
difference partial effect and controlled effect
Controlled effect refers to the observed relationship between two variables within a single category of a control variable.
Partial effect is the summary or overall relationship between two variables after accounting for (i.e., controlling for) a third variable.
